wavelength-modulation spectroscopy for …

WAVELENGTH-MODULATION SPECTROSCOPY FOR

DETERMINATION OF GAS PROPERTIES IN HOSTILE

ENVIRONMENTS

A DISSERTATION

SUBMITTED TO THE DEPARTMENT OF MECHANICAL

ENGINEERING

AND THE COMMITTEE ON GRADUATE STUDIES

OF STANFORD UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

Christopher S. Goldenstein

July 2014

http://creativecommons.org/licenses/by-nc/3.0/us/

This dissertation is online at: http://purl.stanford.edu/fg346yx4996

© 2014 by Christopher Sean Goldenstein. All Rights Reserved.

Re-distributed by Stanford University under license with the author.

This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 United States License.

ii



http://purl.stanford.edu/fg346yx4996

I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.

Ronald Hanson, Primary Adviser


Mark Cappelli


Jay Jeffries

Approved for the Stanford University Committee on Graduate Studies.

Patricia J. Gumport, Vice Provost for Graduate Education

This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file inUniversity Archives.

iii

Abstract

Over the past 40 years, tunable diode laser absorption spectroscopy (TDLAS) sensors

have matured into a practical technology for providing non-intrusive in-situ measure-

ments of gas properties in a number of hostile energy systems. However, the applica-

bility of TDLAS sensors has been limited by a number of fundamental measurement

challenges including: beam-steering, non-absorbing transmission losses, interfering

emission, line-of-sight non-uniformities, and broad and blended absorption spectra at

high pressures.

This work presents the development and demonstration of several novel calibration-

free wavelength-modulation spectroscopy (WMS) techniques and sensors that enable

high-fidelity measurements of gas properties in highly non-uniform gases and high-

pressure gases. These WMS techniques are demonstrated with measurements of gas

temperature, H2O, pressure, and velocity in two model scramjet combustors and a

pulse detonation combustor.

WMS o↵ers many noise- and distortion-rejection benefits; however, the accuracy

of calibration-free WMS techniques has previously relied on a priori knowledge of the

absorption transition’s linewidth. In many cases (e.g., non-uniform gases), this infor-

mation cannot be obtained, which has inhibited the widespread use of calibration-free

WMS. In addition, pressure broadening and the tuning range limitations of modern

tunable diode lasers (TDLs) lead to reduced WMS signals at high pressures where

absorption spectra are spectrally broad. As a result, WMS sensing at high-pressures

has been limited to relatively tame environments with larger path lengths or ab-

sorber concentrations and/or lower noise levels. This work presents solutions to these

challenges.

v

A calibration-free scanned-WMS spectral-fitting routine was developed to provide

measurements of gas properties without needing a priori knowledge of the transi-

tion linewidth. This strategy is analogous to widely-used scanned-wavelength direct-

absorption spectral-ftting techniques where a lineshape model is least-squares fit to

a measured absorbance profile. In scanned-WMS spectral-fitting, the WMS-nf/f

spectrum corresponding to a transition of interest is simulated as a function of gas

properties and laser parameters. A recently-developed brute-force simulation strategy

is used to convert a simulated transmitted-laser-intensity time history into a WMS-

nf signal time history. A single simulated WMS-nf/1f spectrum is then isolated

from the simulated time history and least-squares fit to a measured WMS-nf/1f

time history with the transition linecenter, integrated absorbance, and lineshape pa-

rameters as free parameters. This scanned-WMS spectral-fitting approach was used

to characterize two model-scramjet combustor flow paths.

In both scramjet sensing applications, two TDLs near 1.4 µm were frequency-

multiplexed to simultaneously probe two H2O absorption transitions along a given

line-of-sight. The nominal wavelength of each modulated laser was scanned across

the majority of an H2O absorption transition to recover the WMS-2f/1f spectrum of

each transition. In a near-uniform scramjet flow path within the Stanford Expansion

Tube, this technique was used to provide simultaneous measurements of temperature,

pressure, H2O mole fraction, and velocity at 25 kHz. These measurements are shown

to agree within 5% of expected values. In a highly non-uniform scramjet combus-

tor located at the University of Virginia, this technique was used to measure the

H2O-weighted path-average temperature and H2O column-density to quantify com-

bustion progress at various locations within the combustor. Accurate measurements

were enabled through the use of scanned-WMS spectral-fitting and by probing H2O

transitions with specific lower-state energies.

A two-color mid-infrared tunable diode laser sensor was developed for measure-

ments of temperature and H2O at extreme temperatures (up to 3500 K) and pressures

(up to 50 atm) in a pulse detonation combustor located at the Naval Postgraduate

School in Monterey, CA. Measurements at such extreme conditions were enabled

through the use of strong, fundamental vibration-band H2O absorption near 2.5 µm

vi

and a new methodology for selecting the wavelength and modulation depth of each

laser. The accuracy of this sensor was validated under known conditions behind re-

flected shock waves at temperatures and pressures up to 2700 K and 50 atm. There,

this sensor recovered the known temperature and H2O mole fraction within 3% of

known values. Furthermore, this sensor is demonstrated in a pulse detonation com-

bustor with a sensor bandwidth of 9 kHz.

Thorough details and analysis regarding the development and application of these

new WMS techniques are provided in the following chapters.

vii

Acknowledgements

First and foremost I would like to dedicate my PhD to my late grandparents Norbert

and Cecilia Armour. My grandfather’s journey from a department store stock boy to

CEO while su↵ering through The Great Depression and serving in a World War in-

between will always serve as a humbling reminder to me that there is no replacement

for hard work and dedication. My grandparents persevered through each obstacle

they faced, and not for personal glory, but to provide for their family and to make

sure that their children and grandchildren would have an easier life. Without their

love and generosity I never would have even been given the opportunity to pursue a

PhD so for this, and countless other reasons, I will be eternally grateful to them.

I also must thank the rest of my family, my fiance Angela, and my dearest friends

for their unwavering love and support throughout my life and PhD. My mother Bar-

bara always provided me the support and encouragement I needed, my father Marc

always reminded me to work hard and pursue a career of happiness, my sister Meghan

always gave me a genius to look up to, Angela always gave me purpose outside of the

laboratory, and my friends always found a way to remind me what matters most in

life.

Of course I am also indebted to my Advisor Professor Hanson for the countless,

amazing opportunities he has given me and for simply being a fantastic role model.

Through his relentless expectations and unwillingness to settle for mediocrity he made

me a better engineer and a better man. I simply cannot thank him enough for this.

I have also had the great privilege of working with several other fantastic scientists

and engineers. In particular, Dr. Jay Je↵ries played a huge role in my professional

viii

development. His technical expertise and willingness to help was invaluable through-

out my PhD. The students of the Hanson Group (specifically Ian, Vic, Mitch, Chris,

Ivo, Rito, and Kai) were always willing to lend a helping hand and, in many cases,

provide world-class technical advice. Despite graduating just prior to me joining the

Hanson Group, Greg Rieker (now Professor at the University of Colorado) continu-

ally provided me with technical advice throughout my PhD. Professor Chris Brophy

and Dave Dausen of the Naval Postgraduate School and Professor Chris Goyne and

Dr. Robert Rockwell of the University of Virginia were always incredibly helpful and

supportive during my field trips to their facilities and at helping me analyze the data

I acquired in their facilities.

I would also like to thank Professors Mark Cappelli, Chris Edwards, and Robert

Byer for being on my reading and/or oral committees.

Lastly I would like to thank those that have sponsored me and my work over the

course of my PhD. I cannot thank Mr. Robert Kleist enough for funding my 5-quarter

fellowship. His generosity played a large role in me attending Stanford University. I

would also like to thank AFOSR and Dr. Chiping Li, NASA and Dr. Richard Ga↵ney,

and ISSI and Dr. John Hoke for sponsoring a number of my research projects.

ix

Contents

Abstract v

Acknowledgements viii

1 Introduction 1

1.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Overview of Dissertation . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Fundamentals of Absorption Spectroscopy 7

2.1 The Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Linestrength Conventions and Absorbance . . . . . . . . . . . . . . . 8

2.2.1 Number-Density-Normalized Convention . . . . . . . . . . . . 8

2.2.2 Pressure-Normalized Convention . . . . . . . . . . . . . . . . . 9

2.3 Line-Shifting Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3.1 Pressure-Shift . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3.2 Doppler-Shift . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.4 Line-Broadening and -Narrowing Mechanisms . . . . . . . . . . . . . 11

2.4.1 Doppler Broadening . . . . . . . . . . . . . . . . . . . . . . . 11

2.4.2 Collisional Broadening . . . . . . . . . . . . . . . . . . . . . . 12

2.4.3 Collisional Narrowing . . . . . . . . . . . . . . . . . . . . . . . 15

2.5 Lineshape Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.5.1 The Gaussian Profile . . . . . . . . . . . . . . . . . . . . . . . 16

2.5.2 The Lorentzian Profile . . . . . . . . . . . . . . . . . . . . . . 17

2.5.3 The Voigt Profile . . . . . . . . . . . . . . . . . . . . . . . . . 17

x

2.5.4 The Galatry Profile . . . . . . . . . . . . . . . . . . . . . . . . 17

2.5.5 The Rautian-Sobel’man Profile . . . . . . . . . . . . . . . . . 21

2.5.6 Speed-Dependent Lineshape Profiles . . . . . . . . . . . . . . 21

2.6 Spectroscopic Complexities . . . . . . . . . . . . . . . . . . . . . . . . 22

2.6.1 Breakdown of the Power-Law Broadening Model . . . . . . . . 22

2.6.2 Breakdown of the Impact Approximation . . . . . . . . . . . . 23

2.6.3 Line-mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3 Wavelength-Modulation Spectroscopy 24

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.2 WMS Models and Simulation Strategies . . . . . . . . . . . . . . . . 26

3.2.1 Fixed-WMS Model . . . . . . . . . . . . . . . . . . . . . . . . 26

3.2.2 Scanned-WMS-nf /1f Simulation Strategy . . . . . . . . . . . 27

3.3 Comparison of WMS Techniques in Fourier Space . . . . . . . . . . . 31

3.3.1 Fixed-WMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.3.2 Peak-Picking-Scanned-WMS . . . . . . . . . . . . . . . . . . . 33

3.3.3 Full-Spectrum-Scanned-WMS . . . . . . . . . . . . . . . . . . 36

4 Scanned-WMS-nf /1f Spectral Fitting 39

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.2 Scanned-WMS-nf /1f Spectral-Fitting . . . . . . . . . . . . . . . . . . 40

4.2.1 Scanned-WMS-nf /1f Spectral-Fitting Routine . . . . . . . . . 41

4.2.2 Influence of Spectroscopic Parameters on Scanned-WMS-nf/1f

Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.3 Guidelines for Fitting Scanned-WMS-nf/1f

Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.4 Experimental Demonstrations . . . . . . . . . . . . . . . . . . . . . . 46

4.4.1 Static-Cell Experiments . . . . . . . . . . . . . . . . . . . . . 46

4.4.2 Expansion Tube Experiments . . . . . . . . . . . . . . . . . . 47

4.5 Selection of Modulation Depth . . . . . . . . . . . . . . . . . . . . . . 51

4.5.1 Signal Strength . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.5.2 Sensitivity to A and �⌫c . . . . . . . . . . . . . . . . . . . . . 53

xi

4.5.3 E↵ect of Distortion . . . . . . . . . . . . . . . . . . . . . . . . 54

5 Spectroscopic Database for MIR H2O 58

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

5.2 Experimental Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

5.3 Linestrength Measurements . . . . . . . . . . . . . . . . . . . . . . . 62

5.4 Lineshape Measurements . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.5 Line-Shift Measurements . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.6 High-Pressure Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . 72

6 Sensor Design for Nonuniform Environments 75

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

6.2 Determination of Gas Properties . . . . . . . . . . . . . . . . . . . . . 76

6.2.1 Scanned-Wavelength Direct Absorption (SWDA) . . . . . . . 76

6.2.2 Fixed-Wavelength Direct Absorption (FWDA) . . . . . . . . . 77

6.2.3 Wavelength-Modulation Spectroscopy . . . . . . . . . . . . . . 78

6.3 Types of Nonuniformities . . . . . . . . . . . . . . . . . . . . . . . . . 78

6.3.1 Pressure or Composition . . . . . . . . . . . . . . . . . . . . . 78

6.3.2 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

6.4 Two-Color Strategy for Nonuniform Gases . . . . . . . . . . . . . . . 80

6.4.1 Line-Selection Theory . . . . . . . . . . . . . . . . . . . . . . 81

6.4.2 Optimized Line Selection . . . . . . . . . . . . . . . . . . . . . 84

6.4.3 E↵ective Lineshape Function . . . . . . . . . . . . . . . . . . . 86

6.5 Demonstration of Strategy . . . . . . . . . . . . . . . . . . . . . . . . 88

6.6 Extension to Pressure-Normalized Linestrength Convention . . . . . . 93

6.7 Accuracy of the Linear-Linestrength Approximation . . . . . . . . . . 94

6.7.1 Influence of Size of Temperature Nonuniformity . . . . . . . . 95

6.7.2 Influence of Uncertainty in Mean Gas Temperature . . . . . . 95

7 NIR T and H2O Sensor for High-P and -T 99

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

7.2 Sensor Design and Architecture . . . . . . . . . . . . . . . . . . . . . 100

xii

7.2.1 Wavelength Selection . . . . . . . . . . . . . . . . . . . . . . . 100

7.2.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . 101

7.3 Development of Spectroscopic Database . . . . . . . . . . . . . . . . . 103

7.3.1 Linestrength, H2O-broadening, and N2-pressure-shift measure-

ments at low pressures . . . . . . . . . . . . . . . . . . . . . . 103

7.3.2 N2-broadening measurements at high pressures . . . . . . . . . 105

7.4 Sensor Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

7.5 Sensor Demonstration . . . . . . . . . . . . . . . . . . . . . . . . . . 109

8 MIR T and H2O Sensor for High-P and -T 111

8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

8.2 High-P and -T Measurement Challenges and Solutions . . . . . . . . 112

8.2.1 Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

8.2.2 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

8.3 Wavelength and Modulation Depth Selection . . . . . . . . . . . . . . 115

8.3.1 Optimization Routine . . . . . . . . . . . . . . . . . . . . . . 115

8.3.2 Projected Sensor Performance . . . . . . . . . . . . . . . . . . 119

8.4 Experimental Method and Sensor Validation . . . . . . . . . . . . . . 124

8.4.1 Optical Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

8.4.2 Experimental Method . . . . . . . . . . . . . . . . . . . . . . 125

8.4.3 Shock Tube Results . . . . . . . . . . . . . . . . . . . . . . . . 126

9 T and H2O Sensing in a Scramjet Combustor 129

9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

9.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

9.2.1 University of Virginia Supersonic Combustion Facility (UVaSCF)130

9.2.2 Optical Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

9.3 Line Selection and Evaluation . . . . . . . . . . . . . . . . . . . . . . 133

9.3.1 Line Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

9.3.2 Evaluation of Chosen Lines . . . . . . . . . . . . . . . . . . . 134


9.5 Measurements in Scramjet Combustor . . . . . . . . . . . . . . . . . 138

xiii

10 T, �, and H Sensing in a PDC 144

10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

10.2 Sensor Design and Architecture . . . . . . . . . . . . . . . . . . . . . 146

10.2.1 Diagnostic Strategy . . . . . . . . . . . . . . . . . . . . . . . . 146

10.2.2 Wavelength Selection . . . . . . . . . . . . . . . . . . . . . . . 146

10.2.3 Optical Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

10.3 Calculation of Gas Properties . . . . . . . . . . . . . . . . . . . . . . 149

10.3.1 Calculation of Temperature and Composition . . . . . . . . . 149

10.3.2 Calculation of Enthalpy . . . . . . . . . . . . . . . . . . . . . 151


10.5 Pulse Detonation Combustor and Results . . . . . . . . . . . . . . . . 154

10.5.1 Pulse Detonation Combustor . . . . . . . . . . . . . . . . . . . 154

10.5.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

10.5.3 Uncertainty Analysis . . . . . . . . . . . . . . . . . . . . . . . 156

11 Summary and Future Work 158

11.1 Spectroscopic Database for H2O Near 2474 and 2482 nm . . . . . . . 158

11.2 Sensor Design for Nonuniform Environments . . . . . . . . . . . . . 159

11.3 NIR T and H2O Sensor for High-P and -T . . . . . . . . . . . . . . . 160

11.4 MIR T and H2O Sensor for High-P and -T . . . . . . . . . . . . . . . 161

11.5 Temperature and H2O Sensing in a Scramjet . . . . . . . . . . . . . . 162

11.6 Temperature, Composition, and Enthalpy

Sensing in a PDC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

11.7 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

11.7.1 Scanned-WMS Spectral-Fitting at High-Pressures . . . . . . . 164

11.7.2 E↵ect of Harmonic Sidebands in Scanned-WMS . . . . . . . . 164

11.7.3 “Multi-a WMS” . . . . . . . . . . . . . . . . . . . . . . . . . . 164

A Procedure for Scanned-WMS Spectral Fitting 166

B Solutions to Common Experimental Problems 168

xiv

Bibliography 174

xv

List of Tables

2.1 Best-fit power-law parameters describing the theoretical temperature

dependence of collisional-narrowing coe�cients for N2 and CO2 per-

turbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.1 Comparison between measured and simulated nominally-steady gas pa-

rameters for an expansion tube test. . . . . . . . . . . . . . . . . . . . 51

5.1 Comparison of linestrengths between measurements and HITEMP 2010

database. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

5.2 Comparison of self-broadening coe�cients (HWHM per atm) between

measurements and HITEMP 2010. . . . . . . . . . . . . . . . . . . . 69

5.3 Measured lineshape parameters for H2O, CO2, and N2 collision partners. 70

5.4 Measured lineshape parameters for H2O transitions near wavelengths

studied. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

5.5 Measured N2-pressure-shift coe�cients for the two dominant H2O tran-

sitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

6.1 Types of LOS nonuniformities and required sensor design components

for lineshape-independent and -dependent measurement strategies. . . 81

7.1 Spectroscopic parameters derived from direct-absorption experiments

conducted at 600 to 1325 K. . . . . . . . . . . . . . . . . . . . . . . . 104

7.2 N2-broadening coe�cients inferred from WMS-2f/1f signals at 2 to

25 atm and 700 to 2400 K. . . . . . . . . . . . . . . . . . . . . . . . . 107

xvi

9.1 Relevant spectroscopic parameters for the H2O transitions used in

UVaSCF combustor sensor. . . . . . . . . . . . . . . . . . . . . . . . 134

10.1 Pertinent spectroscopic parameters for the dominant transitions used

by each sensor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

10.2 Laser modulation parameters and low-pass filter cuto↵ frequency. . . 150

10.3 Uncertainty in reported PDC quantities. . . . . . . . . . . . . . . . . 157

xvii

List of Figures

2.1 Theoretical collision integral and binary di↵usion coe�cient calculated

at 1 atm (left) and dynamic friction coe�cient calculated at 1 atm

(right) as a function of temperature for H2O-N2 pair. The temperature

dependence of the collision integral causes the di↵usion coe�cient to

increase with temperature faster than hard-sphere predictions (i.e. T 3/2). 20

3.1 Typical experimental setup used for scanned-WMS-nf/1f experiments. 26

3.2 Examples of simulated laser intensities (a), laser wavenumber (b), ab-

sorbance (c), and scanned-WMS-2f/1f signals (d) as a function of time

for a single scan period. In c, the absorbance at ⌫(t) repeatedly reaches

the peak absorbance (i.e., 0.10) because the scanned and modulated

optical frequency repeatedly passes over the transition linecenter. In d,

the magnitude and shape of the scanned-WMS-2f/1f spectrum varies

between the intensity up-scan and down-scan because the phase shift

between the laser intensity and wavenumber is not equal to ⇡. . . . . 30

3.3 Absorbance spectrum corresponding to simulated WMS signals pre-

sented in this section. . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.4 Frequency spectrum of simulated It(t) for a single laser modulated

at 225 kHz during a fixed-WMS experiment (top) and corresponding

WMS-2f/1f time-history for constant gas conditions (bottom). . . . 33

xviii

3.5 Frequency spectrum of simulated It(t) for a single laser modulated at

225 kHz and sinusoidally scanned at 25 kHz (top) and corresponding

WMS-2f/1f time-history for constant gas conditions (bottom). A 50

kHz lock-in filter was used to extract the WMS-1f and -2f signals. The

WMS-2f/1f signal near linecenter (denoted by red dots) could be used

to measure gas conditions at 50 kHz. The WMS-2f/1f varies slightly

between the intensity up-scan and down-scan because the phase-shift

between the laser intensity and wavelength tuning is greater than ⇡. . 35

3.6 Frequency spectrum of simulated It(t) for a single laser modulated at

225 kHz and sinusoidally scanned across the majority of an absorption

transition (see Fig. 3.3) with fs =1 kHz (top) and 5 kHz (bottom).

Increasing the scan frequency (or amplitude) broadens the frequency

content centered at the harmonics of the modulation frequency. . . . 37

3.7 Simulated WMS-2f/1f time-histories for a single laser modulated at

225 kHz and sinusoidally scanned at 1 kHz (top) and 5 kHz (bottom)

with constant gas conditions. The WMS-2f/1f varies slightly between

the intensity up-scan and down-scan because the phase-shift between

the laser intensity and wavelength tuning is greater than ⇡. . . . . . . 38

4.1 Flow chart for illustrating scanned-WMS-nf/1f spectral-fitting routine. 42

4.2 Simulated peak-normalized-absorbance (a) and -scanned-WMS-2f/1f

(b), -3f/1f (c), and -4f/1f (d) spectra for an optically thin Voigt

lineshape with three values of �⌫c (Lorentzian to Doppler width ratio

of 0.5, 1, and 2) and a fixed A. For scanned-WMS-nf/1f simulations,

a1,M=0.075 cm�1. Changing �⌫c significantly alters the shape of the

absorbance and scanned-WMS-nf/1f spectra away from ⌫o. . . . . . 44

4.3 Scanned-DA and scanned-WMS-2f/1f spectra for a single-scan mea-

surement at 1 kHz. Both scanned-DA and scanned-WMS-2f/1f fits

yield the same A and �⌫c within uncertainty. . . . . . . . . . . . . . 48

4.4 Simplified experimental setup used in expansion tube testing. . . . . . 49

xix

4.5 Scanned-WMS-2f/1f signals for a single expansion tube test with

TDLs near 1391.7 nm (a) and 1343.3 nm (b). The WMS-2f/1f sig-

nals corresponding to a single half-scan (up-scan or down-scan) were

isolated from the time-history and simulated signals were least-squares

fit to each spectrum to infer gas conditions. . . . . . . . . . . . . . . 50

4.6 Measured gas temperature, bulk speed, H2O mole fraction, and �⌫c

for transition near 7185.59 cm�1 (top) and measured pressure (bot-

tom) for a single expansion tube test. Time equal to zero denotes the

arrival of the test gas at the leading TDLAS LOS located 72.5 mm

FLE (From Leading Edge of Combustor). Measured values agree well

with expected values denoted by solid lines. Scanned-WMS pressure

measurements are only shown from 0.125-0.8 ms due to the presence of

helium in the contact surfaces that arrive at the beginning and end of

the test-time. Beyond approximately 0.35 ms, the pressure transducer

measurements are shown as constant at the nominally-steady value due

to the onset of high-frequency and high-amplitude noise that has since

been mitigated by Miller et al. [72]. . . . . . . . . . . . . . . . . . . . 52

4.7 Peak WMS-nf and -nf/1f signals near linecenter (a-b) and sensitivity

of scanned-WMS-nf/1f spectra to A and �⌫c (c) as a function of m.

Results are shown for an H2O transition described by a Voigt profile

with a peak absorbance of 0.1, a L/D = 1, and a FWHM = 0.065 cm�1 53

4.8 Examples of raw (undistorted) and distorted absorbance (a-b) and

scanned-WMS-2f/1f spectra (c). Low frequency distortion (b) signifi-

cantly alters raw absorbance spectrum and its best-fit, but the scanned-

WMS-2f/1f spectrum and its best-fit (c) are only weakly a↵ected by

the distortion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.9 Distortion-induced error in scanned-WMS-2f/1f spectra as a function

of ⌘ for a distortion signal with an amplitude of 1% of the peak raw-

absorbance. Each curve represents a di↵erent value of modulation

index. Error in scanned-WMS-2f/1f spectra goes to zero as ⌘ goes to

zero and infinity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

xx

5.1 Experimental setup used for measuring spectroscopic parameters. . . 61

5.2 Simulated absorbance spectra of probed transitions in pure H2O for a

temperature, pressure, and path length of 1200 K, 25 Torr, and 9.9 cm,

respectively. Simulations were performed using the Voigt profile and

the HITEMP 2010 [74] database with a self-broadening temperature

exponent of 0.75. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.3 Measured absorbance spectra and best-fit Voigt profile for transitions

near 4029.52 cm�1 in pure H2O at 1200 K. The best-fit Voigt profile

yields a maximum residual of 0.52% of the peak absorbance. The best-

fit Galatry profile yields a maximum residual that is 1.5 smaller than

that of the Vogit profile. . . . . . . . . . . . . . . . . . . . . . . . . . 64

5.4 Measured integrated area and linear fit for doublet near 4029.52 cm�1

at 1200 K (left). Slope of the linear fit was used to calculate linestrength.

Measured, best-fit, and HITEMP 2010 predicted values of linestrength

for doublet near 4029.52 cm�1 as a function of temperature (right).

Linestrength shown represents the sum for the doublet pair. HITEMP

2010 underpredicts the linestrength of this doublet pair by 3.8%. Error

bars are too small to be seen. . . . . . . . . . . . . . . . . . . . . . . 65

5.5 Measured absorbance spectra for transitions near 4029.52 cm�1 in CO2

(left) and N2 (right), gas conditions are stated within the figure. The

gull-wing signature in the best-fit Voigt profile residual suggests strong

collisional narrowing. The maximum residual is 2.2 and 4.8% of the

peak absorbance for spectra shown in CO2 and N2, respectively. The

best-fit Galatry profile e↵ectively removes the gull-wing signature and

reduces the maximum residual by ⇡10 times compared to that of the

Voigt profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

xxi

5.6 Collisional-broadening and -narrowing parameters for the doublet near

4029.52 cm�1. Measured collisional width FWHM and � ⇥ P and

two-parameter linear fit used to infer �N2 and �N2 (left). Measured

�N2 and �N2 with best-fit power-law used to determine �N2(296K) and

�N2(296K) and their respective temperature exponents, n. Error bars

are too small to be seen for collisional width, z, and �N2(T ). . . . . . 69

5.7 Comparison between measured absorbance spectra and simulated ab-

sorbance spectra using di↵erent lineshape models and broadening pa-

rameters. Spectra are shown for transitions near 4029.52 cm�1 at 1368

K, 13.25 atm, and 4.5% H2O in N2 (left) and transitions near 4041.92

cm�1 at 1371 K, 14.86 atm, and 4.6% H2O in N2 (right). The simula-

tions performed with Galatry profile derived N2-broadening coe�cients

based on data collected at 0.25 to 1 atm and 900 to 1325 K, presented

in Table 5.3, agrees well with the measured spectra obtained behind

reflected shockwaves in the Stanford HPST. . . . . . . . . . . . . . . 73

6.1 Water mole fraction distribution (left) for simulating path-integrated

absorbance spectrum of a single water vapor transition (right) using

two strategies. The path-integrated absorbance spectrum represents

a simulated direct-absorption measurement. Here, the H2O column

density cannot be accurately determined from a comparison of the peak

of the path-integrated spectrum with that of simulations performed

using path-average gas conditions and a uniform LOS. . . . . . . . . 80

6.2 Linestrength curves shown for H2O with pre-normalized units of cm�2/

molecule-cm�1. The transition lower-state energy sets the temperature

dependence of transition linestrength at a given temperature. The

linestrength curve is characterized by two regions of near-linear tem-

perature dependence and one region of near temperature independence. 82

xxii

6.3 The maximum error in the linear fit (i.e., linear-linestregth approxi-

mation) reaches a local minimum at two values of lower-state energy:

E”L and E”

H . The error in the linear-linestrength approximation is ap-

proximately 7 times smaller at E”L and E”

H than at E”C (the location

corresponding to the most-constant linestrength). Results shown are

for water vapor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

6.4 The maximum error in the linear-linestrength approximation decreases

near exponentially as the mean temperature increases for H2O transi-

tions with a lower-state energy equal to E”L (left) and E”

H (right). The

values of E”L and E”

H increase with the mean temperature. . . . . . . 86

6.5 Simulated absorbance spectrum for a single water vapor transition for

a LOS with the nonuniform water mole fraction distribution shown

in Fig. 6.1 (left). The best-fit Voigt profile accurately replicates the

path-integrated absorbance spectrum shown. . . . . . . . . . . . . . 88

6.6 Temperature and water mole fraction distributions across simulated

LOS. The path-average water mole fraction is 0.08, the path-average

temperature is 1185 K, and T nH2Ois 1390 K. . . . . . . . . . . . . . . 89

6.7 Simulated absorbance spectra for two water vapor transitions cho-

sen according to the new measurement strategy for nonuniform en-

vironments. Simulations were performed with a uniform pressure of 1

atm and with the temperature and water mole fraction distributions

shown in Fig. 6.6. The residual shown is between various simula-

tion techniques and the path-integrated spectra. Simulations with wa-

ter number-density-weighted path-average conditions overpredict peak

absorbance by nearly 20%. Absorbance spectra simulated with path-

average conditions and e↵ective lineshapes (derived from Voigt profile

fitting) matches path-integrated spectra to within 0.5% (top) and 1.3%

(bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

xxiii

6.8 Simulated WMS-2f/1f spectra for two water vapor transitions chosen

according to the new measurement strategy for nonuniform environ-

ments. Simulations were performed with a uniform pressure of 1 atm

and with the temperature and water mole fraction distributions shown

in Fig. 6.6. The residual shown is between various simulation tech-

niques and the path-integrated spectra. Simulations with path-average

conditions overpredict WMS-2f/1f signals by 20%. Simulated WMS-

2f/1f spectra with path-average conditions and e↵ective lineshape

(derived from scanned-WMS spectral fitting) matches path-integrated

spectra to within 0.2% (top) and 0.4% (bottom). . . . . . . . . . . . 92

6.9 The linestrength normalization convention alters the temperature de-

pendence of a given transition’s linestrength. The number density-

normalized linestrength convention leads to a broader linestrength pro-

file that peaks at a higher temperature. . . . . . . . . . . . . . . . . . 93

6.10 Contour lines of constant maximum percent error in the linear-linestrength

approximation for H2O transitions with lower-state energy of E”L (top)

and E”L (bottom) as a function of the mean temperature and size of

the temperature range. The maximum percent error in the linear-

linestrength approximation decreases as the mean temperature increases

and as the size of the temperature range decreases. The linear-linestrength

approximation is accurate to within 2.5% of the mean linestrength over

the majority of temperature space shown. . . . . . . . . . . . . . . . 96

xxiv

6.11 Range of percent error in linestrength approximations as a function of

mean temperature for a temperature range of 500 K and a ± 100 K

uncertainty in the mean temperature. Despite ± 100 K uncertainty in

mean temperature, the linear-linestrength approximation using H2O

transitions with E” = E”L(Tmean) or E”

H(Tmean) remains accurate to

within 2.5% of the corresponding mean linestrength for mean temper-

atures greater than 1000 K. For a temperature range of 500 K and a

± 100 K uncertainty in the mean temperature, the linear-linestrength

approximation with E” = E”H(Tmean) is 3.5 to 6.25 times less sensitive

to uncertainty in mean temperature than the constant-linestrength ap-

proximation with E” = E”C(Tmean) . . . . . . . . . . . . . . . . . . . . 97

7.1 Simulated H2O absorbance spectra for transitions near 7185.59 cm�1

(left) and 6806.03 cm�1 (right) at 1 and 15 atm with a temperature,

H2O mole fraction and path length of 1500 K, 3%, and 5 cm, respectively.101

7.2 Schematic of experimental setup used for temperature and H2O mea-

surements at two locations in the shock tube. . . . . . . . . . . . . . 103

7.3 Measured absorbance spectra and best-fit Voigt profiles for transitions

near 7185.59 cm�1 (left) and 6806.03 cm�1 (right) at 1000 K, 1 atm,

and 3% H2O in N2. Gull-wing residual indicates the presence of colli-

sional narrowing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

7.4 Sensitivity of the WMS-2f/1f signal at linecenter to collisional width

as a function of modulation index (i.e., a) for a H2O transition with a

L/D = 10 and a Voigt FWHM of 0.48 cm�1. . . . . . . . . . . . . . . 106

7.5 N2-broadening coe�cients inferred from WMS-2f/1f signals at known

conditions for the transitions near 7185.59 cm�1 (left ) and 6806.03

cm�1 (right). As expected, the N2-broadening coe�cients appear to

be independent of pressure. . . . . . . . . . . . . . . . . . . . . . . . 107

xxv

7.6 Temperature, pressure, and H2O time histories acquired behind inci-

dent shock (left) and reflected shock (right) for a single experiment.

Dashed lines indicate known values. For both measurement locations,

the WMS-2f/1f sensor recovered the known temperature and H2O

mole fraction within 2.5% with a bandwidth of 30 kHz. The temper-

ature and H2O decrease behind the incident shock near 0.6 ms due to

the arrival of the helium driver gas. . . . . . . . . . . . . . . . . . . 108

7.7 Accuracy and precision of temperature (left) and H2O (right) sensor

for shock tube experiments at temperatures and pressures from 700

to 2400 K and 2 to 25 atm with a sensor bandwidth of 15 kHz. The

nominal accuracy of the temperature and H2O sensor is 2.8 and 4.7%,

respectively, for the conditions shown. . . . . . . . . . . . . . . . . . . 109

7.8 Measured temperature, pressure, and H2O mole fraction time-histories

for a shock-heated, stoichiometric H2O-H2-O2-Ar mixture. Tempera-

ture and H2O results are shown with a 30 kHz bandwidth. Dashed

lines indicate expected values. . . . . . . . . . . . . . . . . . . . . . . 110

8.1 Simulated high-pressure absorbance (top) and WMS-2f/1f spectra

(bottom) near 2474 and 2482 nm. Higher pressure leads to increased

collisional broadening and overlapping transitions. The WMS-2f/1f

signal is largest in regions with large absorbance curvature. . . . . . . 113

8.2 Simulated H2O absorbance spectra at various temperatures for H2O

vibration band (top) and wavelengths studied (bottom). Optical fre-

quencies greater than 4025 cm�1 are less crowded and are dominated

by high-rotational-energy transitions. Changing temperature alters the

shape and magnitude of the absorbance and WMS-2f/1f spectra (bot-

tom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

8.3 E↵ect of modulation depth, a, on high-pressure WMS-2f/1f spectra.

Changing the modulation depth alters the WMS-2f/1f spectrum ac-

cording to the local curvature of the absorbance spectrum. . . . . . . 117

xxvi

8.4 Thermometry performance of several wavelength pairs near 4030 and

4042 cm�1 grouped by their mean and standard deviation in tempera-

ture uncertainty (calculated over the temperature and pressure domain

of interest). Groups are shown for two pairs of modulation depths.

The optimal pair of wavelengths and modulation depths is that which

is closest to the origin (i.e., smallest M). . . . . . . . . . . . . . . . . 120

8.5 Simulated H2O absorbance spectra for transitions near 4030 and 4042

cm�1. The center wavelengths and modulation bounds recommended

by the optimization routine for WMS-2f/1f sensing are shown. . . . 121

8.6 Contour lines of 2f/1f signal as a function of temperature and pressure

for 4029.76 cm�1 (top) and 4041.96 cm�1 (bottom). Simulations were

performed with a path length and H2O mole fraction of 5 cm and 0.10,

respectively. Modulation depths are indicated above each figure. For

a noise level of 0.001, an SNR of 20-200 is expected. . . . . . . . . . 122

8.7 Contour lines of temperature sensitivity (top) and predicted tempera-

ture uncertainty (bottom) for 4029.76 and 4041.96 cm�1 pair with an

uncertainty in 2f/1f of 0.001. Simulations were performed with a path

length and H2O mole fraction of 5 cm and 0.10, respectively. Over the

temperature and pressure domain shown, the estimated uncertainty in

temperature ranges from approximately 0.5 to 2%. . . . . . . . . . . . 123

8.8 Experimental setup used in shock tube experiments. . . . . . . . . . 125

8.9 Measured temperature and H2O mole fraction time-histories acquired

behind reflected shock wave. The sensor recovered the known steady-

state temperature and H2O to within 1.5% of known values. . . . . . 127

8.10 Accuracy of temperature (top) and H2Omole fraction (bottom) sensing

in shock tube experiments. On average, the sensor recovered the known

steady-state temperature and H2O mole fraction within 3.2 and 2.6%

RMS of known values, respectively. Error bars represent measurement

precision given by the standard deviation of the measurement over the

steady-state test-time. . . . . . . . . . . . . . . . . . . . . . . . . . . 128

xxvii

9.1 Photo of UVaSCF (left) and cartoon of combustor with labeled mea-

surement planes (right). Line-of-sight measurements were acquired in

the z-direction through the large windows shown in the photo. . . . . 131

9.2 Schematic of optical setup used in measurements conducted at the

UVaSCF. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

9.3 Simulated absorbance spectra (left) for Lines A, B, and C at 0.8 bar,

1500 K, and 10% H2O with a path length of 3.8 cm. Temperature

sensitivity (right) for line pairs 1 and 2 as a function of temperature.

Line Pair 1 = Lines A and B, Line Pair 2 = Lines A and C. . . . . 135

9.4 Maximum error in linear-linestrength approximation for Lines A and

C as a function of mean temperature for a temperature range of 500 K

(i.e., ± 250 K). The linear-linestrength approximation for Lines A and

C is accurate to within 1.2 and 2.6% of S(Tmean) for mean temperatures

between 1300 and 2000 K. . . . . . . . . . . . . . . . . . . . . . . . . 136

9.5 Example of temperature and H2O mole fraction distributions used to

simulate WMS-2f/1f measurements in a nonuniform reaction zone

(left). Simulated path-integrated WMS-2f/1f spectra and correspond-

ing best-fit for Lines A and C (right). Best-fit spectra recover measured

spectra within less than 0.5% of peak values, and T nH2Oand NH2O to

within 1.5 and 0.3%, respectively. . . . . . . . . . . . . . . . . . . . 137

9.6 Scanned-WMS-2f/1f spectrum and corresponding best-fit (left) for

Line B in a static-cell experiment conducted at 1 bar and 1000 K with

⇡7% H2O by mole. Accuracy of scanned-WMS-2f/1f temperature

sensor (right) using line pairs 1 and 2 as a function of temperature for

static-cell experiments. Line pairs 1 and 2 recover the known temper-

ature to within 2 and 1.25%, respectively. Error bars are too small to

be seen. The known temperature was determined from thermocouple

measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

xxviii

9.7 Example scanned-WMS-2f/1f time-histories for Lines A (top) and

C (bottom) acquired in the UVaSCF cavity flameholder (y=34.5 mm

on Plane I). Each scanned-WMS-2f/1f spectrum yields a measured

temperature and H2O column density. A total of 500 ms of data were

collected at each measurement location. . . . . . . . . . . . . . . . . . 140

9.8 Examples of measured and best-fit scanned-WMS-2f/1f spectra for

Lines A (left) and C (right) acquired in the UVaSCF. The best-fit

spectra match the measured spectra to within 2% of the peak signals. 140

9.9 Example temperature and H2O column density time-histories acquired

in UVaSCF at y = 28.5 mm on Plane I. H2O column density is scaled

by temperature to highlight oscillations due to composition only (as-

suming constant pressure). Smoothed data highlights low-frequency

oscillations in temperature and H2O. . . . . . . . . . . . . . . . . . . 141

9.10 Time-averaged temperature and H2O column density measured with

line pairs 1 and 2 on Plane I (top) and for Planes I and II (bottom).

Results are shown for the UVaSCF operating with a global ethylene-

air equivalence ratio of 0.17. Outside of the reaction zone, the WMS

sensor recovers the expected H2O concentration. Inside the reaction

zone the H2O column density increases between Planes I and II which

indicates that combustion progresses in the flow direction. . . . . . . 143

10.1 Simulated absorbance spectra for H2O (top), CO (bottom left) and

CO2 (bottom right) sensors at 1800 K with 5% H2O, 10% CO2, 0.5%

CO and a 4 cm path length. Simulations were performed using the

hybrid databases described in [29, 30, 118, 126]. . . . . . . . . . . . . 147

10.2 Schematic of optical setup (left) and sensor interface with PDC (right). 151

xxix

10.3 Accuracy of PDC sensors used in shock tube experiments. Each legend

applies to its own panel and those below it. Error bars indicate one

standard deviation of the measurement over the steady-state test time.

The MIR temperature, H2O, and CO sensors are nominally accurate to

within less than 3% of known values. The CO2 and NIR temperature

and H2O sensors are nominally accurate to within 5% of known values. 153

10.4 Time-resolved temperature, H2O, CO, and CO2 results for a single

PDC cycle. Data shown were acquired in the combustion chamber

(left) and nozzle throat (right). In all plots, time = 0 refers to the

arrival of the detonation front at the combustion chamber measurement

plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

10.5 Time-resolved enthalpy flow rate for 3 consecutive cycles. Enthalpy

was calculated assuming choked flow with the measured temperature,

pressure, and composition. . . . . . . . . . . . . . . . . . . . . . . . . 156

xxx

Chapter 1

Introduction

1.1 Background and Motivation

Global demands for improved combustion e�ciency and reduced emissions of green-

house gases and pollutants have led to the development of a variety of novel com-

bustion systems (e.g., homogeneous-charge compression-ignition engines, detonation-

based combustors, and coal gasifiers). However, understanding and optimizing the

performance of these systems requires a number of diagnostics for studying the phys-

ical processes that govern these systems. For example, temperature, pressure, com-

position, and velocity sensors are needed to study chemical kinetics, gas dynamics,

mixing, and heat transfer in these systems. Furthermore, as these combustors ma-

ture, increasingly robust and sensitive diagnostics are required to detect and evaluate

small di↵erences between combustor designs.

Tunable diode laser absorption spectroscopy (TDLAS) has matured into a useful

technique for providing measurements of gas properties in harsh combustion systems

[1]. These sensors operate by detecting the wavelength- and species-specific absorp-

tion of laser light, which can be related to gas conditions using models for the absorp-

tion spectra of interest. TDLAS sensors have been deployed in IC engines [2, 3, 4, 5],

scramjets [6, 7, 8, 9], pulse detonation engines [10, 11, 12, 13], gas turbine engines

[14, 15, 16], and coal gasifiers [17] to name only a few applications. However, despite

1

2 CHAPTER 1. INTRODUCTION

this succcess, a number of measurement challenges including: highly transient, multi-

phase, and nonuniform flows, beamsteering, interfering emission, window fouling, and

strong mechanical vibrations continue to limit the applicability and fidelity of TDLAS

sensors.

Wavelength-modulation spectroscopy (WMS) is one popular TDLAS technique

that o↵ers several noise-, interference-, and distortion-rejection benefits. In all WMS

techniques, the laser wavelength is rapidly modulated (O(10 kHz-1 MHz)) about

a given location on an absorption transition. In doing so, absorption information

is shifted to the harmonics of the modulation frequency, f , and is extracted from

the detector signal using lock-in filters. By modulating at high frequencies, absorp-

tion information is located at frequencies higher than those of many common noise

sources thereby leading to reduced noise levels. For example, Silver [18] and Bomse

et al. [19] found that WMS above 100 kHz o↵ers improved sensitivity and noise

rejection. In addition, Cassidy and Reid [20] first showed that the first-harmonic

signal (1f) of lasers with synchronous intensity- and wavelength-modulation (e.g.,

injection-current tuned diode and quantum cascade lasers) can be used to normal-

ize the higher-harmonic signals, thereby removing their dependence on the “DC”

laser intensity. This characteristic is extremely advantageous in harsh environments

where beamsteering and window fouling can introduce non-absorbing transmission

losses that can compromise the accuracy of conventional direct-absorption techniques.

Since WMS is a di↵erential-absorbance technique, WMS signals are also immune to

emission that varies at frequencies much less than f and/or outside the lock-in filter

passband around the harmonics of interest. Lastly, it is shown in [21] and Ch. 4 that

the modulation depth can be chosen to yield WMS signals that are insensitive to op-

tical distortion e↵ects (e.g., resulting from etalon reflections). Due to these benefits,

WMS has enabled high-fidelity measurements of gas properties in a number of hostile

environments [4, 6, 9, 13, 17, 22, 23, 24].

Despite its many benefits, quantitative WMS measurements can be di�cult to

acquire since the WMS signals are dependent on the transition lineshape, or more

simply, the curvature of the local absorbance spectrum. This complication can be

avoided by performing signal calibration, however, this is not practical in cases where

1.2. OVERVIEW OF DISSERTATION 3

the gas conditions of interest are highly transient, nonuniform, high temperature, high

pressure, or contain many chemical species in uncertain proportions. The calibration-

free WMS model of Rieker et al. [25] solves many of these problems, but requires

elaborate collisional-broadening databases and is limited to cases where the gas con-

ditions are relatively uniform and the collision partners of the absorbing species are

in relatively well-known proportions. Bain et al. [26] developed a method for in-

ferring the absorption lineshape in situ using residual-amplitude modulation, but

this technique is not as sensitive as WMS-2f techniques. In addition, WMS has re-

ceived limited use in high-pressure gases due to weaker WMS signals and the need for

more complete collisional-broadening databases. These challenges have limited the

widespread use of WMS, however, this dissertation presents solutions to all of these

problems.

1.2 Overview of Dissertation

The purpose of this dissertation is to present the design, validation, and demonstra-

tion of several advancements in WMS-based sensing. The primary purpose of the

remaining chapters is outlined below.

• Chapter 2 introduces the fundamentals of absorption spectroscopy along with

a number of complexities that can compromise the accuracy of absorption mod-

els. This chapter is particularly relevant to the development of spectroscopic

databases presented in Ch. 5 and used in Ch. 8 and 10.

• Chapter 3 introduces three common WMS techniques and discusses the distin-

guishing characteristics and nuances associated with each of them. Specifically,

fixed-WMS and two variants of scanned-WMS are covered. These techniques

are used in demonstration measurements presented throughout this work.

• Chapter 4 presents and demonstrates a scanned-WMS spectral-fitting tech-

nique for simultaneous measurements of gas properties and absorption line-

shapes. This technique allows quantitative WMS measurements in uniform and


nonuniform environments without needing a priori knowledge of the transition

collisional width (e.g., from spectroscopic databases). This technique is demon-

strated with simultaneous measurements of temperature, pressure, H2O, and

velocity at 25 kHz in a scramjet combustor flow path. This chapter is based on

[21].

• Chapter 5 presents an empirically derived spectroscopic database for H2O

absorption near 2474 and 2482 nm. Measured linestrengths and H2O-, CO2-,

and N2-broadening parameters, as well as, N2-narrowing parameters are pre-

sented for several high-rotational-energy H2O transitions. Measurements of

H2O absorption are also presented at high pressures (10-15 atm) and highlight

the importance of using empirically derived broadening models. The database

presented in this chapter enabled high-fidelity WMS measurements in a pulse

detonation combustor (see Ch. 10). This chapter is based on [27].

• Chapter 6 presents a two-color absorption spectroscopy technique for mea-

suring the absorbing-species-weighted path-average temperature and column

density in a nonuniform gas. This technique uses transitions with strengths

that scale near linearly with temperature over the domain of the temperature

nonuniformity and empirically derived e↵ective lineshapes. The former compo-

nent is required to ensure a linear dependence on temperature and the latter

component is needed to appropriately account for the path-dependent lineshape

function. This strategy can be used with direct absorption and WMS techniques

and it enabled accurate WMS-based measurements in a scramjet combustor (see

Ch. 9). This chapter is based on [28].

• Chapter 7 presents the design and validation of a near-infrared fixed-WMS

sensor for temperature and H2O in high-pressure and -temperature gases. By

modulating at 160 and 200 kHz this sensor can provide a sensor bandwidth up

to 30 kHz. This sensor was validated in non-reactive shock tube experiments

at temperatures and pressures from 700 to 2400 K and 2 to 25 atm. There,

this sensor recovered the known temperature and pressure within 2.8% and

4.7% RMS, respectively. This sensor was used to provide temperature and H2O

1.2. OVERVIEW OF DISSERTATION 5

measurements in a pulse detonation combustor (see Ch. 10). This chapter is

based on [29].

• Chapter 8 presents a mid-infrared fixed-WMS temperature and H2O sensor

for improved measurements in high-pressure and -temperature gases. By using

H2O transitions in the fundamental vibration band near 2.5 µm, this sensor

achieves 10⇥ larger WMS signals, compared to comparable near-infrared sen-

sors, which enables measurements at higher temperatures and unprecedented

pressures. This sensor was validated behind reflected shock waves where it re-

covered the known temperature and H2O mole fraction within 3.2 and 2.6%,

respectively, at temperatures and pressure up to 2700 K and 50 atm. This sen-

sor was also used to monitor temperature and pressure in a pulse detonation

engine (see Ch. 10). This chapter is based on [30].

• Chapter 9 presents measurements of temperature and H2O acquired in an

ethylene-fueled model scramjet combustor. Measurements in the nonuniform

combustor were enabled through the use of the scanned-WMS spectral-fitting

technique presented in Ch. 4 and the absorption spectroscopy technique devel-

oped for nonuniform environments in Ch. 6. This chapter is based on [9].

• Chapter 10 presents WMS measurements of temperature, H2O, CO2, and CO

in a pulse detonation combustor (PDC). These measurements were combined

with a choked-flow assumption to calculate the time-resolved enthalpy flow rate

exiting the PDC. High-fidelity measurements at unprecedented temperatures

and pressures were enabled through the use of strong mid-infrared absorption.

This work represents the first use of mid-infrared absorption sensors for moni-

toring temperature and combustion products in a PDC. This work was enabled

through the sensor development presented in Ch. 7 and 8. This chapter is based

on [13].

Chapter 11 summarizes the preceding chapters and o↵ers suggestions for future

research. Appendix A presents a procedure for the scanned-WMS spectral-fitting


routine and Appendix B presents solutions to a variety of common experimental

problems.

Chapter 2

Fundamentals of Absorption

Spectroscopy

2.1 The Basics

Quantum mechanics states that molecules are restricted to discrete energy levels

(i.e., molecular energy is quantized). When a molecule acquires or loses energy (e.g.,

from collisions with other molecules), the molecule transitions from one energy level

to another. Similarly, molecules can absorb or emit photons with energy equal to

the energy di↵erence between energy levels IF the transition is allowed by quantum

mechanics. The absorption of monochromatic light through a uniform medium is

described by the Beer-Lambert relation given by Eq. (2.1).

ItIo

= exp[�↵(⌫, T, P,�, L)] (2.1)

Io and It are the incident and transmitted light intensities, ↵ is the absorbance at

optical frequency ⌫, T is the gas temperature, P is the gas pressure, � is the gas

composition vector, and L is the path length through the absorbing gas.

7

8 CHAPTER 2. FUNDAMENTALS OF ABSORPTION SPECTROSCOPY

2.2 Linestrength Conventions and Absorbance

For molecules with a discrete absorbance spectrum (e.g., H2O, CO2, CO), the strength

a given quantum transition (i.e., the linestrength) is typically given in pressure- or

number-density-normalized form. Both conventions are used throughout this work,

and as a result, both are thoroughly described here.

2.2.1 Number-Density-Normalized Convention

With the lower-state energy, E” [cm�1], and frequency of the transition known

(e.g., from spectroscopic databases), the temperature dependence of the transition

linestrength in number-density-normalized form is given by Eq. (2.2):

Sn(T )[cm�1/molecule� cm�2] = Sn(To)Q(To)

Q(T )exp

�hcE”

k

✓1

T� 1

To

◆�

⇥1� exp

✓�hc⌫o

kT

◆�1� exp

✓�hc⌫o

kTo

◆��1

(2.2)

where To [K] is the reference temperature (usually 296 K), Q is the partition function

of the absorbing molecule taken from [31], k [J-K�1] is the Boltzmann constant, h [J-s]

is Planck’s constant, c [cm-s�1] is the speed of light, and ⌫o [cm�1] is the transition

linecenter frequency.

The absorbance can now be described as a function of gas properties using Eq.

(2.3):

↵(⌫) =

Z L

0

X

j

Snj (T )ni�j(⌫, T, P,�)dl (2.3)

which simplifies to Eq. (2.4) if the gas conditions along the line-of-sight (LOS) are

uniform.

2.2. LINESTRENGTH CONVENTIONS AND ABSORBANCE 9

↵(⌫) =X

j

Snj (T )ni�j(⌫, T, P,�)L (2.4)

Here, ni [molecule-cm�3] is the number density of the absorbing species, �j [cm�1]

is the lineshape function of transition j, P [atm] is the gas pressure, � is the gas

composition vector, and L [cm] is the path length through the absorbing gas. A

summation over j is included to account for the possibility of overlapping transitions

at a given ⌫; this e↵ect is particularly important at high pressures.

With the lineshape function defined in normalized form according to Eq. (2.5):

Z +1

�1�d⌫ = 1 (2.5)

the integrated absorbance of transition j, Aj, is defined according to Eq. (2.6):

Aj ⌘Z +1

�1↵j(⌫)d⌫ =

Z L

0

Snj (T )nidl (2.6)

which simplifies to Eq. (2.7) if the LOS is uniform.

Aj ⌘Z +1

�1↵j(⌫)d⌫ = Sn

j (T )niL (2.7)

Here, ↵j(⌫) is the absorbance at ⌫ due to a single transition j.

2.2.2 Pressure-Normalized Convention

In many cases it is more convenient to use the pressure-normalized linestrength con-

vention. In this form, the temperature dependence of SP [cm�2-atm�1] is given by

Eq. (2.8).


SP (T )[cm�2 � atm�1] = SP (To)Q(To)

Q(T )

To

Texp

�hcE”

k

✓1

T� 1

To

◆�

⇥1� exp

✓�hc⌫o

kT

◆�1� exp

✓�hc⌫o

kTo

◆��1

(2.8)

Note the addition of the ToT term. In this form, the absorbance is now given by Eq.

(2.9):

↵(⌫) =

Z L

0

X

j

SPj (T )Pi�j(⌫, T, P,�)dl (2.9)

which simplifies to Eq. (2.10) when the gas conditions along the LOS are uniform.

↵(⌫) =X

j

SPj (T )Pi�j(⌫, T, P,�)L (2.10)

Similar to Eq. (2.7), Aj is now given by Eq. (2.11) if the gas conditions along the

LOS are uniform.

Aj ⌘Z +1

�1↵j(⌫)d⌫ = SP

j (T )PiL (2.11)

2.3 Line-Shifting Mechanisms

2.3.1 Pressure-Shift

The linecenter of a given transition is weakly influenced by pressure, temperature, and

composition due to corresponding changes in the intermolecular potential. Changes

in the intermolecular potential lead to changes in the spacing between energy levels,

and therefore, changes in the frequency of light that is absorbed by the molecule.

This e↵ect is modeled using Eq. (2.12):

2.4. LINE-BROADENING AND -NARROWING MECHANISMS 11

�⌫o,P = ⌫0

o � ⌫o =X

k

Pk�k (2.12)

where �⌫o,P [cm�1] is the pressure-shift in the linecenter frequency and Pk [atm] and

�k [cm�1-atm �1] are the partial pressure and the pressure-shift coe�cient of collision-

partner k, respectively. �Air for rovibrational H2O transitions is typically near -0.02

cm�1-atm �1 at 296 K. The temperature-dependence of �k is typically modeled using

Eq. (2.13):

�k(T ) = �k(To)

✓To

T

◆m

(2.13)

where �k and m are measured or given in spectroscopic databases.

2.3.2 Doppler-Shift

When the absorbing gas moves with a bulk-speed component relative to the direction

of photons, the absorbing molecules see a Doppler-shifted optical frequency. As a

result, the absorption transition linecenter is shifted to higher or lower frequencies

according to Eq. (2.14):

�⌫o,D = ⌫ourel

c(2.14)

where �⌫o,D [cm�1] is the Doppler-shift in linecenter and urel [cm-s�1] is the bulk

speed of the gas relative to the photons. This e↵ect can be exploited to provide

non-intrusive measurements of bulk speed as presented in Sect. 4.4.2.

2.4 Line-Broadening and -Narrowing Mechanisms

2.4.1 Doppler Broadening

Doppler broadening results from the thermal motion of absorbing molecules. Molecules

with a velocity component in the direction of the photon see a Doppler-shifted fre-

quency, and thus, absorb light at shifted frequencies (relative to the stationary frame).


As a result, the absorbing transition is broadened about the transition linecenter.

This di↵ers from the Doppler-shift of linecenter in that Doppler broadening e↵ects

molecules in a given Maxwellian velocity class while the Doppler-shift a↵ects the en-

tire molecular ensemble. In most lineshape profiles, Doppler broadening is accounted

for via the Doppler full-width at half-maximum (FWHM) given by Eq. (2.15) for a

Maxwellian velocity distribution.

�⌫D = 2pln2�⌫

0

D = 7.1623⇥ 10�7⌫o,jp

T/M (2.15)

Here �⌫0D [cm�1] is the 1/e Doppler half-width at half-maximum (HWHM) and M

[g-mol�1] is the molecular weight of the absorbing molecule. It should be noted

that �⌫D is a function of the transition linecenter frequency, the molecular weight

of the absorbing species, and the temperature. As a result, Doppler broadening is

largest for short wavelength transitions (e.g., in the visible), light molecules, and high

temperatures.

2.4.2 Collisional Broadening

When molecules undergo collisions, energy can be transferred internally to di↵er-

ent energy modes (e.g., translation, rotation, vibration) or externally to di↵erent

molecules. Therefore, collisions can shorten the lifetime of a molecule in a given

energy level and, according to the Heisenberg Uncertainty Principle, increase the un-

certainty in the energy level. This leads to a range of energies over which molecules

can undergo a transition between two states which broadens the transition. This

e↵ect is known as “collisional broadening.”

In most lineshape models (e.g., Lorentzian, Voigt, Galatry, Rautian), collisional

broadening is assumed to be homogenous (i.e., equal for all absorbing molecules) and

accounted for via the collisional FWHM, �⌫C [cm�1], given by Eq. (2.16):

�⌫C = 2PX

k

�k�k(T ) (2.16)

where �k [cm�1-atm�1] is the collisional-broadening coe�cient (HWHM) of perturber


k. Therefore, �⌫C e↵ectively represents an ensemble average of collisional broadening.

In reality, this is a simplification, albeit an e↵ective one, of the collisional broadening

process.

An alternative approach is taken in speed-dependent lineshape models (e.g., speed-

dependent Voigt profile). These models recognize that collisional broadening is het-

erogenous within the molecular ensemble, and more specifically that collisional broad-

ening depends on the relative speed between the absorber and perturber. In other

words, depending on where the absorber and perturber lie in their respective velocity

distributions, the collision will be more or less e�cient leading to varying degrees of

collisional broadening. This complication is usually modeled via a second collisional-

broadening parameter, �2,k, which, despite its name, narrows the lineshape compared

to that when it is not included.

J Dependence of �k

Since the spacing between vibrational levels is much larger than that between rota-

tional levels, collision-induced transitions between vibrational levels are less frequent.

As a result, collisional broadening of rovibration (and pure rotational) transitions is

dominated by collision-induced uncertainty in the rotational energy levels. In order

for collisional broadening of such transitions to occur, the absorbing molecule must

experience a collision that is strong enough to move it into the absorbing energy level.

Since the rotational energy level spacing scales with 2BJ , where B is the rotational

constant and J is the rotational quantum number, J can play a significant role in the

probability of state-changing (i.e., lifetime-altering) collisions.

For molecules with small rotational-energy level spacing (e.g., CO), �k is a weak

function of J , since a relatively large fraction of collisions can exchange enough energy

to perturb the absorber’s energy level, regardless of J . However, for molecules with

a large rotational-energy level spacing (e.g., H2O), �k is a strong function of J .

In the case of N2-broadening of H2O at low temperatures, most H2O-N2 collisions

are near resonant for small values of J (J <⇡ 3) due to the small energy level

spacings involved. However, at higher J , collisions become non-resonant. In other

words, collisions with N2 are less e�cient, since the energy required to change the


rotational state of H2O is not balanced by the small changes in rotational energy

allowed for N2 in the primarily populated states [32]. As a result, �N2(296K) for H2O

transitions varies by nearly two orders of magnitude from near 0.1 cm�1-atm�1 for

J < 3 to 0.005 cm�1-atm�1 for J ⇡ 20.

It is worth mentioning, that for a given J , �k for H2O is also highly dependent on

the rotational quantum numbers Ka and Kc, and no obvious dependence upon these

quanta exists. In general, �k is smallest when Ka = J , however, many exceptions

exist [33].

Temperature Dependence of �k

In many cases, collisions are near resonant and highly e�cient. In this case, the

temperature dependence of �k is appropriately modeled using Eq. (2.17) with n near

0.75, however it should be noted that n exhibits a slight temperature dependence.

�k(T ) = �k(To)

✓To

T

◆n

(2.17)

In the case of N2- and O2-broadening of H2O transitions, a wide range of val-

ues for n are expected (-0.3 - 1) and Eq. (2.17) may only be appropriate over a

narrow temperature range (a few hundred K). This ultimately results from a num-

ber of competing physical processes that dictate the temperature dependence of �k.

Temperature influences collisional broadening (i.e., �k) in three main ways [32, 34]:

1. It changes the relative velocity distributions and, therefore, the duration of

time over which the perturber interacts with the absorber and the probability

of collision-induced rotational transitions.

2. It modifies the trajectories of the perturber relative to the absorber.

3. It alters the population distribution of the perturber across its rotational and

vibrational energy levels (i.e., due to Boltzmann statistics).

In regards to N2 and O2 broadening of H2O transitions, these three processes lead

to a complex temperature dependence that varies dramatically with J . As mentioned


previously, N2 and O2 collisions with H2O in low-J states are nearly resonant. As

a result, collisional broadening decreases with increasing temperature primarily due

to the reduction in collision frequency. As J is increased, collisions with N2 and O2

become increasingly non-resonant since the change in energy required to move H2O

into the absorbing energy level is not balanced by that associated with the allowed

changes in N2 or O2 between the primarily populated rotational states. However, as

temperature is increased, the perturber is more likely to be in higher rotational energy

levels (with larger spacing between levels) and collisions become more resonant. This

e↵ect leads to reduce values of n and, for high-J transitions (J > 7), can cause n 0

[32, 34]. In these cases, Eq. (2.17) is expected to be less accurate [33].

2.4.3 Collisional Narrowing

Collisional (i.e., Dicke) narrowing results from a collision-induced reduction in the

Doppler width and was first documented by R. H. Dicke in 1953 [35]. This process

is described in simplest terms using detailed-balancing arguments as follows [36]. At

thermal equilibrium, the population of molecules in a given velocity class is nominally

constant. As a result, Eq. (2.18) must hold

P (vz ! v0z)fM(vz) = P (v0z ! vz)fM(v0z) (2.18)

where P (vz ! v0z) is the probability of a collision changing a molecule’s velocity

in the z-direction from vz to v0z with v

0z > vz, and fM is the Maxwellian velocity

distribution function (derived in the absence of collisions). Since fM is symmetric

about zero and a decreasing function of increasing velocity (i.e., fM(v0z) < fM(vz) ),

P (vz ! v0z) < P (v0z ! vz). In other words, the probability of a velocity-changing

collision decreasing a molecule’s velocity is greater than the probability of the collision

increasing the molecule’s velocity. As a result, collisions e↵ectively narrow the velocity

distribution function compared to that predicted by fM and, thus, reduce the Doppler

broadening predicted by fM .

In most practical applications, collisional narrowing is less significant compared


to Doppler- and collisional-broadening. However, for molecules with large rotational-

energy level spacing (e.g., H2O, HF, HCl), lineshape models that address collisional

narrowing are often necessary, since only strong collisions are rotationally inelastic

(i.e., lead to collisional broadening) and the collisional-broadening to -narrowing ratio

is small. Furthermore, collisional narrowing is expected to be most significant when

the mean-free path is comparable to �/2⇡ where � is the wavelength of the transition.

As a result, collisional narrowing is typically studied and observed at modest number

density.

2.5 Lineshape Functions

The lineshape function of a given transition is simply a probability-distribution func-

tion that describes how Aj is distributed in optical-frequency space. The lineshape

function is undoubtedly the most complicated aspect of absorption spectroscopy.

However, despite its complexity, a number of relatively simple, and e↵ective line-

shape models have been and, continue to be, developed. Here, a brief description of

several of the most commonly used lineshape models is provided.

2.5.1 The Gaussian Profile

The Gaussian profile accounts for Doppler broadening only. As a result, the Gaussian

profile is most appropriate when Doppler broadening is large (e.g., high temperatures,

light molecules, short wavelength transitions) and collisions are infrequent (i.e., col-

lisional broadening and velocity-changing collisions are negligible). For gases with a

Maxwellian velocity distribution function, the Gaussian profile is given by Eq. (2.19).

�D(⌫) =2

�⌫D

✓ln2

⇡

◆1/2

exp

"�4ln2

✓⌫ � ⌫o�⌫D

◆2#

(2.19)

�D(⌫o) =2

�⌫D

✓ln2

⇡

◆1/2

(2.20)

2.5. LINESHAPE FUNCTIONS 17

2.5.2 The Lorentzian Profile

The Lorentzian profile, given by Eq. (2.21), addresses collisional broadening only

and assumes the broadening is independent of molecular speed (i.e., homogenous).

As a result, the Lorentzian profile is most appropriate when Doppler broadening is

negligible (i.e., low temperatures, heavy absorbers, long wavelength transitions) and

collisions are e�cient (i.e., speed-dependence of collisions is negligible).

�L(⌫) =1

2⇡

�⌫C

(⌫ � ⌫o)2 +��⌫C2

�2 (2.21)

2.5.3 The Voigt Profile

The Voigt profile, given by the convolution of the Gaussian and Lorentzian profiles

Eq. (2.22), is one of the most widely used lineshape models, since it accounts for

both Doppler- and collisional-broadening and is relatively simple to implement. The

Voigt profile assumes Doppler- and collisional-broadening are uncorrelated and does

not account for velocity-changing collisions.

�V (x, y) =y

⇡

Z +1

�1d⇣

exp(�⇣2)

y2 + (x� ⇣)2= Re[w(x, y)] (2.22)

Here, x = (⌫ � ⌫o)/�⌫0D is the normalized optical frequency relative to linecenter,

y = P�/�⌫0D is the normalized collisional-broadening parameter, and w(x, y) is the

complex probability function. Many numerical approximations have been developed

for the Voigt profile due to its computational cost. The algorithm developed by

Humlicek [37] (later enhanced by Kuntz [38] and corrected by Ruyten [39]) is one of

the most widely used. Using Eq. (2.22), the absorbance due to a single transition is:

↵j(⌫) = Aj�D(⌫o)�V (⌫) (2.23)

2.5.4 The Galatry Profile

For molecules with large rotational-energy level spacing (e.g., H2O, HCl, and HF),

lineshape models that account for collisional narrowing (i.e., Dicke narrowing [35])


are often needed to model observed spectra at modest number density. The Galatry

profile [40], given by Eq. (2.24), addresses collisional narrowing via the soft colli-

sion model which assumes that many collisions are required to significantly alter the

velocity of the absorber (i.e., the velocity of an absorber before and after a single

collision are correlated). Due to its complexity, several numerical approximations for

the Galatry profile have been developed [41]. The Galatry profile is typically used

when the molecular masses of the collision partners do not di↵er substantially or for

more general situations to account for weak, glancing collisions that result from the

long-range forces of the intermolecular potential function [42]. The Galatry profile

reduces to the Voigt profile when z = 0.

�G(x, y, z) =1p⇡Re

✓Z 1

0

d⌧exp

�ix⌧ � y⌧ +

1

2z2[1� z⌧ � exp(�z⌧)]

�◆(2.24)

The absorbance due to a single transition is now given by Eq. (2.25).

↵j(⌫) = Aj�D(⌫o)�G(⌫) (2.25)

The collisional-narrowing parameter, z, is given by Eq. (2.26),

z = PX

k

�k�k/�⌫0

D (2.26)

where �k [cm�1-atm�1] is the collisional-narrowing coe�cient of perturber k. Similar

to the collisional-broadening coe�cient, the temperature dependence of �k is modeled

according to Eq. (2.27).

�k(T ) = �k(To)

✓To

T

◆n

(2.27)

Again, n exhibits a slight temperature dependence as shown in Table 2.1.

If the molecular weight of the absorber is much less than that of the collision

partner, �k can be compared with the dynamic friction coe�cient �diff given by Eq.

(2.28).


�Diff (T ) =kT

2⇡cm1D12104 (2.28)

Here, m1 [kg-molec�1] is the mass of the absorbing molecule and D12 [cm2-s�1] is the

binary mass di↵usion coe�cient of the absorbing species 1 in the bath gas species 2

given by Eq. (2.29) [43]

D12(T ) = 0.0026280

pT 3(M1 +M2)/2M1M2

P�212⌦

1,112 (T12)

f 212(T12) (2.29)

where �12 [A] and ✏12 [J] are the e↵ective force constants for the pair-interaction,

T12 is the reduced temperature given by kT/✏12, ⌦12 is the dimensionless reduced

collision integral evaluated at T12, and f(2)12 is a dimensionless higher-order correction

parameter ranging from 1.0001 to 1.008 for T12 ranging from 0.3 to 400. Relations for

�12 and ✏12 are given by Hirschfelder et al. [43] and are repeated in Lepere et al. [44];

however, it is important to note that for the work presented here these parameters are

a function of the Stockmayer parameters for H2O and the Lennard-Jones parameters

for either N2 or CO2 [43]. As shown, �Diff is linearly dependent on pressure, and

therefore should be normalized by pressure before comparisons are made with the

collisional-narrowing coe�cient, �k.

The temperature dependence of D12, ⌦12, and �Diff are shown in Fig. 2.1 for the

H2O-N2 pair. Values for ⌦12 are taken directly from [43]. Since the collision integral is

inversely dependent on temperature, the di↵usion coe�cient predicted by Eq. (2.29)

increases with temperature faster than T 3/2 (i.e., the result of a hard-sphere collision

model). As a result, according to Eq. (2.28), �Diff decreases with temperature

faster than T�1/2. To quantify this temperature dependence more appropriately, an

analog to Eq. (2.27) was best-fit to the theoretical value of �Diff calculated with

Eq. (2.29) and Eq. (2.28). Fig. 2.1 (right) shows that the power-law model captures

the predicted temperature dependence well, however di↵erences do exist. The best-fit

power-law coe�cients for the H2O-N2 and H2O-CO2 pair are given in Table 2.1 for four

di↵erent ranges of temperature. The best-fit temperature exponent decreases slightly

for higher values of temperature, analogous to the temperature-dependent behavior of

collisional-broadening coe�cients [45]. This ultimately results from the fact that the


collision integral becomes a weak function of temperature as temperature increases.

As a result, in the high-temperature limit D12 scales with T 3/2 and �Diff scales

with T�1/2. In any case, one would expect experimentally determined temperature

exponents for the collisional-narrowing coe�cient to range from 0.5 to near 0.9 for

the experiments presented in Ch. 5. Furthermore, one would expect the temperature

exponent of the CO2 collisional-narrowing coe�cient to be greater than that of N2.

0

0.5

1

1.5

2

Co

llisi

on

In

teg

ral

300 600 900 12000

1

2

3

4

Temperature [K]

D12 [

cm2/s

]

D12

shown for

H2O−N

2 Pair

300 600 900 12000

0.01

0.02

0.03

0.04

Temperature [K]

βD

iff [

cm−

1/a

tm]

CalculatedBest Power−Law Fit

Results shown for H

2O−N

2 Pair

Figure 2.1: Theoretical collision integral and binary di↵usion coe�cient calculated at1 atm (left) and dynamic friction coe�cient calculated at 1 atm (right) as a functionof temperature for H2O-N2 pair. The temperature dependence of the collision integralcauses the di↵usion coe�cient to increase with temperature faster than hard-spherepredictions (i.e. T 3/2).

Table 2.1: Best-fit power-law parameters describing the theoretical temperature de-pendence of collisional-narrowing coe�cients for N2 and CO2 perturbers.

Table 1 Best-fit power-law parameters describing the theoretical temperature dependence of collisional-narrowing coefficients for N2 and CO2 perturbers.

Temperature Range [K] Theoretical H2O-N2 Best-Fit Parameters

Theoretical H2O-CO2 Best-Fit Parameters

βDiff (296 K ) [cm-1 atm-1]

n


n

296-650 0.0305 0.85 0.0424 0.91 650-900 0.0286 0.75 0.0386 0.79 900-1325 0.0257 0.66 0.0373 0.75 296-1325 0.0299 0.79 0.0415 0.85

Table 2 Comparison of linestrengths between measurements and HITEMP 2010 database.

vo [cm-1] E” [cm-1] Transition v '1 v '2 v '3 ← v"1 v"2 v"3

S(296 K) [cm-2 atm-1]/Uncertainty

J 'K '−1K '1 ← J "K "−1K "1 Measured HITEMP ’10

4027.937 2426.196 0 0 1 0 0 0 14 4 11 13 4 10 5.98E-5 (2.1%) 6.04E-5 (5-10%) 4027.988 2550.882 0 0 1 0 0 0 15 2 13 14 2 12 3.40E-5 (2.7%) 3.21E-5 (5-10%) 4028.156†† 2451.841††(2.9%) NA NA NA NA 4.10E-5 (23%) NA 4028.164 2631.284 0 0 1 0 0 0 16 2 15 15 2 14 9.10E-5 (3.5%) 1.11E-4 (5-10%) 4028.178 2631.269 0 0 1 0 0 0 16 1 15 15 1 14 4028.257 2551.483 0 0 1 0 0 0 15 3 13 14 3 12 1.13E-4 (2.5%) 1.11E-4 (5-10%) 4029.429 2748.099 0 0 1 0 0 0 14 6 9 13 6 8 8.39E-6 (4%) 1.07E-5 (5-10%) 4029.524 2660.945 0 0 1 0 0 0 17 1 17 16 1 16 1.10E-4 (2.3%) 1.06E-4 (5-10%) 4029.524 2660.945 0 0 1 0 0 0 17 0 17 16 0 16 4039.998 1581.336 1 0 0 0 0 0 11 5 6 10 4 7 8.16E-4 (3.5%) 7.71E-4 (5-10%) 4040.293 2872.274 0 0 1 0 0 0 16 2 14 15 2 13 2.45E-5 (3%) 2.41E-5 (5-10%) 4040.368 2952.394 0 0 1 0 0 0 17 2 16 16 2 15 2.59E-5 (3%) 2.37E-5 (5-10%) 4040.375 2952.387 0 0 1 0 0 0 17 1 16 16 1 15 4040.486 2872.581 0 0 1 0 0 0 16 3 14 15 3 13 8.13E-6 (4.1%) 7.84E-6 (5-10%) 4040.665 2746.023 0 0 1 0 0 0 15 4 12 14 4 11 4.13E-5 (2.5%) 3.99E-5 (5-10%) 4041.776 5258.631 0 1 1 0 1 0 19 2 18 18 2 17 5.00E-10 (4%) 4.33E-10 (10-20%) 4041.776 5258.631 0 1 1 0 1 0 19 1 18 18 1 17 4041.923 2981.359 0 0 1 0 0 0 18 0 18 17 0 17 2.43E-5 (2.7%) 2.25E-5 (5-10%) 4041.923 2981.359 0 0 1 0 0 0 18 1 18 17 1 17 4042.118 5204.749 0 1 1 0 1 0 18 2 16 17 2 15 3.01E-10 (8.1%) 3.85E-10 (10-20%) 4042.179 5241.742 0 1 1 0 1 0 20 0 20 19 0 19 4.38E-10 (7.5%) 5.24E-10 (10-20%) 4042.179 5241.742 0 1 1 0 1 0 20 1 20 19 1 19 4042.304 2756.415 0 0 1 0 0 0 14 6 8 13 6 7 2.53E-5 (3.5%) 2.47E-5 (5-10%) Uncertainties are given in parentheses. Linestrength reported for doublets is the sum of the two transitions. The linecenter frequency and lower-state energy of all transitions listed in HITEMP 2010 were fixed in the fitting routine used to infer S(296 K) Unless stated otherwise, source of quoted HITEMP 2010 linestrengths is Toth [40] †Source of HITEMP 2010 linestrength is Barber et al. [41] ††Denotes an experimentally observed transition that is not listed in HITEMP 2010.


2.5.5 The Rautian-Sobel’man Profile

The Rautian-Sobel’man profile [46], given by Eq. (2.30), addresses collisional nar-

rowing via the hard collision model that assumes that the velocity of each collision

partner after a collision is uncorrelated with its velocity prior to the collision. Like

the Galatry profile, the Rautian-Sobel’man profile reduces to the Voigt profile when

z = 0. The reader should note that z is lineshape-profile specific, and therefore,

cannot be mixed across lineshape models.

�R(x, y, z) = Re

w(x, y + z)

1�p⇡w(x, y + z)

�(2.30)

Again, w is the complex probability function which can be evaluated using the Hum-

licek algorithm [37] and the absorbance due to a single transition is given by Eq.

(2.31).

↵j(⌫) = Aj�D(⌫o)�R(⌫) (2.31)

2.5.6 Speed-Dependent Lineshape Profiles

A fascinating and thorough description of a variety of speed-dependent lineshape pro-

files is provided in [47]; as a result, only a brief discussion is provided here to broaden

the reader’s awareness on this topic. All of the lineshape profiles discussed previously

use ensemble-averaged lineshape parameters (e.g., collisional-broadening coe�cient)

and, therefore, ignore the molecular speed-dependence of the lineshape parameters.

In reality, this is a simplification as the collisional-broadening coe�cient and pressure-

shift coe�cient for a given absorber depends on its speed (i.e., where the absorber

lies in the speed-distribution function). Speed-dependent profiles address the speed-

dependence of such parameters by incorporating additional lineshape parameters.

For example, the speed-dependent Voigt profile [48, 49] introduces a speed-dependent

collisional-broadening coe�cient (�2,k) and a speed-dependent pressure-shift coe�-

cient (�2,k). As mentioned in 2.4.2, �2,k accounts for the speed-dependence of the

collisional-broadening cross section which e↵ectively leads to a narrowed-lineshape.


�2,k introduces a slight asymmetry into the lineshape profile. As a result, these line-

shape profiles provide superior accuracy compared to simpler models, albeit, at in-

creased complexity.

2.6 Spectroscopic Complexities

The purpose of this section is to briefly introduce the reader to several spectroscopic

complexities that can compromise the accuracy of absorption spectra models. It

should be noted, however, that the latter two issues discussed here (i.e., breakdown

of the impact approximation and line mixing) were not relevant to any of the work

presented in this thesis.

2.6.1 Breakdown of the Power-Law Broadening Model

While the power-law broadening model (Eq. (2.17)) is widely used and su�ciently

accurate in most situations, it is important to note that it is an approximation to re-

ality. In many cases the accuracy of this model can be improved by recognizing that n

exhibits a slight temperature dependence. For linear molecules (e.g., CO, CO2), the-

ory and experiments suggest that the magnitude of n should decreases slightly with

increasing temperature [45, 50, 51] indicating that the collisional-broadening coe�-

cient becomes a weaker function of temperature as temperature increases. However,

for H2O, a number of competing physical processes can cause collisional-broadening

coe�cients to exhibit a complex temperature-dependence that varies strongly with

rotational quantum number [32]. As a result, it is particularly important to verify

the accuracy of the broadening power-law and minimize extrapolation of power-law

broadening parameters to temperatures di↵erent than those which the data were ob-

tained at. However, if broadening parameters must be extrapolated, it is better to

extrapolate to higher temperatures and, if doing so, determine �(To) and n from the

highest temperature data possible.

2.6. SPECTROSCOPIC COMPLEXITIES 23

2.6.2 Breakdown of the Impact Approximation

All Lorentzian-based lineshape models (e.g., Voigt, Galatry, Rautian etc.) rely on

the accuracy of the impact approximation. The impact approximation assumes that

collisions between molecules are instantaneous and neglects energy-level perturbations

induced via intermolecular forces. As the density of a gas is increased, the molecules

are in close proximity with collision partners more frequently. As a result, the e↵ects of

intermolecular forces become more significant, and the impact approximation breaks

down. Ultimately this leads to increased absorbance in the wings (i.e., regions far

from linecenter) of the lineshape. Hartmann et al. [52] suggests that the impact

approximation is valid for regions of the lineshape that satisfy Eq. (2.32):

2⇡c|⌫ � ⌫o|tcoll << 1 (2.32)

where tcoll [s] is the duration of the collision given by Eq. (2.33).

tcoll =1

g

✓�⌫cN

c

g

◆(2.33)

Here g is the mean relative speed between collision partners and N is the number

density of the gas.

2.6.3 Line-mixing

Line-mixing (not to be confused with “line blending” or “overlapping”) occurs when

two transitions are collisionally coupled. In this case, inelastic collisions shu✏e

molecules between the upper and lower states of the two transitions. As a result,

the sum of two lineshape profiles no longer appropriately models the absorbance due

to these transitions and absorbance in the wings is transferred to optical frequencies

in-between the two transitions. This process is only important when (1) the di↵er-

ence in energy between the lower and upper states is comparable to the translational

energy of the molecules and (2) when the distance between the two transitions is less

than the collisional FWHM. As a result, this process is usually negligible at pressures

less than 100 atm for H2O [53].

Chapter 3

Wavelength-Modulation

Spectroscopy

3.1 Introduction

The purpose of this chapter is to describe three common WMS techniques and to

discuss the important distinctions between them. In fixed-WMS (or simply “WMS”),

one or more TDLs located on an absorption transition are injection current tuned

with a high-frequency (10 kHz - 1 MHz) sinusoidal modulation. This injection cur-

rent tuning causes simultaneous wavelength and intensity variation. The interaction

between the rapidly modulated laser wavelength and the absorption feature lineshape

introduces frequency content in the transmitted signal that is centered at the har-

monics of the modulation frequency, f . As a result, information regarding absorption

is shifted to high frequencies, O(10 kHz - 1 MHz), which lie above those of many

common noise sources [54]. Since the harmonic signals generally decrease in strength

with increasing harmonic, the 1st- and 2nd-harmonics have been used most. Further-

more, by employing 1f -normalization the WMS signals are independent of the DC

light intensity. As a result, WMS-nf/1f signals are immune to emission and non-

absorbing transmission losses that vary at frequencies much less than f and/or outside

the passband around the 1f and nf of each laser [20, 55, 56, 25]. For these reasons,

first-harmonic-normalized WMS with second-harmonic detection (WMS-2f/1f) has

24

3.1. INTRODUCTION 25

been used extensively in harsh environments where emission, beam-steering, and par-

ticulate scattering can significantly compromise the accuracy of conventional direct-

absorption techniques.

In scanned-WMS, an additional low-frequency (1 Hz - 10 kHz) scanning sinusoid

is used to tune the nominal laser wavelength across a portion of an absorption feature

while the modulation sinusoid is used to rapidly tune the laser wavelength about the

time-varying nominal wavelength. As a result, this technique can be used to mea-

sure scanned-WMS-nf spectra corresponding to one or more absorption transitions.

The primary advantage of this WMS-variant is that it provides additional spectral

information which can be used to infer lineshape- and lineshift-parameters or simply

to identify the WMS-nf signals at a known wavelength (e.g., linecenter) to guard

against laser wavelength drift or an unknown shift of an absorption feature. As a re-

sult, this technique is preferred; however, the injection current scan introduces several

complications that will be discussed in Sect. 3.3.

Fig. 3.1 illustrates a representative experimental setup for scanned-WMS exper-

iments conducted in our laboratory. A desktop computer running LabView and a

National Instruments PXI chassis are used to generate the signals used to scan and

modulate each laser, and to acquire all detector signals. TDLs are typically scanned

sinusoidally to reduce the width of the frequency bands centered at the modulation

harmonics and, therefore, prevent frequency crosstalk. As a result, multiple lasers can

be frequency multiplexed more easily. The temperature and current of each laser are

controlled with a commercially available laser controller. For TDLs in a fiber pigtail

configuration, multiple lasers are multiplexed using commercially available multiplex-

ers and splitters. When possible, polarization-maintaining (PM) single-mode (SM)

fibers are used to deliver the laser light to the test article. The laser light is then

collimated and directed across the test gas. When measuring the gas velocity, at

least one line-of-sight (LOS) is directed across the test gas at an angle to detect the

Doppler-shifted absorption. The transmitted light is detected with high-bandwidth

(3-150 MHz) photodetectors and only the raw detector signal is recorded by the

data-acquisition system (DAQ). If necessary, the detector signal is passed through

anti-aliasing filters prior to acquisition. WMS signals are extracted from the detector

26 CHAPTER 3. WAVELENGTH-MODULATION SPECTROSCOPY

signal with digital lock-in filters during post-processing.

+ fs

fm,2

DAQ

NI Chassis

fs

fm,1

+

Laser Controller

Test Gas

Direction of Flow

fm,1 � fm,2

Diode Lasers Detector

Fiber Combiner and Splitter

Optical Fiber

Figure 3.1: Typical experimental setup used for scanned-WMS-nf/1f experiments.

3.2 WMS Models and Simulation Strategies

In order to convert measured WMS signals to gas properties, measured signals must

be compared with simulated signals. All WMS models rely on an accurate absorption

spectrum model, albeit of varying complexity, to simulate WMS signals as a function

of gas properties (see Chapter 2). However, WMS models additionally address the

influence of the laser intensity- and wavelength-modulation. Numerous researchers

have developed models for WMS signals [25, 57, 58, 59, 60, 61, 26, 62], however, only

the most recent and accurate models [25, 62] are discussed and used here.

3.2.1 Fixed-WMS Model

Throughout this work, fixed-WMS signals were simulated using the calibration-free

WMS model presented by Rieker et al. [25]. This method is valid for all wavelengths,

3.2. WMS MODELS AND SIMULATION STRATEGIES 27

optical depths, lineshapes, gas conditions, and properly accounts for the higher-order

intensity modulation terms that become significant with large modulation amplitudes.

In this method, the complete absorbance spectrum (i.e., of all transitions) is simu-

lated as a function of gas properties and a Fourier expansion is performed upon the

simulated time-varying transmitted intensity to calculate the WMS signals. By us-

ing two wavelengths that exhibit a di↵erent temperature dependence, the two-color

ratio of WMS-2f/1f signals can be used to calculate the gas temperature with pres-

sure known. With the temperature and pressure known, the absorbing species mole

fraction can be inferred from the WMS-2f/1f signal at a single color.

3.2.2 Scanned-WMS-nf /1f Simulation Strategy

Additional considerations are required to accurately simulate scanned-WMS signals.

Here, the brute-force scanned-WMS-nf /1f simulation strategy presented by Sun et

al. [62] is used to convert measured signals to gas properties. This strategy uses

digital lock-in filters to extract the simulated scanned-WMS-nf/1f signals from the

simulated transmitted laser-intensity time-history, It(t). This method is advanta-

geous, since it properly accounts for all forms of intensity tuning that can severely

complicate the Fourier analysis methods used to simulate conventional WMS signals

[57, 63, 59, 60, 25]. When possible, measured background signals are used to model

the incident laser intensity, Io(t). In doing so, any background absorbance and distor-

tion e↵ects (e.g., etalons) are accounted for in the simulated scanned-WMS signals.

However, in the absence of background absorption and etalon-induced reflections,

Io(t), can be modeled using Eq. (3.1):

Io(t) = Io,S(t) + Io,M(t) (3.1)

where Io,S(t) and Io,M(t) are the components of the laser intensity that describe how

the laser intensity responds to the injection-current scan and modulation and are

given by Eq. (3.2) and Eq. (3.3), respectively.

Io,S(t) = Io[1

2+ i1,Ssin(!st+ ✓1,S) + i2,Ssin(2!st+ ✓2,S)] (3.2)


Io,M(t) = Io[1

2+ i1,Msin(!M t+ ✓1,M) + i2,Msin(2!M t+ ✓2,M)] (3.3)

Here, subscripts S and M indicate parameters that correspond to the intensity scan

and modulation, respectively, Io is the DC laser intensity, ! = 2⇡f [rad/s] where f [Hz]

is the user-specified frequency of the injection-current scan or modulation sinusoid, i1

and i2 are the first- and second-order mean-intensity-normalized intensity amplitudes,

respectively, and ✓1 and ✓2 are the absolute phase-shifts of the first- and second-order

intensity sinusoids. Io is scaled by 12 in Eq. (3.2) and Eq. (3.3) because it is counted

twice in Eq. (3.1). While, the DC laser intensity must be known when measuring or

characterizing Io(t), changes in the DC laser intensity or emission that occur during

actual measurements do not need to be accounted for in the simulation.

Similar to Io(t), the optical frequency of a single laser is modeled by Eq. (3.4):

⌫(t) = ⌫L + ⌫S(t) + ⌫M(t) (3.4)

where ⌫S(t) and ⌫M(t) are given by Eq. (3.5) and Eq. (3.6), respectively.

⌫S(t) = a1,Ssin(!St+ 1,S) + a2,Ssin(2!St+ 2,S)] (3.5)

⌫M(t) = a1,Msin(!M t+ 1,M) + a2,Msin(2!M t+ 2,M)] (3.6)

Here, ⌫L [cm�1] is the center optical frequency of the laser, a1 and a2 [cm�1] are the

first- and second-order scan or modulation depths, and 1 and 2 are the absolute

phase-shifts of the first- and second-order optical frequency sinusoids. It is important

to note that the absolute phase-shifts are dependent on the timing of the DAQ trigger.

The parameters i1, i2, ✓1, and ✓2 are easily obtained from fitting Eq. (3.2) and Eq.

(3.3) (with 12 replaced with 1) to measured laser intensity time-histories and a1, a2,

1, and 2 are obtained from fitting Eq. (3.5) and Eq. (3.6) to the corresponding

etalon data as demonstrated by Li et al. [60]. In addition, note that Eq. (3.1) and Eq.

(3.4) represent an idealized case in which the laser’s intensity and optical frequency

response to the injection current scan and modulation can be treated as independent

3.2. WMS MODELS AND SIMULATION STRATEGIES 29

of each other. This idealization simplifies the characterization of i1, i2, ✓1, ✓2, a1, a2,

1, and 2 as the laser’s response to the scan and modulation can be characterized

separately. Lastly, the second-order terms in eqs. (3.2), (3.3), (3.5) and (3.6) result

from the laser’s nonlinear response to the injection-current tuning. While Li et al.

[60] showed that these terms are small (0.1-2%) compared to their corresponding

first-order terms, the ease with which they are accounted for warrants their inclusion

in eqs. (3.2), (3.3), (3.5) and (3.6).

After measuring or simulating Io(t), the transmitted light intensity can be calcu-

lated using the Beer-Lambert relation (shown below for a uniform path):

It(t) = Io(t)exp

"�X

j

Aj�j(⌫(t), T, P,�)

#(3.7)

where the summation yields the spectral absorbance, ↵(⌫(t)), at the time-varying

optical frequency ⌫(t), �j is the lineshape function of transition j, and Aj is the

integrated absorbance of transition j given by Eq. (3.8).

Aj =

Z 1

�1↵(⌫) d⌫ (3.8)

Here, Sj(T ) [cm�2-atm�1] is the temperature-dependent linestrength of transition j,

T [K] is the gas temperature, Pi [atm] is the partial pressure of the absorbing species,

� is the gas composition vector, and L [cm] is the optical path length through the

absorbing gas. The transition lineshape was typically modeled by the Voigt profile,

but any valid lineshape profile can be used. After calculating It(t), the simulated

scanned-WMS-nf /1f signals, Snf/1f (t), can be extracted from It(t) using digital lock-

in filters. When using the phase-insensitive approach, It(t) is multiplied by a reference

cosine wave and sine wave at nf to extract the Xnf (t) and Ynf (t) components,

respectively. TheX and Y components are then low-pass filtered and used to calculate

Snf/1f (t) given by Eq. (3.9):


Snf/1f (t) =q

X2nf (t) + Y 2

nf (t)/q

X21f (t) + Y 2

1f (t)

= f(A,�j, laser dynamics)

which states that the Snf/1f (t) signals are a function of the transition integrated

absorbance, the lineshape function, and known laser dynamics.

This simulation technique is demonstrated in Fig. 3.2 which shows simulated

time-varying incident and transmitted light intensities (a), optical frequency (b), cor-

responding absorbance (c) and scanned-WMS-2f/1f signal (d) for a single laser cen-

tered on an H2O absorption transition. In the simulation, the laser intensity and

optical frequency were scanned at 1 kHz with a1,S = 0.155 cm�1 and modulated at

160 kHz with a1,M=0.075 cm�1. The corresponding absorbance spectrum is given

by a Voigt lineshape centered at 7185.59 cm�1 with a peak absorbance of 0.10 and

a FWHM of 0.065 cm�1 . The simulated scanned-WMS-2f/1f signal was extracted

1

1.25

1.5

1.75

I o(t

) o

r I t(t

)

Io(t)

It(t)

0 0.25 0.5 0.75 17185.2

7185.6

7186

Time, ms

ν(t

) o

r ν

s(t)

ν(t)ν

s(t)

AbsorptionSignature

a.

b.

0

0.04

0.08

0.12

Ab

sorb

an

ce

Absorbance at ν(t)

Absorbance at νs(t)

0 0.25 0.5 0.75 10

0.1

0.2

0.3

Time, ms

WM

S−

2f/

1f

WMS−2f/1f Background

WMS−2f/1f

c.

d.a

1,s

Outer 2 WMS−2f/1f Lobes

Figure 3.2: Examples of simulated laser intensities (a), laser wavenumber (b), ab-sorbance (c), and scanned-WMS-2f/1f signals (d) as a function of time for a singlescan period. In c, the absorbance at ⌫(t) repeatedly reaches the peak absorbance (i.e.,0.10) because the scanned and modulated optical frequency repeatedly passes overthe transition linecenter. In d, the magnitude and shape of the scanned-WMS-2f/1fspectrum varies between the intensity up-scan and down-scan because the phase shiftbetween the laser intensity and wavenumber is not equal to ⇡.

3.3. COMPARISON OF WMS TECHNIQUES IN FOURIER SPACE 31

from the simulated It(t) with a 10 kHz digital lock-in filter and the scanned-WMS-

2f/1f background signal corresponding to Io(t) was subtracted using the methodol-

ogy presented by Rieker et al. [25]. A 10 kHz filter was used because the wavelength

scanning distributes the scanned-WMS-nf signals across a band of frequencies (10

kHz here) centered at each harmonic. More information regarding this can be found

in Sect. 3.3.

3.3 Comparison of WMS Techniques in Fourier

Space

All WMS techniques rely on the ability to convert the raw detector signal into WMS-nf

signals. In practice, this is done by passing the raw-detector signal (i.e., It(t)), through

a lock-in filter during post-processing (or prior to data acquisition) to extract the

WMS-nf signal of interest from the detector signal. However, without understanding

how each WMS technique and its parameters e↵ect the raw detector signal in Fourier

space, sensical WMS-nf signals cannot be obtained.

This section will compare three common WMS techniques and discuss a variety

of nuances associated with each technique. All simulations presented in this section

are for a single laser interrogating the absorbance spectrum shown in Fig. 3.3.

3.3.1 Fixed-WMS

In fixed-WMS, the wavelength of each laser is sinusoidally modulated about a fixed

wavelength corresponding to a given location on an absorption transition (e.g., the

transition linecenter) . The modulation shifts absorption information to the harmon-

ics of the modulation frequency and, if the gas conditions are constant, leads to a

WMS-nf signal that is constant in time. This is shown in the bottom panel of Fig.

3.4. As a result, this method is analogous to fixed-wavelength direct absorption and

extreme care must be taken to ensure that the laser wavelength is centered at the

proper wavelength. This must be verified empirically [64] due to the modulation-

induced shift in the laser wavelength.


7185 7185.2 7185.4 7185.6 7185.8 71860

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Optical Frequency, cm−1

Ab

sorb

an

ce

Figure 3.3: Absorbance spectrum corresponding to simulated WMS signals presentedin this section.

In the frequency domain, an FFT (Fast-Fourier Transform) of It(t) reveals that it is

dominated by narrow features centered at the harmonics of the modulation frequency.

This can be seen at the top panel of Fig. 3.4 and has several important implications

that illustrate why this technique is commonly used in high-bandwidth applications.

(1) The measurement bandwidth of this technique is equal to the passband of the

lock-in filter used to extract the WMS-nf signals of interest. In other words, if a

lock-in filter with a 10 kHz lowpass filter is used, the measurement bandwidth is 10

kHz. (2) Using this technique, multiple lasers can be frequency-multiplexed more

easily due to the comparatively simple frequency spectrum of It(t); however, one

must be careful to isolate the harmonics of interest from beat signals introduced via

frequency-multiplexing of multiple lasers.


0 200 400 600 800 1000

10−4

10−3

10−2

10−1

100

101

Frequency, kHz

FF

T o

f I t(t

)

Fixed−WMS for a Single Laser with fm

= 225 kHz

1f

2f

3f4f

2 2.02 2.04 2.06 2.08 2.10

0.04

0.08

0.12

0.16

Time, ms

WM

S−

2f/1f

Fixed−WMS for a Single Laser with fm

= 225 kHz

Figure 3.4: Frequency spectrum of simulated It(t) for a single laser modulated at225 kHz during a fixed-WMS experiment (top) and corresponding WMS-2f/1f time-history for constant gas conditions (bottom).

3.3.2 Peak-Picking-Scanned-WMS

Scanned-WMS techniques are commonly used to provide additional spectral infor-

mation, and therefore, improve sensor robustness. In peak-picking-scanned-WMS (or


PPSWMS), the laser wavelength is modulated about a time-varying (i.e., scanned)

nominal wavelength. However, the amplitude of the wavelength scan is small (O(0.01

cm�1)) such that the nominal wavelength is simply tuned about a small region cen-

tered at the linecenter of the transition. This is done to identify the maximum

WMS-nf signal which corresponds to a known wavelength (e.g., linecenter for the

WMS-2f signal).

In this technique, the corresponding WMS-nf signal varies in time due to the

varying nominal wavelength. This is shown in the bottom panel of Fig. 3.5 for a sin-

gle laser sinusoidally scanned at 25 kHz and modulated at 225 kHz. Since the laser

wavelength is scanned over the absorption transition linecenter twice per period, a

scan rate of 25 kHz yields a measurement rate of 50 kHz (i.e., the frequency at which

the nominal laser wavelength passes over the transition linecenter). An FFT of It(t)

(shown in the top panel of Fig. 3.5) again reveals that the signal is dominated by in-

formation centered at the harmonics of the laser modulation frequency, however now

discrete sidebands appear adjacent to each harmonic. These sidebands are spaced

at the scan frequency (25 kHz here) and describe how the WMS-nf signals vary in

time due to the varying nominal wavelength. As a result, in order to capture all of

the information introduced by the wavelength scan, a lock-in filter with a passband

large enough to capture these sidebands must be used. In practice, however, the

user can be selective in rejecting higher-order sidebands depending on the bandwidth

requirements. In peak-picking-scanned-WMS-2f sensing, a lock-in filter with a pass-

band equal to two-times the scan frequency (50 kHz here) is su�cient to resolve the

signal content of interest. This is not the case for full-spectrum-scanned-WMS which

is discussed in the next section.

After extracting the WMS-nf signals of interest, the WMS-nf signal is usually

downsampled such that only the values at a known wavelength (e.g., linecenter) are

used since these can easily and accurately be compared to simulated signals without

being susceptible to errors introduced via laser wavelength drift or pressure-shift. For

example, in the WMS-2f/1f signal shown in Fig. 3.5 only the local peak values

are used to calculate gas properties. As a result, the e↵ective measurement rate is

equal to two-times the scan frequency (i.e., 50 kHz here) and the sensor bandwidth


is reduced to 25 kHz due to the Nyquist criterion. This is a key distinction from

fixed-WMS where a 50 kHz filter would provide a bandwidth of 50 kHz.

0 200 400 600 800 1000

10−4

10−3

10−2

10−1

100

Frequency, kHz

FF

T o

f I t(t

)Peak−Picking−SWMS for a Single Laser with

fm

= 225 kHz & fs = 25 kHz

1f & Sidebands

2f & Sidebands 3f

& Sidebands4f

& SidebandsSideband

2 2.02 2.04 2.06 2.08 2.10

0.04

0.08

0.12

0.16

Time, ms

WM

S−

2f/

1f

∆t = 1/(2fs)

=0.02 ms

Peak−Picking−SWMS for a Single Laser with fm

= 225 kHz & fs = 25 kHz2f/1f Signal

near Linecenter

Down−scanUp−scan Up−scan Down−scan Up−scan

Figure 3.5: Frequency spectrum of simulated It(t) for a single laser modulated at225 kHz and sinusoidally scanned at 25 kHz (top) and corresponding WMS-2f/1ftime-history for constant gas conditions (bottom). A 50 kHz lock-in filter was usedto extract the WMS-1f and -2f signals. The WMS-2f/1f signal near linecenter(denoted by red dots) could be used to measure gas conditions at 50 kHz. TheWMS-2f/1f varies slightly between the intensity up-scan and down-scan because thephase-shift between the laser intensity and wavelength tuning is greater than ⇡.


3.3.3 Full-Spectrum-Scanned-WMS

In full-spectrum-scanned-WMS (FSSWMS), the nominal laser wavelength is tuned

over the majority of an absorption transition to recover the corresponding WMS-

nf/1f spectrum. This technique is rich in spectral information which enables it to

be used for simultaneous temperature, composition, velocity, pressure, and lineshape

measurements via scanned-WMS spectral-fitting techniques discussed in Ch. 4 and

[21].

The additional information provided by this technique comes at the cost of com-

paratively complex and highly-transient WMS-nf signals that require numerous fre-

quency components to describe them. This is illustrated best in the frequency spec-

tra shown in Fig. 3.6 and the corresponding simulated WMS-2f/1f time-histories

shown in Fig. 3.7. In FSSWMS, the frequency spectrum of It(t) is dominated by

broadband-like features (i.e., numerous densely-packed sidebands) centered at the

harmonics of the modulation frequency. These sidebands describe how the WMS-nf

signals changes across the absorption transition lineshape. By comparing the top and

bottom panels of Fig. 3.6 it is clear that by scanning across the absorption transi-

tion faster (e.g., by increasing fs or as) the sidebands around each harmonic occupy

a larger portion of the frequency spectrum. For example, the frequency bands cen-

tered at the 2f occupy ± 15 kHz for a scan frequency of 1 kHz and ± 70 kHz for a

scan frequency of 5 kHz! In other words, if the entire WMS-2f spectrum is used to

provide a single measurement, a sensor bandwidth of 5 kHz would require a 70 kHz

filter assuming all the sidebands are used in the measurement. One could elect to use

narrower filters and reject higher-order sidebands, however, this approach requires

further research and development.


0 200 400 600 800 1000

10−4

10−3

10−2

10−1

100

Frequency, kHz

FF

T o

f I t(t

)Full−Spectrum−SWMS for a Single Laser with

fm

= 225 kHz & fs = 1 kHz

1f & Sidebands

2f & Sidebands 3f

& Sidebands 4f & Sidebands

0 200 400 600 800 1000

10−4

10−3

10−2

10−1

100

Frequency, kHz

FF

T o

f I t(t

)

Full−Spectrum−SWMS for a Single Laser with fm

= 225 kHz & fs = 5 kHz

1f & Sidebands

2f & Sidebands 3f

& Sidebands 4f & Sidebands

Figure 3.6: Frequency spectrum of simulated It(t) for a single laser modulated at 225kHz and sinusoidally scanned across the majority of an absorption transition (see Fig.3.3) with fs =1 kHz (top) and 5 kHz (bottom). Increasing the scan frequency (or am-plitude) broadens the frequency content centered at the harmonics of the modulationfrequency.


1.25 1.5 1.75 2 2.250

0.04

0.08

0.12

0.16

Time, ms

WM

S−

2f/1f


= 225 kHz & fs = 1 kHz

Down−scan

2f/1f Signalnear

Linecenter

Up−scan

1.25 1.5 1.75 2 2.250

0.04

0.08

0.12

0.16

Time, ms

WM

S−

2f/1f


= 225 kHz & fs = 5 kHz

Figure 3.7: Simulated WMS-2f/1f time-histories for a single laser modulated at 225kHz and sinusoidally scanned at 1 kHz (top) and 5 kHz (bottom) with constant gasconditions. The WMS-2f/1f varies slightly between the intensity up-scan and down-scan because the phase-shift between the laser intensity and wavelength tuning isgreater than ⇡.

Chapter 4

Scanned-WMS-nf /1f Spectral

Fitting

4.1 Introduction

While WMS techniques o↵er many attributes, quantitative WMS measurements can

be challenging since WMS signals depend on the transition lineshape. To overcome

this, in situ signal calibration can be performed with a known gas mixture; how-

ever, this is not practical in situations where the gas conditions of interest are poorly

known, highly transient, nonuniform, or di�cult to characterize in a controlled set-

ting (e.g., high-temperature and -pressure gases). As a result, several researchers have

developed calibration-free WMS techniques [25, 60, 61, 26, 62]. For example, Rieker

et al. [25] developed an analytical model for simulating WMS signals as a function of

easily obtainable laser parameters and an absorption spectrum model. While useful

and widely applicable, this method requires accurate models for the transition line-

shape parameters (e.g., collisional-broadening coe�cients), which typically requires

extensive laboratory work such as that presented in Ch. 5. This challenge can be

avoided by using the methodology of Bain et al. [26] who developed a calibration-free

methodology for measuring the absorption lineshape and gas composition using resid-

ual amplitude-modulation (RAM) signals; however, this technique is not as sensitive

39

40 CHAPTER 4. SCANNED-WMS-NF/1F SPECTRAL FITTING

as WMS-2f techniques in cases of low absorbance. Most recently, Sun et al. [62] de-

veloped a calibration-free technique for accurately simulating both fixed-wavelength

and scanned-wavelength WMS signals. Here we build upon the calibration-free WMS

method developed by Sun et al. [62] and present the development and demonstra-

tion of a generic, widely applicable scanned-WMS-nf/1f strategy for simultaneously

determining the gas temperature, pressure, composition, velocity and the transition

lineshape. In this strategy, simulated scanned-WMS-nf/1f spectra are least-squares

fit to measured scanned-WMS-nf/1f spectra with only the transition linecenter, in-

tegrated absorbance, and linewidths (collisional and/or Doppler) as free parameters.

Gas conditions are inferred directly from the best-fit parameters in a manner that is

analogous to scanned-wavelength direct-absorption (scanned-DA) methods [65, 66].

This technique di↵ers from other WMS techniques [25, 60, 22] in two significant

ways: (1) this scanned-WMS-nf/1f technique does not require prior knowledge of

the transition linewidth and (2) scanned-WMS-nf/1f signals are simulated using the

brute-force approach of Sun et al. [62], which properly accounts for non-ideal filtering

e↵ects and wavelength-dependent intensity variations resulting from etalon-induced

reflections and/or background absorbance. As a result, this technique is better suited

for environments where the transition linewidth is di�cult to model. Examples of this

include: (i) gases with multiple chemical species in uncertain proportions, (ii) high-

temperature gases, and (iii) nonuniform gases. In addition, guidelines for selecting an

appropriate scan amplitude, modulation depth, and harmonic are provided. Lastly,

this strategy is demonstrated with two-color scanned-WMS-2f/1f measurements of

gas temperature, pressure, composition, velocity, and the transition lineshape in a

well-characterized supersonic flow.

4.2 Scanned-WMS-nf /1f Spectral-Fitting

In Chapter 2 it was shown that scanned-WMS-nf/1f signals depend on the integrated

absorbance and lineshape of an absorption transition. Here it will be shown that these

relationships can be exploited by a scanned-WMS-nf/1f spectral-fitting routine to

infer the transition linecenter, integrated absorbance, and lineshape parameters in a

4.2. SCANNED-WMS-NF/1F SPECTRAL-FITTING 41

uniform gas. This method can also be used in nonuniform environments and this is

discussed thoroughly in Ch. 6.

4.2.1 Scanned-WMS-nf /1f Spectral-Fitting Routine

The technique presented here is analogous to widely used scanned-DA spectral-fitting

techniques [65, 67, 27]. Simulated scanned-WMS-nf/1f spectra are least-squares fit

to measured scanned-WMS-nf/1f spectra using the simulation strategy presented

in Sect. 3.2.2 and the Levenburg-Marquardt algorithm. Due to the phase shift be-

tween the intensity and wavelength scan, measured and simulated spectra must both

correspond to an intensity up-scan or down-scan. In most cases, ⌫o, A, and �⌫c are

free-parameters in the fitting routine, and �⌫D is fixed at the known value (given by

the temperature). If the temperature is not known a priori, the fitting routine should

be performed iteratively as discussed later. During each iteration of the fitting rou-

tine, the scanned-WMS function is called to generate the scanned-WMS-nf/1f time-

history (shown in Fig. 3.2) corresponding to the absorbance spectrum described by

the free parameters (e.g., ⌫o, A, and �⌫c). A single scanned-WMS-nf/1f spectrum is

then isolated from the complete simulated time-history and the sum-of-squared error

(SSE) between the measured and simulated spectra is calculated to quantify the accu-

racy of the simulated scanned-WMS-nf/1f spectrum. The fitting routine converges

upon a unique solution once the SSE is minimized. The steps of this algorithm are

displayed in Fig. 4.1 Once the fitting routine has converged, the best-fit parameters

are used to calculate gas properties as done in scanned-DA techniques. ⌫o can be used

to determine the bulk flow speed U = (�⌫o/⌫o)(c/2 sin(✓)), A can be used to calculate

the gas temperature, T = f(A2/A1), or composition, �i = A/S(T )PL , and �⌫c can

be used to calculate the gas pressure, P = �⌫c/2�(T ), if the collisional-broadening

coe�cient of the mixture is known. U [cm/s] is the bulk speed of the gas, c [cm/s]

is the speed of light, �⌫o [cm�1] is the Doppler shift of the transition linecenter, ✓

[rad] is the angle of the laser beam relative to the flow, and �i is the mole fraction of

the absorbing species. This technique is compared with scanned-DA in Sect. 4.4.1.

In several situations, additional considerations are required for accurately fitting


Lowpass Filter Lock-in at nfm�

cos(2�nfmt) sin(2�nfmt)

Xnf (t) Ynf (t)Snf /1 f (t)

Measured or Simulated Laser Io(t) and Simulated Laser v(t)

Beer’s Law

Simulated Laser It(t)

Isolate Single Snf/1f(t) Spectrum

Calculate Sum-of-Squared Error (SSE) Between Simulated and Measured Snf/1f(t)

Guess Parameters e.g. vo, A, �vc or �vD

Has Simulation Converged? NO

Update

YES Calculate Gas Properties From Best-Fit

Parameters

Figure 4.1: Flow chart for illustrating scanned-WMS-nf/1f spectral-fitting routine.

scanned-WMS-nf/1f spectra. If the temperature is not known a priori, �⌫D should

be fixed to an estimated value and the fitting routine should be repeated with an

updated �⌫D until the temperature derived from the two-color ratio of best-fit inte-

grated absorbances matches that for which �⌫D was fixed. While in theory both �⌫c

and �⌫D can be treated as free parameters, this increases computational time and can

reduce the accuracy of all best-fit parameters if optical distortion e↵ects are present

(as in scanned-DA methods). As a result, we recommend the iterative procedure.

In addition, if neighboring transitions exist, they should be accounted for in the ab-

sorbance spectrum used to calculate the scanned-WMS-nf/1f spectrum during each

iteration. If the neighboring transitions are considerably weaker or spaced su�ciently

far away such that they weakly influence the scanned-WMS-nf/1f spectra near the

line of interest, the spectroscopic parameters needed to model the neighboring tran-

sitions should be constrained to intelligently chosen estimates. The fitting routine

should then be repeated with updated parameters for the neighboring lines until the

best-fit parameters of the dominant line have converged. These parameters should

be updated to reflect the gas conditions corresponding to the best-fit parameters of

4.2. SCANNED-WMS-NF/1F SPECTRAL-FITTING 43

the dominant line. If the neighboring transitions are strong and in close proximity

to the line of interest, their spectroscopic parameters should be floated in the fitting

routine; however, this situation is not ideal.

4.2.2 Influence of Spectroscopic Parameters on Scanned-WMS-

nf/1f Spectra

Influence of ⌫o

Small changes in ⌫o shift the scanned-WMS-nf/1f spectrum in wavelength space

and, therefore, time. However, since the laser intensity and wavelength both vary in

time due to the injection current scan, large adjustments in ⌫o can also correspond

to significant changes in the local laser intensity. This can cause the magnitude

and shape of the scanned-WMS-nf/1f spectrum to vary significantly. To avoid this

complication, intelligent guess values for ⌫o should be used. This can be done by

using the location of the 2f peak as a reference.

Influence of A

In the optically thin limit (↵ < 0.05), the WMS-2f/1f signal at linecenter scales

near linearly with the integrated absorbance of the transition [25]. Similarly, it can

be shown that, for a fixed modulation depth, the shape of scanned-WMS-nf/1f spec-

tra is nearly independent of the integrated absorbance. In other words, the transition

integrated absorbance scales the entire absorbance and scanned-WMS-nf/1f spectra

when within the optically thin limit. Outside the optically thin limit this relation-

ship is more complicated, however, the spectral-fitting routine presented in this work

remains valid.

Influence of �⌫c

Since �⌫D is set by the temperature, the influence of the transition lineshape will be

examined in the context of changes in �⌫c. To simplify this analysis we will limit our

discussion to a fixed modulation depth and a Voigt lineshape. The influence of the


7185.4 7185.6 7185.80

0.25

0.5

0.75

1

Frequency, cm−1

Ab

sorb

an

ce N

orm

aliz

ed

to

1

7185.4 7185.6 7185.80

0.25

0.5

0.75

1

Frequency, cm−1

WM

S−

2f/1f N

orm

aliz

ed

to

1

∆νc,o

∆νc,o

x 2

∆νc,o

x 4

a. b.

7185.4 7185.6 7185.80

0.25

0.5

0.75

1

Frequency, cm−1

WM

S−

3f/1f N

orm

aliz

ed

to

1

7185.4 7185.6 7185.80

0.25

0.5

0.75

1

Frequency, cm−1

WM

S−

4f/1f N

orm

aliz

ed

to

1

c. d.

Figure 4.2: Simulated peak-normalized-absorbance (a) and -scanned-WMS-2f/1f(b), -3f/1f (c), and -4f/1f (d) spectra for an optically thin Voigt lineshape withthree values of �⌫c (Lorentzian to Doppler width ratio of 0.5, 1, and 2) and a fixedA. For scanned-WMS-nf/1f simulations, a1,M=0.075 cm�1. Changing �⌫c signif-icantly alters the shape of the absorbance and scanned-WMS-nf/1f spectra awayfrom ⌫o.

modulation depth is discussed in Sect. 4.5. Fig. 4.2 illustrates how varying �⌫c by a

factor of two and four alters the absorption spectra (a) and corresponding scanned-

WMS-2f/1f , -3f/1f , and -4f/1f spectra (b-d). Since varying �⌫c also changes the

magnitude of the absorbance and scanned-WMS-nf/1f signals, the spectra in Fig.

4.2 are normalized by their peak value (i.e., normalized to 1) to highlight changes in

spectral shape. Fig. 4.2a shows that by increasing �⌫c the normalized absorption

spectra broaden, most significantly, in the wings of the transition. Similarly, increas-

ing �⌫c broadens the scanned-WMS-nf/1f spectra, however, this e↵ect is much less

pronounced near the transition linecenter. In addition, increasing �⌫c significantly al-

ters the height of the outer scanned-WMS-nf/1f lobes. This is significant because it

shows that the transition lineshape alters scanned-WMS-nf/1f spectra in a di↵erent

manner (shape alteration) compared to ⌫o and A.

4.3. GUIDELINES FOR FITTING SCANNED-WMS-NF/1F SPECTRA 45

4.3 Guidelines for Fitting Scanned-WMS-nf/1f

Spectra

This section presents guidelines for using the scanned-WMS-nf/1f spectral-fitting

technique successfully. The analysis used to formulate many of these guidelines is

presented in Sect. 4.5.

1. a1,S should be equal to or greater than the spacing between the peaks of the

outer two scanned-WMS-2f/1f lobes (shown in Fig. 3.2d). In order for the

spectral-fitting routine to determine multiple spectroscopic parameters, each

parameter must influence scanned-WMS-nf/1f spectra in a unique manner.

Since the magnitude of scanned-WMS-nf/1f spectra near the transition line-

center is highly dependent on both the transition integrated absorbance and

lineshape (for modest m), the influence of each parameter on the scanned-

WMS-nf/1f spectrum cannot be easily separated. However, by scanning over

the majority of the transition lineshape, the lineshape-induced shape alteration

provides the necessary information to enable robust measurements of integrated

absorbance and lineshape. This is supported by Figs. 4.2b-d which show that

the shape of scanned-WMS-nf/1f spectra is most significantly influenced by

the transition lineshape in the wings of the absorption transition.

2. a1,M should be chosen such that:

(a) The scanned-WMS-nf signal is large compared to the noise level in the

experiment. (See Sect. 4.5.1)

(b) The scanned-WMS-nf/1f spectrum is sensitive to the spectroscopic quan-

tities of interest (e.g., A, �⌫c). (See Sect. 4.5.2)

(c) The scanned-WMS-nf/1f signal decouples from the distortion signals (e.g.,

from etalon reflections) present in the experiment. (See Sect. 4.5.3)

(d) The modulation index, m=a1,M/(FWHM/2), is large (i.e., at least 1.25


times greater than the value corresponding to peak WMS-nf signal) if the

actual absorbance spectrum is poorly modeled by the lineshape function

of choice (e.g., Voigt function). In doing so, scanned-WMS-nf/1f spectra

become less sensitive to the shape of the absorbance spectra (See Sect.

4.5.2), and as a result, the scanned-WMS-nf/1f spectral-fitting routine

becomes more robust against inadequacies in modeling the shape of the

absorbance spectrum. This strategy is e↵ective at reducing the influence

of lineshape complexities that can result from collisional e↵ects (e.g., colli-

sional narrowing) [67, 27] and LOS nonuniformities in gas conditions [28].

(e) Harmonic signals greater than two should not be used if the actual ab-

sorbance spectrum is poorly modeled by the lineshape function of choice

(e.g., Voigt function) because, for a given m, the scanned-WMS-nf/1f

signals become more sensitive to the transition lineshape as the harmonic

is increased. (See Sect. 4.5.2)

4.4 Experimental Demonstrations

In this section, the scanned-WMS-nf/1f spectral-fitting technique is demonstrated

with measurements of temperature and H2Omole fraction in a static cell and measure-

ments of temperature, pressure, H2O mole fraction, velocity, and transition lineshape

in the Stanford Expansion Tube.

4.4.1 Static-Cell Experiments

Experimental Details

An experimental setup similar to that shown in Fig. 3.1 was used to measure the

gas temperature and water mole fraction in a 76.2 cm long heated static cell [68].

Measurements were conducted in H2O-N2 mixtures at a pressure of 1 atm and at

temperatures up to 1325 K. Two distributed-feedback (DFB) TDLs near 1391.7 and

1469.3 nm were used to probe H2O absorption transitions near 7185.59 and 6806.03

4.4. EXPERIMENTAL DEMONSTRATIONS 47

cm�1. The measured linestrengths given by Goldenstein et al. [29] were used to calcu-

late the gas temperature and composition from the best-fit integrated absorbance of

each transition. In scanned-WMS experiments, each laser was scanned with a1,S=0.2

cm�1 at 1 kHz. The laser near 1391.7 nm was modulated at 160 kHz with a1,M=0.08

cm�1 and the laser near 1469.3 nm was modulated at 200 kHz with a1,M=0.06 cm�1.

For comparison, scanned-DA measurements were also collected. In scanned-DA ex-

periments, each laser was scanned 1 cm�1 with a 1 kHz sawtooth.

Results

Fig. 4.3 shows scanned-DA and corresponding scanned-WMS-2f/1f spectra for a

single-scan measurement of the H2O transition near 7185.59 cm�1. The data were

taken sequentially (⇡ 5 minutes apart) using the same experimental setup and test

conditions. The gas temperature, pressure, and composition were 298 K, 1 atm, and

1.3% H2O in N2 by mole, respectively. In all fitting routines, �⌫D was fixed at the

value given by the known temperature, and ⌫o, A, and �⌫c were free parameters.

The integrated absorbance and collisional width obtained from the scanned-DA and

scanned-WMS-2f/1f spectral-fitting routines agree within 2 and 3%, respectively,

and the 95% confidence interval in A and �⌫c obtained from the best-fit scanned-

WMS-2f/1f spectrum are 0.29 and 0.32%, respectively, which are 10 and 40% smaller

than those of the corresponding best-fit scanned-DA spectrum. In addition, the two-

color ratio of integrated absorbances obtained from the scanned-WMS-2f/1f spectral-

fitting routine was used to calculate the gas temperature within 1.5% of thermocouple

measurements at 600 to 1325 K. These results show that the scanned-WMS-nf/1f

spectral-fitting routine can be used to determine gas properties with high accuracy.

4.4.2 Expansion Tube Experiments

Experimental Details

The experimental setup used is thoroughly described in [69] and more details regard-

ing the Stanford Expansion Tube can be found in [70]. A simplified experimental

setup is shown in Fig. 4.4. Briefly, the Stanford Expansion Tube is a 6 inch diameter,


7185.2 7185.4 7185.6 7185.80

0.04

0.08

0.12

0.16A

bso

rbance

DataFit

7185.4 7185.6 7185.80

0.1

0.2

0.3

0.4

WM

S−

2f/1f

DataFit

7185.2 7185.4 7185.6 7185.8−5

−2.5

0

2.5

5

Frequency, cm−1

Resi

dual,

%

7185.4 7185.6 7185.8−5

−2.5

0

2.5

5

Frequency, cm−1

Figure 4.3: Scanned-DA and scanned-WMS-2f/1f spectra for a single-scan measure-ment at 1 kHz. Both scanned-DA and scanned-WMS-2f/1f fits yield the same Aand �⌫c within uncertainty.

12 m long tube that produces high-enthalpy gaseous flows with flight Mach numbers

between 4 and 9. Initially, the tube is divided into three sections separated by poly-

carbonate diaphragms. The driver section is filled with high-pressure helium, the

driven section is filled with the test gas (air-H2O), and the expansion section is also

filled with helium. At a prescribed pressure, the first diaphragm is ruptured and a

shock wave travels into the test gas setting it into motion and raising its temperature

and pressure. Once the shock wave reaches the second diaphragm, it ruptures and the

helium expansion gas is set into motion at a velocity greater than that of the driver

gas, thereby expanding the test gas to a higher velocity and a lower temperature and

pressure. First, the helium expansion gas reaches the test article, then the air-H2O

test gas, and lastly the driver gas. The steady-state test-time was approximately

0.5 ms. For the measurements presented here, two DFB TDLs located near 1391.7

and 1343.3 nm were used to probe H2O transitions near 7185.59 and 7444.36 cm�1.

The lasers were multiplexed and split onto three SM fibers that were routed into the

test section. A model scramjet combustor was placed in the flowpath and one LOS

4.4. EXPERIMENTAL DEMONSTRATIONS 49

He Driver Gas

Air-H2O Test Gas

He Exp. Gas

TDLAS LOS Direction of Flow

Interrogated Flow Path

Expansion Tube Dump Tank

Diaphragms

Tube for Fiber Optics

Detectors

TDLs

Figure 4.4: Simplified experimental setup used in expansion tube testing.

traversed the combustor perpendicular to the flow path, while the other two LOS

traversed the combustor at angles of 135� and 45� relative to the direction of the flow

for velocimetry. The path length of the perpendicular beam was 7.5 cm. Each laser

was scanned sinusoidally with a1,S=0.075 cm�1 at 12.5 kHz to give a data rate of

25 kHz (due to use of the up-scan and down-scan). The laser near 1391.7 nm was

modulated at 637.5 kHz with a1,M=0.056 cm�1 and the laser near 1343.3 nm was

modulated at 825 kHz with a1,M=0.07 cm�1. InGaAs detectors with a bandwidth of

150 MHz were used and the detector signals were sampled at 65 MS/s. The WMS

signals were extracted from the raw detector signal with 80 kHz Butterworth filters

and the same filter was used to simulate the WMS signals in the fitting routine.

Results

Calculations performed with measured shock speeds, fill pressures, and the ideal

expansion tube relations developed by Trimpi [71] suggest that the nominal temper-

ature, static pressure, and bulk speed of the air-H2O test gas were approximately

1100 K, 0.4 atm, and 1850 m/s, respectively. Fig. 4.5 shows the measured scanned-

WMS-2f/1f signals for each laser during a single experiment. A simulated scanned-

WMS-2f/1f spectrum was least-squares fit to each individual scanned-WMS-2f/1f

spectrum corresponding to a single scan (up-scan or down-scan) to infer ⌫o, A, and


�⌫c of each transition at a particular moment in time. The fitting routine was per-

formed iteratively with a fixed �⌫D as discussed in Sect. 4.2.1. The peak-normalized

residual of the best-fit scanned-WMS-2f/1f spectrum was typically less than 2.5% of

the peak signal. Fig.4.6 (top) presents measured time-histories for the gas tempera-

ture, H2O mole fraction, bulk speed, and �⌫c for the transition near 7185.59 cm�1 for

a single experiment. Fig. 4.6 (bottom) presents static pressure measurements from

both piezo-electric transducers and the scanned-WMS-2f/1f spectral-fitting method

using the measured �⌫c. In all plots, time equal to zero indicates the arrival of the

test gas at the perpendicular LOS.

0

0.1

0.2

0.3

WM

S−

2f/

1f

0 0.25 0.5 0.75 10

0.1

0.2

0.3

Time, ms

WM

S−

2f/

1f

νo ~ 7444.36 cm−1

νo ~ 7185.59 cm−1

Example of Single Spectrum

SteadyTest−Time

Arrival of Test Gas

Departure ofTest Gas

a.

b.

Figure 4.5: Scanned-WMS-2f/1f signals for a single expansion tube test with TDLsnear 1391.7 nm (a) and 1343.3 nm (b). The WMS-2f/1f signals corresponding toa single half-scan (up-scan or down-scan) were isolated from the time-history andsimulated signals were least-squares fit to each spectrum to infer gas conditions.

Initially, the gas conditions are transient and reach their nominally-steady values

near 0.15 ms. The values obtained from scanned-WMS-2f/1f spectral fitting are

listed in Table 4.1 and are in good agreement with theoretical predictions [71] and

independently measured pressures (Fig. 4.6). The scanned-WMS-2f/1f measured

temperature, pressure, and bulk speed agree within 5, 3.8, and 1.5% of theoretical

4.5. SELECTION OF MODULATION DEPTH 51

Table 4.1: Comparison between measured and simulated nominally-steady gas pa-rameters for an expansion tube test.

17

Fig. 9 Measured gas temperature, bulk speed, H2O mole fraction, and Δvc for transition near 7185.59 cm-1 (left) and measured pressure (right) for a single expansion tube test. Time equal to zero denotes the arrival of the test gas at the leading TDLAS LOS located 72.5 mm FLE (From Leading Edge of Combustor). Measured values agree well with expected values denoted by solid lines. Scanned-WMS pressure measurements are only shown from 0.125-0.8 ms due to the presence of helium in the contact surfaces that arrive at the beginning and end of the test-time. Beyond approximately 0.35 ms the pressure transducer measurements are shown as constant at the nominally-steady value due to the onset of high-frequency and high–amplitude noise that has since been mitigated [43].

Table 1. Comparison between measured and simulated nominally-steady gas parameters for an expansion tube test.

Scanned-WMS-2f/1f Spectral Fits

Scanned-WMS-2f/1f Peaks

Semi-Ideal

T [K] 1160 ± 83 1155 ± 42 1105 P [atm] 0.410 ± 0.053 NA 0.395 U [m/s] 1882 ± 52 1846 ± 51 1855 XH2O 0.082 ± 0.009 0.080 ± 0.005 0.08 Δvc [cm-1/atm] 0.021 ± 0.002 NA NA *Uncertainty bounds represent ± 1 standard deviation over the nominally-steady test time. *Semi-Ideal predictions were calculated according to Trimpi [42] with measured shock speeds and fill pressures. *Δvc is quoted for the transition near 7185.59 cm-1. The expected value for Δvc is 0.021 cm-1/atm. 6 Conclusion

Here we presented the development and initial demonstration of a calibration-free scanned-WMS-nf/1f strategy for determining gas temperature, pressure, composition, velocity and transition lineshape. This strategy exhibits several important benefits that enable accurate absorption measurements in many harsh environments of practical importance. 1) By modulating at high frequencies (>100 kHz) and employing 1f-normalization, this strategy offers higher SNR compared to direct-absorption techniques and is immune to non-absorbing transmission losses and interfering emission that vary at frequencies other than the harmonics of the modulation frequency. 2) This strategy enables accurate calibration-free WMS measurements of gas properties without

0

400

800

1200

1600

Tem

pera

ture

, K

0 0.25 0.5 0.75 10

500

1000

1500

2000

Bulk

Spe

ed, m

/s

00.030.060.090.12

X H2O

0 0.25 0.5 0.75 10

0.02

0.04

0.06

Time, ms

6i c, c

m−1

−0.5 0 0.5 10

0.2

0.4

0.6

Time, ms

Pres

sure

, atm

Ptransducer 67.5 mm FLE

PSWMS 6ic 72.5 mm FLE

Ptransducer 162.5 mm FLE

predictions, respectively, which is within the experimental uncertainty. However,

some of these di↵erences can likely be attributed to non-ideal e↵ects (e.g., boundary

layer growth) that are not accounted for in the calculations. The average scanned-

WMS-2f/1f pressure agrees within 1.7% of that from the nearest pressure transducer.

Lastly, the temperature, H2O mole fraction, and bulk speed results for the nominally-

steady test-time agree within 2.5% of those presented by Strand and Hanson [69]

who used the peak values of the WMS-2f/1f signal at linecenter to calculate gas

properties. These small di↵erences likely result from the collisional-broadening models

used by Strand and Hanson [69].

4.5 Selection of Modulation Depth

Selecting an appropriate modulation depth (a1,M) is critical to the success of all WMS

sensors. For a given harmonic and absorbance spectrum, a1,M dictates the WMS

signal strength and sensitivity to the transition lineshape [25]. Furthermore, a1,M can

be selected to reduce the influence of distortion that can compromise the accuracy of a

given measurement. This section discusses how a1,M a↵ects the scanned-WMS-nf/1f

signal strength and sensitivity to A, �⌫c, and sinusoidal distortion.


0

400

800

1200

1600

Tem

pera

ture

, K

0 0.25 0.5 0.75 10

500

1000

1500

2000

Bulk

Speed, m

/s

0

0.03

0.06

0.09

0.12

XH

2O

0 0.25 0.5 0.75 10

0.02

0.04

0.06

Time, ms

∆ν

c, cm

−1

−0.5 0 0.5 10

0.2

0.4

0.6

Time, ms

Pre

ssure

, atm

Ptransducer

67.5 mm FLE

PSWMS

∆νc 72.5 mm FLE

Ptransducer

162.5 mm FLE

Figure 4.6: Measured gas temperature, bulk speed, H2O mole fraction, and �⌫cfor transition near 7185.59 cm�1 (top) and measured pressure (bottom) for a singleexpansion tube test. Time equal to zero denotes the arrival of the test gas at theleading TDLAS LOS located 72.5 mm FLE (From Leading Edge of Combustor).Measured values agree well with expected values denoted by solid lines. Scanned-WMS pressure measurements are only shown from 0.125-0.8 ms due to the presenceof helium in the contact surfaces that arrive at the beginning and end of the test-time.Beyond approximately 0.35 ms, the pressure transducer measurements are shown asconstant at the nominally-steady value due to the onset of high-frequency and high-amplitude noise that has since been mitigated by Miller et al. [72].

4.5.1 Signal Strength

Fig. 4.7 (left) shows how the peak values of the WMS-nf and -nf/1f signals near

the transition linecenter depend on m for the second, third, and fourth harmonics.


0 2 4 6 80

0.01

0.02

0.03

0.04

Modulation Index (m)

Pe

ak

WM

S−

nf

2f3f4f

0 2 4 6 80

0.1

0.2

0.3

0.4

0.5

Modulation Index (m)

Pe

ak

WM

S−

nf/

1f

2f/1f3f/1f4f/1f

a. b.

0 1 2 3 4 5 6 7 80

0.5

1

1.5

2

2.5

3

3.5

Modulation Index ( m)

Se

nsi

tivity

to

A o

r ∆

νc (

i.e.,

δA o

r δ ∆

νc)

nf/1f and DA Sensitivity to ADA Sensitivity to ∆ν

c

2f/1f Sensitivity to ∆νc



c.

Figure 4.7: Peak WMS-nf and -nf/1f signals near linecenter (a-b) and sensitivityof scanned-WMS-nf/1f spectra to A and �⌫c (c) as a function of m. Results areshown for an H2O transition described by a Voigt profile with a peak absorbance of0.1, a L/D = 1, and a FWHM = 0.065 cm�1

Results are shown for an absorption lineshape characterized by a Voigt profile with a

peak absorbance of 0.1, a FWHM of 0.065 cm�1, and a Lorentzian to Doppler width

ratio (L/D) of 1. The scanned-WMS-2f , -3f , and -4f signals near linecenter peak at

m near 2.2, 3.5, and 3.8, respectively; however, this result depends on the absorbance

magnitude. The scanned-WMS-2f/1f , -3f/1f , and -4f/1f signals peak near m of

1.1, 1.7 and 2.3, respectively. In addition, the peak value of the scanned-WMS-nf

signal decreases as the harmonic increases. Thus, the modulation depth and harmonic

should be chosen to yield su�cient signal strength.

4.5.2 Sensitivity to A and �⌫c

The sensitivity, �q, of the total scanned-WMS-nf/1f spectrum to any quantity,

q, is given by �q = SSDN/[(q2 � q1)2/q2 where SSDN is the normalized sum-of-

squared di↵erences in the scanned-WMS-nf/1f signal given by SSDN =PN

i=1(S2,i�S1,i)2/

PNi=1 S

2i . q1, q2, and q are the first, second, and mean values of q, respectively,

S1,i is the scanned-WMS-nf/1f signal at ⌫ corresponding to q1, S2,i is the scanned-

WMS-nf/1f signal at ⌫ corresponding to q2, Si is the scanned-WMS-nf/1f signal

at ⌫ corresponding to q, and N represents the number of data points comprising the

scanned-WMS-nf/1f spectrum. As a result, �q represents the unit change in the


scanned-WMS-nf/1f spectrum per unit change in q.

Fig. 4.7 (right) shows �A and ��⌫c as a function of m for an optically thin case. For

comparison, analogous results for the scanned-DA spectral-fitting technique are also

shown. For this study, a1,S was approximately equal to the spacing between the peaks

of the outer two scanned-WMS-2f/1f lobes (shown in Fig. 3.2d) as recommended

in Sect. 4.2.1. Several important trends are shown in Fig. 4.7 (right). Firstly, the

scanned-DA and scanned-WMS-nf/1f spectra exhibit a sensitivity to A of one, and

this does not vary with m. Secondly, ��⌫c decreases rapidly with increasing m and, for

a given m, increases as the harmonic is increased. Furthermore, ��⌫c is considerably

larger than �A at small m, and considerably smaller than �A at large m. This is

significant because it states that a1,M can be selected to tune a scanned-WMS-nf/1f

sensor’s sensitivity to A (i.e., composition and temperature) or �⌫c (i.e., pressure

or collisional-broadening coe�cient). Lastly, Fig. 4.7 (right) shows that ��⌫c can be

both smaller and larger than that corresponding to the scanned-DA spectrum.

4.5.3 E↵ect of Distortion

In some cases, wavelength-dependent optical-distortion e↵ects resulting from etalon-

induced reflections can be di�cult to avoid. If not addressed, optical distortion can

alter the WMS-nf background signals which leads to a “distorted” WMS-nf signal

(compared to that corresponding to an experiment without distortion). Furthermore,

such distortion e↵ects can be time-varying due to alignment relaxation or transient

thermal and mechanical stresses in windows [73]. Here it is shown how the period

of a sinusoidal distortion signal influences scanned-WMS-nf/1f signals and how the

results vary with a1,M . The influence of sinusoidal distortion is investigated here

due to its similarity to intensity fluctuations resulting from etalon-induced reflec-

tions. A sine wave centered at an absorption transition linecenter was superimposed

upon a simulated absorbance spectrum as shown in Fig. 4.8a-b. The distortion-

induced error in the corresponding scanned-WMS-nf/1f spectrum was quantified by

the normalized sum-of-squared error, SSEN , given by SSEN =PN

i=1(SDistorted,i �


SRaw,i)2/PN

i=1 S2Raw,i where SRaw,i is the scanned-WMS-nf/1f signal at ⌫ correspond-

ing to the raw (i.e., undistorted) absorbance spectrum and SDistorted,i is the scanned-

WMS-nf/1f signal at ⌫ corresponding to the distorted absorbance profile. Since

SSEN depends on the distortion period and a1,M, it is simplest to study SSEN as

a function of a dimensionless variable, ⌘ = TD/2a1,M where TD [cm�1] is the period

of the distortion signal. Large values of ⌘ denote distortion that varies slowly in

comparison to the modulation depth and small values of ⌘ denote distortion that

changes rapidly in comparison to the modulation depth. For cases where ⌘ is much

larger than unity, it is intuitive to expect WMS-nf/1f signals to decouple from the

distortion as they do from all DC signal components. For cases where ⌘ is much less

than unity, it is also intuitive to expect the WMS-nf/1f signals to decouple from

the distortion since the distortion averages to zero over the modulation period. For

moderate values of ⌘, a more complicated coupling relationship is expected. Fig. 4.8b

shows an example absorbance spectrum that has been distorted by a low-frequency

sinusoid (TD = 0.9 cm�1) and the corresponding scanned-WMS-2f/1f spectrum. The

scanned-WMS-2f/1f spectrum is for a1,M=0.075 cm�1 (i.e., ⌘=6 for TD = 0.9 cm�1

). The raw absorbance spectrum is significantly altered by the distortion function and

the integrated absorbance and collisional width inferred from fitting a Voigt profile

to the distorted absorbance spectrum are 32 and 40% larger than that of the raw

absorbance spectrum. However, due to the relatively large value of ⌘, the best-fit

scanned-WMS-2f/1f spectrum is nearly immune to the distortion as it recovers A

and �⌫c of the raw absorbance spectrum to within 1%.

Fig. 4.9 shows how the distortion-induced SSEN varies as a function of ⌘ for a

modulation index of 1 to 5. Results are shown for an absorption transition described

by a Voigt profile with a peak absorbance of 0.10, FWHM of 0.065 cm�1, and L/D

of 1. The amplitude of the distortion function is 0.001 (i.e., 1% of absorbance at

linecenter) and TD varies from 0.01 to 10 cm�1. As expected, SSEN approaches zero

as ⌘ goes to zero and infinity. These results are most significant because they state

that for a known distortion signal, a1,M can be chosen such that scanned-WMS-nf/1f

spectra decouple from the distortion function and yield accurate measurements. For

all values of m, SSEN peaks near an ⌘ of unity. In addition, all SSEN curves oscillate


7185.4 7185.5 7185.6 7185.7 7185.8−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

Frequency, cm−1

Ab

sorb

an

ce

AbsorbanceDistortion FunctionDistorted Absorbance

TD

a.

7185.45 7185.6 7185.750

0.04

0.08

0.12

Frequency, cm−1

Ab

sorb

an

ce

Distortion

Raw Absorbance

Distorted Absorbance

Fit

7185.45 7185.6 7185.750

0.1

0.2

0.3

Frequency, cm−1

WM

S−

2f/

1f

Raw WMS−2f/1f

Distorted WMS−2f/1f

Fit

b. c.

Figure 4.8: Examples of raw (undistorted) and distorted absorbance (a-b) andscanned-WMS-2f/1f spectra (c). Low frequency distortion (b) significantly altersraw absorbance spectrum and its best-fit, but the scanned-WMS-2f/1f spectrumand its best-fit (c) are only weakly a↵ected by the distortion.

0 1 2 3 4 5 60

1.25

2.5

3.75

5x 10

−3

η

SS

EN

2f/1f with m = 12f/1f with m = 22f/1f with m = 32f/1f with m = 42f/1f with m = 5

Primary Error Band

Figure 4.9: Distortion-induced error in scanned-WMS-2f/1f spectra as a function of⌘ for a distortion signal with an amplitude of 1% of the peak raw-absorbance. Eachcurve represents a di↵erent value of modulation index. Error in scanned-WMS-2f/1fspectra goes to zero as ⌘ goes to zero and infinity.


in phase with the same frequency for ⌘ less than one. In general, all curves trend

similarly with ⌘, however, di↵erences exist which indicates that the distortion-induced

error in the WMS-2f/1f spectrum is not only a function ⌘. The exact reason for this,

however, is beyond the scope of this work.

Chapter 5

Spectroscopic Database for H2O

Near 2474 and 2482 nm

5.1 Introduction

All absorption sensors rely on accurate spectroscopic parameters (e.g. linecenter fre-

quency, linestrength, lower-state energy, and lineshape parameters) and lineshape

models to model the absorbance spectra of the target species as a function of gas

conditions. For high-pressure environments common to many engines and industrial

applications, it is particularly important to use accurate collisional-broadening param-

eters to predict the spectral absorbance at a given pressure. As a result, considerable

experimental and theoretical work has been done to develop accurate spectroscopic

databases [65, 67, 74, 75, 44, 76].

For molecules with large rotational energy level spacing (e.g., H2O, HCN, and

HF), lineshape models that account for the phenomenon of collisional (i.e. Dicke)

narrowing are typically required to accurately model the absorbance spectra at mod-

est number density [77, 78, 79, 80]. Dicke narrowing [35] is typically understood

using uncertainty principle arguments, and intuitive explanations for this process are

presented in [42]. In short, Dicke narrowing can be thought of as a collision-induced

reduction of the Doppler width that results from velocity-changing collisions that

reduce the average thermal velocity of the absorbing molecules with respect to the

58

5.2. EXPERIMENTAL METHOD 59

observer. Dicke narrowing is expected when the mean free path is comparable to

�/2⇡, where � is the wavelength of the transition [45]. Furthermore, pronounced

collisional narrowing is expected to be observed when the rotational spacing of the

transition is large compared to the thermal energy, kT . In this case, only strong col-

lisions are rotationally inelastic which leads to smaller levels of collisional broadening

and hence smaller transition widths [42]. Lineshape models addressing this process

usually employ either the soft- or the hard-collision model. The hard-collision model

[46, 81] assumes that the velocity of each collision partner is uncorrelated with its

velocity prior to the collision, while the soft-collision model assumes many collisions

are required to significantly alter the velocity of a given molecule. The soft-collision

model of the Galatry profile [40] is typically used when the molecular masses of the

collision partners do not di↵er substantially or for more general situations to account

for weak, glancing collisions that result from the long-range forces of the intermolec-

ular potential function [42]. As a result, the Galatry profile is commonly used to

describe collisional narrowing of H2O transitions in N2 and CO2 and is used here.

Here we present measurements of transition linestrength and lineshape parame-

ters for 17 H2O transitions near 2474 and 2482 nm. Lineshape parameters and their

temperature exponents are reported for H2O, CO2, and N2 perturbers. Measure-

ments were conducted in a heated static-cell at temperatures and pressures ranging

from 650-1325 K and 2-760 Torr, respectively. High-pressure measurements were

acquired behind reflected shock waves in the Stanford High-Pressure Shock Tube

(HPST) [82] at temperatures and pressures near 1400 K and 14 atm, respectively. To

our knowledge, these are the first reported high-resolution measurements of collision-

ally narrowed H2O spectra that have N2-broadening coe�cients that increase with

temperature.

5.2 Experimental Method

The experimental arrangement used to measure spectroscopic parameters is shown in

Fig. 5.1. A similar setup and procedure are given in [83]. A three-zone quartz optical

60 CHAPTER 5. SPECTROSCOPIC DATABASE FOR MIR H2O

cell fitted with wedged windows to suppress etalon interference was used in all experi-

ments. The two outer zones were evacuated to prevent unwanted absorption along the

optical path and the center zone was filled with a test mixture at a uniform, controlled

temperature between 650 and 1325 K (Thermo Scientific Thermolyne-79300). Three

type-K thermocouples (Omega) with an accuracy of 0.75% were mounted along the

9.9 cm long center zone in equally spaced intervals to measure the temperature of

the test gas. During all testing conditions, the maximum di↵erence between thermo-

couple measurements was 0.52%. It was not necessary to purge regions of the optical

path outside of the furnace because the high lower-state energy of the transitions in

the wavelength region of interest prevented detectable absorbance in the ambient.

During pure H2O experiments, an airtight flask (Chemglass Life Sciences AF-0094)

filled with distilled H2O was used to fill the optical cell with water vapor. Prior to

testing, the water flask was exposed to vacuum for 30 minutes to remove gaseous

impurities. Mixtures were prepared in a jet-stirred aluminum cylinder. The cylinder

was filled with water vapor up to 20% below the saturation pressure and then filled

to 800 Torr with the bath gas (N2 or CO2). Mixtures were allowed to di↵usively mix

for 8 hours prior to testing. To ensure a constant mixture fraction within a given set

of experiments, the optical cell was first filled to the maximum testing pressure and

then partially evacuated to a lower pressure for each test. The pressure in the optical

cell was measured with two MKS Baratron capacitance manometers (100 and 1000

Torr full-scale) with an accuracy of ± 0.12%.

Two DFB diode lasers (Nanoplus) operating near 2474 and 2482 nm were used

sequentially to probe water vapor transitions in the ⌫3 fundamental vibration band.

Each laser produced a nominal power output near 4 mW with a spectral linewidth

less than 3 MHz [84]. Due to the narrow linewidth of these lasers, instrument broad-

ening was deemed negligible (order of one-thousandth of transition full-width at half-

maximum) and was not accounted for in the data analysis. The lasers were mounted

in commercially available diode laser mounts (ILX Lightwave LDM-4412) and main-

tained at constant temperature (ILX Lightwave LDC-3900). The laser light was

collimated with 4 mm focal length, anti-reflection (AR) coated aspheric lenses (Thor-

labs C036TME-D) to minimize back-reflections into the laser cavity. A fused silica

5.2. EXPERIMENTAL METHOD 61

Test Gas

Vacuum Pump

9.9 cm

Type-K Thermocouples

Detector Focusing Lens

P P Nanoplus DFB Diode Laser

2474 or 2482 nm

Solid Ge Etalon

Beam Splitter

ILX Controller

Function Generator

3-zone Quartz Cell

Uniform Test Section

Furnace

Collimating Lens

BP Filter

60 cm

DAQ

Figure 5.1: Experimental setup used for measuring spectroscopic parameters.

beamsplitter (Thorlabs BSW23) was used to direct 50% of the laser light to a 7.65

cm long germanium solid etalon for wavelength tuning characterization. The free-

spectral range (FSR) of the etalon at the laser wavelengths was determined to be

0.0156 cm�1 using the data provided in [85]. A narrow-bandpass filter (Spectrogon

NB-2470-050 nm) was used to reduce the level of collected emission and a 20 mm

focal length zinc-selenide lens was used to focus the transmitted light onto InGaAs

detectors (Thorlabs PDA10D) with a bandwidth of 15 MHz.

During testing, the lasers were injection-current tuned with a 100 Hz sawtooth

over an optical frequency range of approximately 1.25 cm�1 and the recorded signals

were sampled at 5 MHz. During post-processing, the recorded signals were smoothed

with a 500 kHz lowpass filter which reduced electronic noise to an absorbance of

3x10�4. As a result, the signal-to-noise ratio (SNR) ranged from 150 to 1600 over

the experimental domain. A third-order polynomial was fit to the nonabsorbing re-

gions of the intensity scan to infer the baseline laser intensity, Io, over regions of

absorption. The spectral absorbance was calculated using Eq. (2.1) after the baseline

emission was subtracted from the recorded laser intensity. Spectroscopic parameters

were extracted from the data by fitting Voigt and Galatry lineshapes to the mea-

sured absorbance profiles. For spectra in pure H2O, the Voigt profile was deemed


accurate and its best-fit integrated area and collisional width were used to calculate

the transition linestrength and self-broadening coe�cient, respectively. For spectra

in CO2 and N2, the Voigt and Galatry profiles were both used to infer lineshape-

function-specific collisional-broadening coe�cients for a given perturber at a given

temperature. Collisional-narrowing coe�cients were also inferred from Galatry pro-

file fits. A numerical approximation was used to calculate the Voigt profile [86] and the

Galatry profile was calculated using the algorithms given by Varghese et al. [41, 45].

Lineshape profiles were fit to the data with a fixed-Doppler width (calculated at the

independently measured temperature) and the transition linecenter, integrated area,

and collisional width as free parameters. For Galatry profile fitting, the narrowing

parameter, z, was also a free-parameter. This additional free-parameter makes the

Galatry function less robust, and thus, it should only be used when significant colli-

sional narrowing exists. It should also be noted that multi-line fits were performed

in cases when neighboring transitions in close proximity were detected. The fitting

procedure minimized the sum-of-squared error between the measured absorbance and

the modeled absorbance using the Levenberg-Marquardt algorithm. At each test con-

dition, this fitting procedure was repeated for 25 laser scans and the average results

were used to calculate spectroscopic parameters.

5.3 Linestrength Measurements

Scanned-wavelength direct absorption was used to measure the linestrength of 17 H2O

transitions located near 4029 and 4041 cm�1. Fig. 5.2 shows the simulated absorbance

spectra of the probed transitions in pure H2O at temperature and pressure of 1200

K and 25 Torr, respectively. The HITEMP 2010 database successfully predicts the

existence of all probed transitions except one measured near 4028.156 cm�1. The

linecenter frequency of this transition was calculated using the measured relative

position to its nearest neighboring transition predicted by HITEMP 2010 [74].

The integrated area of a given transition was obtained from a fit of the experi-

mental spectrum to theory, as discussed in the previous section. Fig. 5.3 shows the

absorbance spectra and best-fit Voigt profiles for two transitions near 4029.52 cm�1.

5.3. LINESTRENGTH MEASUREMENTS 63

The maximum residual for the best-fit Voigt profile shown is 0.52% of the peak ab-

sorbance, which is 1.5 times larger than that of the best-fit Galatry profile. This

small error in the Voigt fit suggests a small contribution from collisional narrowing.

Furthermore, for pure H2O mixtures the integrated area obtained from best-fit Voigt

profiles was typically within 1% of that of the Galatry profile. As a result, the Voigt

profile was used to infer spectroscopic parameters for all spectra measured in pure

H2O due to its superior robustness and computational e�ciency.

The integrated area for each transition at a given temperature was measured at a

minimum of 10 values of pressure ranging from 2 to 22 Torr. Due to collisional and

Doppler broadening, individual doublet transitions could not be resolved. As a result,

doublet pairs were treated as a single transition due to their small spacing (order of

0.0001-0.02 cm�1) and similar lower-state energy (order of 0.001-0.001 cm�1 di↵er-

ence between transitions). The linestrength was then inferred from the slope of the

two-parameter linear fit through the area vs. pressure curve, shown for the doublet

near 4029.52 cm�1 in Fig. 5.4 (left). While only the slope of the linear fit is needed

to calculate the transition linestrength, two parameter fits were performed to prevent

any potential constant o↵set in the measured areas from influencing the linestrength

calculation. This procedure is primarily done to guard against a potential o↵set in

4027.5 4028.5 4029.5 4030.50

0.2

0.4

0.6

Frequency [cm−1]

Ab

sorb

an

ce

4039.5 4040.5 4041.5 4042.50

0.2

0.4

0.6

Frequency [cm−1]

Figure 5.2: Simulated absorbance spectra of probed transitions in pure H2O for atemperature, pressure, and path length of 1200 K, 25 Torr, and 9.9 cm, respec-tively. Simulations were performed using the Voigt profile and the HITEMP 2010[74] database with a self-broadening temperature exponent of 0.75.


0

0.2

0.4

0.6A

bso

rbance

−101

−0.55 −0.5 −0.45 −0.4 −0.35 −0.3−1

01

Relative Frequency [cm−1]Resi

dual [

%]

Experiment

Voigt Fit

νo = 4029.52 cm−1

1200 K, 22.5 Torr Neat H2O

Voigt

Galatry

Figure 5.3: Measured absorbance spectra and best-fit Voigt profile for transitionsnear 4029.52 cm�1 in pure H2O at 1200 K. The best-fit Voigt profile yields a maxi-mum residual of 0.52% of the peak absorbance. The best-fit Galatry profile yields amaximum residual that is 1.5 smaller than that of the Vogit profile.

the pressure measurement (e.g., calibration error). Due to the high lower-state energy

of the probed transitions, measurements with su�cient SNR could only be acquired

at high temperatures, 650-1325 K. As a result, the linestrength at the reference tem-

perature, 296 K, was inferred from fitting Eq. (2.8) to measured linestrengths over a

range of temperatures. Initially, a two-parameter fit was performed with the lower-

state energy and reference linestrength as free-parameters. If the best-fit lower-state

energy was within 2% of that predicted by HITEMP 2010, the linecenter frequency

and lower-state energy given by HITEMP were deemed correct and fixed in the fitting

routine, and only the reference linestrength was treated as a free-parameter in the

fitting routine. A two-parameter fit was performed for the transition that was not

predicted by HITEMP 2010. The measured linestrength, best-fit linestrength, and

linestrength predicted by HITEMP 2010 for the doublet near 4029.52 cm�1 are shown

in Fig. 5.4 as a function of temperature. A summary of the experimental results and

comparison with HITEMP 2010 is provided in Table 5.1. The best-fit linestrengths

5.4. LINESHAPE MEASUREMENTS 65

0 5 10 15 20 250

0.005

0.01

0.015

0.02

Pressure [Torr]

Inte

gra

ted

Are

a [

cm−

1]

300 600 900 1200 15000

0.02

0.04

0.06

Temperature [K]

Lin

est

ren

gth

[cm

−2/a

tm]

Measurement

Best−Fit

HITEMP 2010

νo = 4029.521/5214 cm−1

E" = 2660.9453 cm−1

Figure 5.4: Measured integrated area and linear fit for doublet near 4029.52 cm�1 at1200 K (left). Slope of the linear fit was used to calculate linestrength. Measured,best-fit, and HITEMP 2010 predicted values of linestrength for doublet near 4029.52cm�1 as a function of temperature (right). Linestrength shown represents the sumfor the doublet pair. HITEMP 2010 underpredicts the linestrength of this doubletpair by 3.8%. Error bars are too small to be seen.

agree within uncertainty with those of HITEMP 2010 except for the transitions near

4028.17 cm�1 and 4029.43 cm�1. Unless stated otherwise, the linecenter frequency

and lower-state energy listed in HITEMP 2010 were used and fixed in the fitting

routine used to infer S(296 K). The experimental uncertainties quoted in Table 5.1

result from uncertainties in pressure, temperature, baseline fitting, lineshape fitting,

and from the statistical error associated with the best-fit used to infer the reference

linestrength (and lower-state energy if needed). The dominant source of error is the

statistical uncertainty in fitting the linestrength profile to the data. The experimen-

tal uncertainty in S(296 K) for the transition near 4028.156 cm�1 is largest because

it is blended amongst a stronger transition and because it was inferred from a two

parameter fit with the lower-state energy as a free-parameter.

5.4 Lineshape Measurements

Lineshape parameters were measured for unresolved doublets near 4029.52 cm�1 and

4041.92 cm�1 in H2O, CO2, and N2 (the rotational and vibrational quantum num-

bers are given in Table 5.1). Again, doublets were treated as a single transition in


Table 5.1: Comparison of linestrengths between measurements and HITEMP 2010database.

Table 1 Best-fit power-law parameters describing the theoretical temperature dependence of collisional-narrowing coefficients for N2 and CO2 perturbers.

Temperature Range [K] Theoretical H2O-N2 Best-Fit Parameters

Theoretical H2O-CO2 Best-Fit Parameters


n


n

296-650 0.0305 0.85 0.0424 0.91 650-900 0.0286 0.75 0.0386 0.79 900-1325 0.0257 0.66 0.0373 0.75 296-1325 0.0299 0.79 0.0415 0.85

Table 2 Comparison of linestrengths between measurements and HITEMP 2010 database.

vo [cm-1] E” [cm-1] Transition v '1 v '2 v '3 ← v"1 v"2 v"3

S(296 K) [cm-2 atm-1]/Uncertainty

J 'K '−1K '1 ← J "K "−1K "1 Measured HITEMP ’10

4027.937 2426.196 0 0 1 0 0 0 14 4 11 13 4 10 5.98E-5 (2.1%) 6.04E-5 (5-10%) 4027.988 2550.882 0 0 1 0 0 0 15 2 13 14 2 12 3.40E-5 (2.7%) 3.21E-5 (5-10%) 4028.156†† 2451.841††(2.9%) NA NA NA NA 4.10E-5 (23%) NA 4028.164 2631.284 0 0 1 0 0 0 16 2 15 15 2 14 9.10E-5 (3.5%) 1.11E-4 (5-10%) 4028.178 2631.269 0 0 1 0 0 0 16 1 15 15 1 14 4028.257 2551.483 0 0 1 0 0 0 15 3 13 14 3 12 1.13E-4 (2.5%) 1.11E-4 (5-10%) 4029.429 2748.099 0 0 1 0 0 0 14 6 9 13 6 8 8.39E-6 (4%) 1.07E-5 (5-10%) 4029.524 2660.945 0 0 1 0 0 0 17 1 17 16 1 16 1.10E-4 (2.3%) 1.06E-4 (5-10%) 4029.524 2660.945 0 0 1 0 0 0 17 0 17 16 0 16 4039.998 1581.336 1 0 0 0 0 0 11 5 6 10 4 7 8.16E-4 (3.5%) 7.71E-4 (5-10%) 4040.293 2872.274 0 0 1 0 0 0 16 2 14 15 2 13 2.45E-5 (3%) 2.41E-5 (5-10%) 4040.368 2952.394 0 0 1 0 0 0 17 2 16 16 2 15 2.59E-5 (3%) 2.37E-5 (5-10%) 4040.375 2952.387 0 0 1 0 0 0 17 1 16 16 1 15 4040.486 2872.581 0 0 1 0 0 0 16 3 14 15 3 13 8.13E-6 (4.1%) 7.84E-6 (5-10%) 4040.665 2746.023 0 0 1 0 0 0 15 4 12 14 4 11 4.13E-5 (2.5%) 3.99E-5 (5-10%) 4041.776 5258.631 0 1 1 0 1 0 19 2 18 18 2 17 5.00E-10 (4%) 4.33E-10 (10-20%) 4041.776 5258.631 0 1 1 0 1 0 19 1 18 18 1 17 4041.923 2981.359 0 0 1 0 0 0 18 0 18 17 0 17 2.43E-5 (2.7%) 2.25E-5 (5-10%) 4041.923 2981.359 0 0 1 0 0 0 18 1 18 17 1 17 4042.118 5204.749 0 1 1 0 1 0 18 2 16 17 2 15 3.01E-10 (8.1%) 3.85E-10 (10-20%) 4042.179 5241.742 0 1 1 0 1 0 20 0 20 19 0 19 4.38E-10 (7.5%) 5.24E-10 (10-20%) 4042.179 5241.742 0 1 1 0 1 0 20 1 20 19 1 19 4042.304 2756.415 0 0 1 0 0 0 14 6 8 13 6 7 2.53E-5 (3.5%) 2.47E-5 (5-10%) Uncertainties are given in parentheses. Linestrength reported for doublets is the sum of the two transitions. The linecenter frequency and lower-state energy of all transitions listed in HITEMP 2010 were fixed in the fitting routine used to infer S(296 K) Unless stated otherwise, source of quoted HITEMP 2010 linestrengths is Toth [40] †Source of HITEMP 2010 linestrength is Barber et al. [41] ††Denotes an experimentally observed transition that is not listed in HITEMP 2010.

††Indicates a transition not listed in HITEMP 2010

the lineshape fitting procedure due to their close proximity and similar lower-state

energy. Fig. 5.5 shows the experimental absorbance spectra with residuals for Voigt

and Galatry fits for the doublet near 4029.52 cm�1 in CO2 (left) and N2 (right). The

pronounced gull-wing residual of the Voigt fit indicates the presence of collisional nar-

rowing [42]. This behavior is expected for transitions with large rotational quantum

numbers since this typically corresponds to transitions with a smaller collisional-

broadening to -narrowing ratio [45]. The maximum residual of the Voigt fits shown

is 2.2 and 4.8% of the peak absorbance for CO2 and N2, respectively. The larger dif-

ference in molecular mass for the H2O-CO2 pair suggests more pronounced collisional

narrowing; however, the strong collisional broadening of CO2 mitigates this e↵ect.

As a result, the Voigt profile is more appropriate for spectra in CO2 than in N2. The

Galatry profile e↵ectively removes the gull-wing signature and reduces the maximum


0

0.1

0.2

0.3A

bso

rba

nce

−505

−0.55 −0.5 −0.45 −0.4 −0.35 −0.3−5

05

Relative Frequency [cm−1]

Re

sid

ua

l [%

]

Experiment

Galatry Fit

1200 K, 750 Torr CO2 with 2.0 % H

2O by Mole

Galatry

Voigt0

0.1

0.2

0.3

−505

−0.55 −0.5 −0.45 −0.4 −0.35 −0.3−5

05

Relative Frequency [cm−1]

1200 K, 760 Torr N2 with 2.5 % H

2O by Mole

Figure 5.5: Measured absorbance spectra for transitions near 4029.52 cm�1 in CO2

(left) and N2 (right), gas conditions are stated within the figure. The gull-wingsignature in the best-fit Voigt profile residual suggests strong collisional narrowing.The maximum residual is 2.2 and 4.8% of the peak absorbance for spectra shown inCO2 and N2, respectively. The best-fit Galatry profile e↵ectively removes the gull-wing signature and reduces the maximum residual by ⇡10 times compared to that ofthe Voigt profile.

residual by a factor of 10 for both CO2 and N2 perturbers. The remaining asymmetry

in the residual of the Galatry profile may result from a correlation between velocity-

changing collisions and state-perturbing collisions [87] or from the speed dependence

of lineshape parameters [49]. For the spectra shown for CO2 perturbers, the integrated

area and collisional width of the Galatry fit are 2 and 8% larger than that of the Voigt

fit, respectively. This indicates that the Voigt profile is less accurate for this spectra

at these conditions. As expected, this discrepancy is worse for the spectrum shown for

N2 perturbers where the integrated area and collisional width of the Galatry fit are 5

and 20% larger than that of the Voigt fit. Results for the doublet near 4041.92 cm�1

are similar for spectra collected in N2; however, it was found that the Voigt profile is an

adequate lineshape model for its spectra in CO2. These lineshape function-dependent

results are consistent with those seen by others [67, 42, 88, 89], but it is important

to note that the true integrated area is not dependent on the lineshape function.

The integrated area inferred from fitting theory to measured spectra, however, does

depend on the lineshape function if the lineshape functions used are not equally


accurate. This di↵erence in best-fit integrated areas across lineshape functions can

be mitigated by using di↵erent objective functions in the fitting routine, as done by

Nagali et al. [87]. However, the most accurate lineshape function should always be

used to infer the true integrated area.

At each temperature, the collisional width and narrowing parameter (if necessary)

were measured for both doublets at 10 or more pressures ranging from 0.2 to 1 atm.

The collisional-broadening and -narrowing coe�cients were inferred from the slope

of the two-parameter linear fit to the data, shown in Fig. 5.6 (left). For mixtures,

the collisional-broadening coe�cient of the bath gas species was calculated using Eq.

(2.16) and the self-broadening coe�cient determined from pure H2O experiments. In

Fig. 5.6 (left) the linear fit to the collisional width has an o↵set of 0.0004 cm�1 (i.e.,

2% of the maximum collisional width measured) at zero pressure. This small o↵set

could result from pressure calibration errors or from extrapolating the fit outside the

experimental domain. The linear fit to the N2-narrowing parameters goes to zero at

0.1 atm. This may result from the pressure dependence of the Galatry narrowing

parameter [75, 79, 90], or may simply indicate that the Galatry profile is ill-suited

for the corresponding spectra at pressures below those studied here. For pure H2O

experiments, this procedure was repeated at 10 di↵erent temperatures between 650

and 1325 K. For experiments in CO2 and N2, experiments were performed at 14

di↵erent temperatures between 900 and 1325 K. The collisional-broadening and -

narrowing coe�cients at the reference temperature of 296 K and the corresponding

temperature exponent were inferred from the two-parameter best-fit of Eq. (2.17)

to the data. The experimental results and best-fit power-law for the collisional-

broadening and -narrowing coe�cients of the doublet near 4029.52 cm�1 are shown

in Fig. 5.6 (right) for N2 perturbers. A reference temperature of 296 K was used in the

power-law fitting to be consistent with the HITEMP and HITRAN databases [74, 91].

However, measurements of such parameters at 296 K should deviate slightly from the

best-fit parameters reported here due to the inherent temperature dependence of the

collisional-broadening and -narrowing coe�cient temperature exponents.

Table 5.2 compares the experimentally derived best-fit self-broadening coe�cients

at 296 K for a Voigt profile with those predicted by HITEMP 2010. Two di↵erent


0

0.01

0.02

0.03

Co

llisi

on

al W

idth

[cm

−1]

0 0.2 0.4 0.6 0.8 10

0.01

0.02

0.03

Total Pressure, atm

β x

P [

cm−

1]

0.005

0.015

0.025

γ N2 [

cm−

1/a

tm]

800 1000 1200 14000.005

0.015

0.025

Temperature [K]

βN

2 [

cm−

1/a

tm]

Figure 5.6: Collisional-broadening and -narrowing parameters for the doublet near4029.52 cm�1. Measured collisional width FWHM and � ⇥ P and two-parameterlinear fit used to infer �N2 and �N2 (left). Measured �N2 and �N2 with best-fit power-law used to determine �N2(296K) and �N2(296K) and their respective temperatureexponents, n. Error bars are too small to be seen for collisional width, z, and �N2(T ).

Table 5.2: Comparison of self-broadening coe�cients (HWHM per atm) betweenmeasurements and HITEMP 2010.

2

Table 3 Comparison of self-broadening coefficients (HWHM per atm) between measurements and HITEMP 2010.

vo [cm-1] E” [cm-1] γ H2O(296 K) [cm-1 atm-1] n

Measured HITEMP ’10 Measured 4029.52† 2660.95 0.151 (6.5%) 0.128/0.208†† (5-10%/Est.) 0.64 (9%) 4041.92† 2981.36 0.123 (8%) 0.105/0.195†† (5-10%/Est.) 0.42 (13%)

†Denotes a doublet transition. Best-fit parameters derived from measurements conducted at 650 to 1325 K and 2 to 25 torr Broadening coefficients for both transitions of each doublet are quoted for HITEMP Unless stated otherwise, self-broadening coefficients at 296 K listed in HITEMP 2010 are taken from Toth [40] †† Self-broadening at 296 K listed in HITEMP 2010 are smoothed values from Antony and Gamache [49] All broadening coefficients quoted here are for use with the Voigt profile Uncertainties are given in parentheses.

Table 4 Measured lineshape parameters for H2O, CO2, and N2 collision partners.

vo [cm-1]

Collision Partner

Lineshape Function

γ (296 K )

[cm-1 atm-1] n β(296 K )

[cm-1 atm-1] n

4029.52 H2O Voigt 0.1510 (6.5%) 0.64 (9%) CO2 Voigt 0.0345 (5%) 0.78 (6%) CO2 Galatry 0.0284 (5%) 0.51 (6%) 0.0343 (12%) 0.73 (16%) N2 Voigt 0.0059 (10%) -0.13 (15%) N2 Galatry 0.0086 (4%) -0.15 (12%) 0.0293 (12%) 0.51 (15%)

4041.92 H2O Voigt 0.123 (8%) 0.42 (13%) CO2 Voigt 0.0325 (5%) 0.67 (7%) N2 Voigt 0.0040 (8%) -0.30 (14%) N2 Galatry 0.0075 (7%) -0.21 (13%) 0.0290 (13%) 0.56 (17%)

Best-fit parameters for CO2 and N2 perturbers derived from measurements conducted at 900 to 1325 K and 0.25 to 1 atm. Broadening coefficients are given as HWHM per atm. Uncertainties are given in parentheses.

†Indicates a doublet transition

broadening coe�cients are predicted for each transition of the doublet, however, these

values are expected to be similar within a given doublet [92, 93] despite the large dif-

ferences predicted by HITEMP 2010. The measured values for both doublets are

closest to that predicted for the stronger transition of the doublet. The best-fit self-

broadening coe�cients at 296 K are within 2% and 4% of the linestrength-weighted

average broadening coe�cient of each doublet predicted by HITEMP. In an e↵ort to

provide more realistic uncertainty bounds, the reported uncertainties include contri-

butions from temperature, pressure, baseline fitting, lineshape profile fitting, and the

95% confidence interval obtained from the two-parameter power-law fit. The latter

source of uncertainty is typically not reported, despite the fact that it represents

nearly 90% of the uncertainty in the values reported in Tables 5.2-5.3.


Table 5.3: Measured lineshape parameters for H2O, CO2, and N2 collision partners.

2

Table 3 Comparison of self-broadening coefficients (HWHM per atm) between measurements and HITEMP 2010.

vo [cm-1] E” [cm-1] γ H2O(296 K) [cm-1 atm-1] n

Measured HITEMP ’10 Measured 4029.52† 2660.95 0.151 (6.5%) 0.128/0.208†† (5-10%/Est.) 0.64 (9%) 4041.92† 2981.36 0.123 (8%) 0.105/0.195†† (5-10%/Est.) 0.42 (13%)

†Denotes a doublet transition. Best-fit parameters derived from measurements conducted at 650 to 1325 K and 2 to 25 torr Broadening coefficients for both transitions of each doublet are quoted for HITEMP Unless stated otherwise, self-broadening coefficients at 296 K listed in HITEMP 2010 are taken from Toth [40] †† Self-broadening at 296 K listed in HITEMP 2010 are smoothed values from Antony and Gamache [49] All broadening coefficients quoted here are for use with the Voigt profile Uncertainties are given in parentheses.

Table 4 Measured lineshape parameters for H2O, CO2, and N2 collision partners.

vo [cm-1]

Collision Partner

Lineshape Function

γ (296 K )

[cm-1 atm-1] n β(296 K )

[cm-1 atm-1] n

4029.52 H2O Voigt 0.1510 (6.5%) 0.64 (9%) CO2 Voigt 0.0345 (5%) 0.78 (6%) CO2 Galatry 0.0284 (5%) 0.51 (6%) 0.0343 (12%) 0.73 (16%) N2 Voigt 0.0059 (10%) -0.13 (15%) N2 Galatry 0.0086 (4%) -0.15 (12%) 0.0293 (12%) 0.51 (15%)

4041.92 H2O Voigt 0.123 (8%) 0.42 (13%) CO2 Voigt 0.0325 (5%) 0.67 (7%) N2 Voigt 0.0040 (8%) -0.30 (14%) N2 Galatry 0.0075 (7%) -0.21 (13%) 0.0290 (13%) 0.56 (17%)

Best-fit parameters for CO2 and N2 perturbers derived from measurements conducted at 900 to 1325 K and 0.25 to 1 atm. Broadening coefficients are given as HWHM per atm. Uncertainties are given in parentheses.

Table 5.4: Measured lineshape parameters for H2O transitions near wavelengths stud-ied.

Table 1. Measured lineshape parameters for H2O transitions near wavelengths studied.

vo

E”

Transition J 'K '−1K '1 ← J "K "−1K "1

γ (To )

H2O

n H2O

γ (To )

N2 n

N2 β(To )

N2 n

N2 4027.937 2426.196 14 4 11 13 4 10 0.22(1) 0.57(1) 0.038(1) 0.44(2) - - 4027.988 2550.882 15 2 13 14 2 12 0.19(2) 0.49(2) 0.021(2) 0.17(3) - - 4028.156† 2451.841† NA NA 0.11(4) 0.52(4) 0.0048(4) -0.67(4) - - 4028.164 2631.284 16 2 15 15 2 14 0.11(3) 0.14(3) 0.010(2) -0.13(3) - - 4028.178 2631.269 16 1 15 15 1 14 4028.257 2551.483 15 3 13 14 3 12 0.18(2) 0.48(2) 0.021(2) 0.09(3) - - 4029.429 2748.099 14 6 9 13 6 8 0.43(3) 1.38(3) 0.021(3) -0.08(3) - - 4039.998 1581.336 11 5 6 10 4 7 0.51(3) 1.02(3) 0.125(3) 1.10(3) - - 4040.293 2872.274 16 2 14 15 2 13 0.14(3) 0.37(3) 0.036(2) 0.64(2) - - 4040.368 2952.394 17 2 16 16 2 15 0.09(4) 0.13(4) 0.0073(2) -0.22(2) - - 4040.375 2952.387 17 1 16 16 1 15 4040.486 2872.581 16 3 14 15 3 13 0.31(3) 1.26(3) 0.022(3) 0.15(3) - - 4040.665 2746.023 15 4 12 14 4 11 0.20(2) 0.58(2) 0.029(3) 0.21(3) - - 4042.304 2756.415 14 6 8 13 6 7 0.39(1) 0.94(1) 0.088(1) 0.84(1) - - 4029.524 2660.945 17 1 17 16 1 16 0.15(1) 0.64(1) 0.0086(1) -0.15(2) 0.0293(2) 0.51(3) 4029.524 2660.945 17 0 17 16 0 16 4030.729 4889.488 19 1 19 18 1 18 0.19(4) 0.66(4) 0.0023(4) -0.43(4) C:0.0293 C:0.51 4030.729 4889.488 19 0 19 18 0 18 4041.776 5258.631 19 2 18 18 2 17 0.17(4) 0.55(4) 0.0094(4) -0.08(4) C:0.029 C:0.56 4041.776 5258.631 19 1 18 18 1 17 4041.923 2981.359 18 0 18 17 0 17 0.12(1) 0.42(2) 0.0075(1) -0.21(2) 0.029(2) 0.56(3) 4041.923 2981.359 18 1 18 17 1 17 4042.179 5241.742 20 0 20 19 0 19 0.18(4) 0.7(4) 0.0024(4) -0.63(4) C:0.029 C:0.56 4042.179 5241.742 20 1 20 19 1 19

†Indicates a transition that is not listed in HITEMP 2010. Units of all quantities are as given in Section 2.1 C: indicates the parameter was constrained in the fitting routine. Uncertainty Codes: (1)5-10%, (2)10-15%, (3)15-20%, and (4) >20% vo, E”, and local quanta are taken from HITEMP 2010 [26]. Measured linestrengths for these transitions are also provided in [17]. Parameters for doublets near 4029.524 and 4041.923 cm-1 were taken from [17]. If β(To )

is provided, N2 lineshape parameters are for use with the Galatry profile. All other parameters are quoted for the Voigt profile. Table 2. Measured N2-pressure-shift coefficients for the two dominant H2O transitions.

vo

E”

J 'K '−1K '1 ← J "K "−1K "1

δ (To ) N2

m N2

4029.524 2660.945 17 1 17 16 1 16 -0.021(2) 1.71(2) 4029.524 2660.945 17 0 17 16 0 16 4041.923 2981.359 18 0 18 17 0 17 -0.025(2) 1.91(2) 4041.923 2981.359 18 1 18 17 1 17

†Indicates a transition not listed in HITEMP 2010If �(To) is not listed, collisional-broadening parameters are for use with the Voigtprofile. All other parameters are for use with the Galatry profile.


Table 5.3 presents the best-fit lineshape parameters for H2O, CO2, and N2 collision

partners. The reported uncertainty is calculated in the same fashion as the results

reported in Table 5.2. All reported collisional-broadening coe�cients at 296 K for the

doublet near 4041.92 cm�1 are smaller than that of the doublet near 4029.52 cm�1.

This is expected due to the larger rotational quantum numbers of the doublet near

4041.92 cm�1. The values of �(296K) reported for Voigt profiles are considerably

smaller than those derived from the corresponding Galatry profiles, as expected, ex-

cept for the doublet near 4029.52 cm�1 in CO2. This anomalous behavior may result

from extrapolating the power-law fit of high-temperature (900-1325 K) broadening

coe�cients to 296 K or may indicate that the Galatry profile is not well-suited for the

transition near 4029.52 cm�1 in CO2. However, it is worth noting that a similar result

was observed by Li et al. [67] for an H2O transition in Ar. For CO2, the Galatry

profile returned a smaller temperature exponent for the broadening coe�cient which

is consistent with results seen by Li et al. [67]. For N2, the Voigt and Galatry profile

fits returned a negative broadening temperature exponent for both doublets. This

behavior has been observed for H2O transitions in air by Toth et al. [94] and is pre-

dicted by theory for some high-rotational energy H2O transitions [95]. The Galatry

profile returned a temperature exponent for the collisional-broadening coe�cient that

is smaller in magnitude than that of the Voigt for the doublet near 4041.92 cm�1,

however, the two values agree within uncertainty for the doublet near 4029.52 cm�1.

The inferred values of �(296K) for the two doublets in N2 and CO2 agree within un-

certainty with the corresponding value of �Diff (296K) predicted by a power-law fit

to Eq. (2.28) over the same temperature domain as the experiments (900-1325 K). In

addition, the measured temperature exponents for all presented collisional-narrowing

coe�cients are bound by the limits predicted by theory presented in Chapter 1, and

the temperature exponent of the N2-narrowing coe�cients are less than that of CO2

as expected. The ratio of collisional-broadening to -narrowing, r = �/�, is weakly

dependent on temperature for the doublet near 4029.52 cm�1 in CO2, as it scales

with T 0.22. This result is predicted by theory [42] and is similar to results reported

by Li et al. [67] for HO transitions in Ar. For both doublets in N2, however, r is

a strong function of temperature and scales with T 0.66 and T 0.77, respectively. This


result further stresses the importance of using accurate lineshape models, particularly

when the results will be extrapolated beyond the domain of experiments from which

they were derived.

5.5 Line-Shift Measurements

N2-pressure-shift coe�cients were measured for the doublets near 4029.52 and 4041.92

cm�1. This was done in a manner analogous to the determination of collisional-

broadening coe�cients. However, instead of performing a linear-fit to collisional-

width versus pressure, a linear-fit was applied to the transition linecenter versus

pressure. This procedure was repeated at several temperatures to obtain the best-fit

power-law parameters presented in Table 5.5.

Table 5.5: Measured N2-pressure-shift coe�cients for the two dominant H2O transi-tions.

Table 1. Measured lineshape parameters for H2O transitions near wavelengths studied.

vo

E”

Transition J 'K '−1K '1 ← J "K "−1K "1

γ (To )

H2O

n H2O

γ (To )

N2 n

N2 β(To )

N2 n

N2 4027.937 2426.196 14 4 11 13 4 10 0.22(1) 0.57(1) 0.038(1) 0.44(2) - - 4027.988 2550.882 15 2 13 14 2 12 0.19(2) 0.49(2) 0.021(2) 0.17(3) - - 4028.156† 2451.841† NA NA 0.11(4) 0.52(4) 0.0048(4) -0.67(4) - - 4028.164 2631.284 16 2 15 15 2 14 0.11(3) 0.14(3) 0.010(2) -0.13(3) - - 4028.178 2631.269 16 1 15 15 1 14 4028.257 2551.483 15 3 13 14 3 12 0.18(2) 0.48(2) 0.021(2) 0.09(3) - - 4029.429 2748.099 14 6 9 13 6 8 0.43(3) 1.38(3) 0.021(3) -0.08(3) - - 4039.998 1581.336 11 5 6 10 4 7 0.51(3) 1.02(3) 0.125(3) 1.10(3) - - 4040.293 2872.274 16 2 14 15 2 13 0.14(3) 0.37(3) 0.036(2) 0.64(2) - - 4040.368 2952.394 17 2 16 16 2 15 0.09(4) 0.13(4) 0.0073(2) -0.22(2) - - 4040.375 2952.387 17 1 16 16 1 15 4040.486 2872.581 16 3 14 15 3 13 0.31(3) 1.26(3) 0.022(3) 0.15(3) - - 4040.665 2746.023 15 4 12 14 4 11 0.20(2) 0.58(2) 0.029(3) 0.21(3) - - 4042.304 2756.415 14 6 8 13 6 7 0.39(1) 0.94(1) 0.088(1) 0.84(1) - - 4029.524 2660.945 17 1 17 16 1 16 0.15(1) 0.64(1) 0.0086(1) -0.15(2) 0.0293(2) 0.51(3) 4029.524 2660.945 17 0 17 16 0 16 4030.729 4889.488 19 1 19 18 1 18 0.19(4) 0.66(4) 0.0023(4) -0.43(4) C:0.0293 C:0.51 4030.729 4889.488 19 0 19 18 0 18 4041.776 5258.631 19 2 18 18 2 17 0.17(4) 0.55(4) 0.0094(4) -0.08(4) C:0.029 C:0.56 4041.776 5258.631 19 1 18 18 1 17 4041.923 2981.359 18 0 18 17 0 17 0.12(1) 0.42(2) 0.0075(1) -0.21(2) 0.029(2) 0.56(3) 4041.923 2981.359 18 1 18 17 1 17 4042.179 5241.742 20 0 20 19 0 19 0.18(4) 0.7(4) 0.0024(4) -0.63(4) C:0.029 C:0.56 4042.179 5241.742 20 1 20 19 1 19

†Indicates a transition that is not listed in HITEMP 2010. Units of all quantities are as given in Section 2.1 C: indicates the parameter was constrained in the fitting routine. Uncertainty Codes: (1)5-10%, (2)10-15%, (3)15-20%, and (4) >20% vo, E”, and local quanta are taken from HITEMP 2010 [26]. Measured linestrengths for these transitions are also provided in [17]. Parameters for doublets near 4029.524 and 4041.923 cm-1 were taken from [17]. If β(To )

is provided, N2 lineshape parameters are for use with the Galatry profile. All other parameters are quoted for the Voigt profile. Table 2. Measured N2-pressure-shift coefficients for the two dominant H2O transitions.

vo

E”

J 'K '−1K '1 ← J "K "−1K "1

δ (To ) N2

m N2

4029.524 2660.945 17 1 17 16 1 16 -0.021(2) 1.71(2) 4029.524 2660.945 17 0 17 16 0 16 4041.923 2981.359 18 0 18 17 0 17 -0.025(2) 1.91(2) 4041.923 2981.359 18 1 18 17 1 17

5.6 High-Pressure Spectra

To confirm the accuracy of the reported N2-broadening coe�cients at larger Lorentzian

width to Doppler width (L/D) ratios, scanned-wavelength direct absorption measure-

ments were conducted in high-pressure H2O-N2 mixtures behind reflected shockwaves

in the Stanford HPST. Measurements were conducted in a similar fashion to those

reported by Nagali et al. [96], and details regarding the Stanford HPST are given by

Petersen and Hanson [82]. Fig. 5.7 shows a comparison between a single-scan mea-

surement of the absorption spectra near 4029.52 (left) and 4041.92 cm�1 (right) and

5.6. HIGH-PRESSURE SPECTRA 73

simulations performed with three di↵erent spectra models (i.e., di↵erent lineshape

function and/or di↵erent broadening coe�cients).

All simulations shown in Fig. 5.7 used the measured linestrength and self-broadening

parameters reported in Tables 5.1-5.2. Fig. 5.7 shows that the peak absorbance pre-

dicted by simulations performed with the Voigt profile and air-broadening parameters

predicted by HITEMP 2010 is nearly a factor of 3 larger than the measured values.

This discrepancy is largely because HITEMP 2010 predicts positive air-broadening

coe�cient temperature exponents (n= 0.41) for both doublets, which leads to smaller

collisional broadening at high temperatures and thus, a larger peak absorbance. This

di↵ers from the results presented here, which state that the N2-broadening coe�cients

increase with temperature. Some of the error in this simulated spectra can also be

attributed to the fact that air-broadening coe�cients typically di↵er from those of

N2 by 10-15% [96]. Simulations performed with the Voigt profile and N2-broadening

coe�cients derived from Voigt profile fits to low-pressure spectra at 900 to 1325 K

(given in Table 5.3) improves agreement with the measured spectra, however, these

4029.2 4029.4 4029.6 4029.80

0.2

0.4

0.6

0.8

Frequency [cm−1]

Ab

sorb

an

ce

20 Torr NeatH

2O Simulation

4041.5 4041.75 4042 4042.250

0.2

0.4

0.6

0.8

Frequency [cm−1]

Ab

sorb

an

ce

Measurement

Sim. w/ Derived fromVoigt Fits at Low P

Sim. w/ Derived fromGalatry Fits at Low P

Sim. w/ HT ’10 γair

γN2

γN2

Figure 5.7: Comparison between measured absorbance spectra and simulated ab-sorbance spectra using di↵erent lineshape models and broadening parameters. Spec-tra are shown for transitions near 4029.52 cm�1 at 1368 K, 13.25 atm, and 4.5% H2Oin N2 (left) and transitions near 4041.92 cm�1 at 1371 K, 14.86 atm, and 4.6% H2Oin N2 (right). The simulations performed with Galatry profile derived N2-broadeningcoe�cients based on data collected at 0.25 to 1 atm and 900 to 1325 K, presented inTable 5.3, agrees well with the measured spectra obtained behind reflected shockwavesin the Stanford HPST.


simulations overpredict the peak absorbance by 26 and 38%, respectively. The simula-

tions performed with the Galatry profile and N2-broadening coe�cients derived from

Galatry profile fits to low-pressure spectra at 900 to 1325 K (given in Table 4) are the

most accurate and recover the peak-absorbance to within 3.4 and 4%, respectively. As

a result, we recommend the use of the Galatry profile and our Galatry profile derived

N2-broadening parameters to accurately model this spectra over a wide range of L/D

values. It should be noted, however, that simulations performed with the Voigt pro-

file and broadening coe�cients derived from Voigt fits to high-pressure spectra would

likely perform well at high pressure due to the greater L/D ratio which reduces the

importance of collisional narrowing e↵ects that act upon the Doppler width. The

significance of the results presented here is twofold. Firstly, the measured spectra

presented illustrate that if significant collisional narrowing exists during lineshape

characterization experiments, Voigt profile-derived broadening coe�cients cannot be

used to accurately model absorbance spectra in a L/D regime that is outside that

from which the broadening coe�cients were experimentally derived. For the spectra

measured in static-cell experiments, the L/D ranged from 0.5-1.25 and the best-fit

Voigt profile consistently underpredicted the peak absorbance by 3-5% depending on

pressure and temperature. For the HPST experiments, the L/D was 14-15 and simu-

lations performed with the Voigt profile and N2-broadening coe�cients derived from

Voigt profile fits to low-pressure spectra overpredicts the peak absorbance by 26-38%,

a greater than fivefold increase in error. As a result, it is clear that it is essential to

use appropriate lineshape models when measuring broadening coe�cients that will

be used to simulate spectra outside of the domain of lineshape characterization ex-

periments. Secondly, the good agreement between the measured spectra and spectra

simulated with the Galatry profile-derived broadening coe�cients further supports

the accuracy of the Galatry profile derived N2-broadening parameters reported in

Table 5.3.

Chapter 6

Sensor Design for Nonuniform

Environments

6.1 Introduction

Many important applications require absorption spectroscopy measurements to char-

acterize highly-nonuniform environments that result from heat transfer, flow mixing,

combustion, and phase change. For example, absorption measurements have been

used to study flames [97], quantify combustion progress in engines [98], and mea-

sure bulk flow speed and temperature in various facilities [99, 8]. As a result, some

researchers have developed absorption spectroscopy strategies for nonuniform flows.

More specifically, strategies have been designed to: identify nonuniformities [100, 6],

reduce sensitivity to nonuniformities [98, 100, 101], address boundary layer e↵ects

[97, 8, 102], provide active control of nonuniform flows [103, 104], and actively resolve

LOS distributions of temperature [105, 106]. In addition, techniques have been devel-

oped for comparing measurements acquired across a nonuniform LOS with absorp-

tion signals calculated with computational fluid dynamics (CFD) solutions [99, 107].

While each of these strategies o↵ers specific benefits, many of these strategies are

confined to limited circumstances and the most quantitative techniques involve com-

paratively complex data processing routines.

Here we present a new, widely applicable strategy that provides quantitative LOS

75

76 CHAPTER 6. SENSOR DESIGN FOR NONUNIFORM ENVIRONMENTS

measurements in nonuniform environments without added complexity. This strat-

egy uses two-color TDLAS to measure the absorbing-species column density, Ni,

and the absorbing-species number-density-weighted path-average temperature, T ni ,

in nonuniform environments. T ni and Ni are defined mathematically in eqs. (6.2)

and (6.9). This strategy has been developed for both lineshape-independent and -

dependent measurement strategies. It will be shown that by using transitions with

strengths that scale linearly with temperature and empirically-derived e↵ective line-

shapes, measured spectra can be used to infer Ni and T ni without knowing how the

gas conditions vary along the LOS. In addition, while this strategy is initially dis-

cussed in the context of perfectly isolated water-vapor transitions, this strategy can

be used with any absorbing species and in partially blended spectra (see Section 6.5).

First, the fundamentals of absorption spectroscopy are discussed in the context of

scanned-wavelength direct absorption (SWDA), fixed-wavelength direct absorption

(FWDA), and wavelength-modulation spectroscopy (WMS). Then it is shown that

LOS nonuniformities in temperature, pressure, and composition can introduce large

errors in inferred gas conditions and how the new strategy presented here is immune

to these errors. The underlying assumptions of this strategy are then evaluated to

show that this strategy can be used in, but is not limited to, highly-nonuniform en-

vironments where the temperature varies along the LOS by up to 700 K. Lastly, this

strategy is demonstrated in partially blended spectra with simulated SWDA, FWDA,

and WMS signals for a LOS with temperature and water mole fraction gradients com-

parable to those seen in hydrogen-air di↵usion flames.

6.2 Determination of Gas Properties

6.2.1 Scanned-Wavelength Direct Absorption (SWDA)

In SWDA, the laser wavelength is tuned over the majority of an absorption feature to

measure the integrated area and lineshape directly. The temperature can be inferred

from the ratio of integrated areas of two transitions with di↵erent lower-state energy.

If the gas is uniform along the optical path, this ratio, R2�,A, reduces to the two-color

6.2. DETERMINATION OF GAS PROPERTIES 77

ratio of transition linestrengths and is given by Eq. (6.1).

R2�,A ⌘ A2

A1=

Sn2 (T )nL

Sn1 (T )niL

=Sn2 (T )

Sn1 (T )

(6.1)

If the path length and gas temperature are known, the absorbing-species number

density can be found from the integrated area of a single transition using Eq. (2.7).

If the gas pressure is also known and an appropriate equation of state exists, the

absorbing-species mole fraction can also be found from the area. If the path length

through the absorbing gas is not known, or the absorbing species is nonuniformly

distributed along the LOS, the absorbing-species column density, Ni [molecules/cm2],

defined by Eq. (6.2) can be used to quantify the gas composition.

Ni ⌘Z L

0

nidl (6.2)

6.2.2 Fixed-Wavelength Direct Absorption (FWDA)

When laser limitations, sensor bandwidth requirements, or blended spectra prohibit

a direct measurement of the integrated area, FWDA is often used to infer the temper-

ature and gas composition from the measured absorbance at particular wavelengths.

This technique, however, typically requires accurate knowledge of the transition line-

shape and its dependence on gas conditions. When the lineshape function is known

and the gas along the LOS is uniform, the temperature can be calculated from a

two-color ratio of absorbance, R2�,↵, given by Eq. (6.3).

R2�,↵ ⌘ ↵2

↵1=

A2�⌫,2(⌫2, T, P,�)

A1�⌫,1(⌫1, T, P,�)(6.3)

In most cases, this two-color ratio exhibits a strong dependence on temperature,

and only a weak dependence on pressure and composition. As a result, the tempera-

ture can be found from a measured two-color ratio of absorbance and the composition

can be found from the peak absorbance of a single transition. For best results, this

process is iterative to account for the influence of the gas composition on the lineshape

function.


6.2.3 Wavelength-Modulation Spectroscopy

If the signal-to-noise ratio (SNR) is low or it is di�cult to recover the incident light

intensity, it is often advantageous to use WMS-2f/1f . For a linecenter measurement

through an optically thin gas (↵ <0.05) and an assumed first-order intensity modu-

lation with a phase shift of ⇡, the 2f/1f signal is approximately given by Eq. (6.4)

[25].

2f/1f ⇡ 1

io⇡

Z ⇡

�⇡

Z L

0

Sn(T )ni�⌫(⌫o + a cos ✓)dl cos(2✓)d✓ (6.4)

Here, a is the laser modulation depth [cm�1], and io is the mean-intensity-normalized

intensity modulation amplitude. If the conditions across the LOS are uniform, Eq.

(6.4) simplifies to Eq. (6.5).

2f/1f ⇡ 1

io⇡Sn(T )niL

Z ⇡

�⇡

�⌫(⌫o+a cos ✓) cos(2✓)d✓ = AG[�⌫(T, P,�, ⌫), a, io] (6.5)

As a result, Eq. (6.5) shows that in this idealized case, the 2f/1f signal at a partic-

ular optical frequency is given by the product of the integrated area and a function,

G, that is dependent on the lineshape function and known laser parameters. As a

result, temperature and composition can be inferred from measured 2f/1f signals in

a manner that is analogous to that of FWDA.

6.3 Types of Nonuniformities

6.3.1 Pressure or Composition

If the gas temperature is uniform and the gas composition and/or pressure are nonuni-

form along the LOS, the integrated area can be calculated using Eq. (6.6).

A = Sn(T )

Z L

0

nidl = Sn(T )Ni (6.6)

6.3. TYPES OF NONUNIFORMITIES 79

In this case, the integrated area of a particular transition can be accurately repre-

sented as a function of temperature and absorbing-species column density only. The

spectral absorbance, however, is additionally influenced by the transition lineshape

function which cannot be removed from the path integral when variations in either

composition, pressure, or temperature cause the collisional and Doppler widths to

vary along the LOS. While Eq. (2.3) remains valid, the absorbance can no longer be

predicted with path-average conditions due to the now path-dependent lineshape. As

a result, in this case the absorbance at any given optical frequency depends on the

linestrength, column density, and the distribution functions describing how the gas

composition and/or pressure vary along the LOS. The e↵ect of a nonuniform com-

position is particularly important when the collisional-broadening coe�cients vary

strongly with collision partner (e.g., polar molecules such as H2O). However, it should

be noted, that if the broadening coe�cients of a given transition are equal for all act-

ing collision partners, a nonuniform composition does not a↵ect the lineshape.

To illustrate the e↵ect of nonuniform composition on absorbance, the absorbance

of a single water vapor transition located near 7203.9 cm�1 was simulated at 1500 K

and 1 atm with a nonuniform distribution of mole fraction shown in Fig. 6.1 (left).

The mole fraction distribution function was generated to be representative of the nat-

urally occurring composition gradients seen in flames and jets. The path-integrated

absorbance, calculated according to Eq. (2.3) represents a simulated SWDA mea-

surement and is significantly di↵erent than simulations performed with path-average

conditions along a uniform LOS. Due to the elevated collisional broadening in the

water-rich regions along the LOS, the peak absorbance of the path-integrated simu-

lation is 16% smaller than that of the simulation performed with path-average con-

ditions and a uniform LOS. While both simulations were performed with the same

temperature, pressure, and water column density, the water column density would

be underpredicted by approximately 16% if it was inferred from comparing the peak

absorbance of the path-integrated spectrum with that of simulations performed using

path-average conditions and a uniform LOS.


0 2.5 5 7.5 100

0.06

0.12

0.18

0.24

Measurement Path, cm

Wate

r M

ole

Fra

cti

on

Path−Average Value

7203.65 7203.8 7203.95 7204.10

0.02

0.04

0.06

Frequency, cm−1

Ab

so

rban

ce

Simulated Path−Integrated Absorbance

Simulated Absorbance w/ Path−Averaged Conditions

Overpredicts Peak−Absorbance by 16%

Uniform T = 1500 KUniform P = 1 atmNonuniform X

H2O

Figure 6.1: Water mole fraction distribution (left) for simulating path-integratedabsorbance spectrum of a single water vapor transition (right) using two strategies.The path-integrated absorbance spectrum represents a simulated direct-absorptionmeasurement. Here, the H2O column density cannot be accurately determined froma comparison of the peak of the path-integrated spectrum with that of simulationsperformed using path-average gas conditions and a uniform LOS.

6.3.2 Temperature

If the gas temperature varies along the LOS and the transition linestrength is non-

linearly dependent on temperature, the integrated area and absorbance cannot be

simplified beyond their path-integral forms shown in eqs. (2.3) and (2.6). In this

case, the absorbing-species-weighted path-average gas conditions cannot be predicted

from the integrated area without knowledge of how the gas conditions vary along the

LOS. Furthermore, the lineshape function is nonlinearly dependent on temperature

through its dependence on the collisional and Doppler widths. As a result, when the

gas temperature varies along the LOS, lineshape function complexities analogous to

those presented in the previous section influence path-integrated absorbance spectra.

6.4 Two-Color Absorption Spectroscopy Strategy

for Nonuniform Gases

Here we introduce a new absorption spectroscopy strategy that enables accurate TD-

LAS measurements of Ni and T ni in nonuniform environments. This strategy relies on

6.4. TWO-COLOR STRATEGY FOR NONUNIFORM GASES 81

two primary components: 1). line selection and 2). utilization of empirically-derived

e↵ective lineshapes ( ⌫). Table 6.1 describes under what circumstances each of these

design components are required.

6.4.1 Line-Selection Theory

The line selection criteria put forth by Zhou et al. [108] are useful for designing

sensors for uniform gases; however, additional considerations are needed when the

gas is nonuniform. Namely, when the gas temperature is nonuniform along the op-

tical path, it is imperative to use absorption transitions with strengths that are ei-

ther 1). independent of temperature or 2). that scale linearly with temperature

over the domain of the temperature nonuniformity. Fig. 6.2 shows that the transi-

tion linestrength is nearly independent of temperature at the linestrength peak and

that the linestrength scales near linearly with temperature in two regions located on

each side of the linestrength peak. In addition, Fig. 6.2 shows that a larger lower-

state energy shifts the linestrength curve to higher temperatures and broadens the

linestrength peak and regions of linear temperature dependence. This is significant

because it more generally states that the lower-state energy sets the temperature

dependence of the transition linestrength. Past work has been done to exploit the

region of temperature independence [98, 100], however, this strategy can su↵er from

large errors if the mean gas temperature is di↵erent than what the optimal transition

was selected for or if the temperature nonuniformity is large. This is because the

region of temperature independence is comparatively small and that the constant-

linestrength approximation breaks down rapidly away from the peak linestrength.

Table 6.1: Types of LOS nonuniformities and required sensor design components forlineshape-independent and -dependent measurement strategies.

12

absorbance spectra can now be accurately modeled as a function of the integrated area and empirically known lineshape function only. If lines with a linearly-temperature-dependent linestrength are used in conjunction with this technique, the absorbance spectra and WMS signals observed across a nonuniform LOS can be modeled as a function of the empirically determined lineshape function, Ni, and Tni only.

Fig. 5 Simulated absorbance spectrum for a single water vapor transition for a LOS with the nonuniform water mole fraction distribution shown in Fig. 1 (left). The best-fit Voigt profile accurately replicates the path-integrated absorbance spectrum shown.

Table 1 Types of LOS nonuniformities and required sensor design components for lineshape-independent and –dependent measurement strategies.

Case Need Linear-S(T)? Need ψv? Nonuniform P No Yes, if lineshape dependent Nonuniform χi with γi ≠ γj No Yes, if lineshape dependent Nonuniform χi withγi =γj for all j No No Nonuniform T Yes Yes, if lineshape dependent 5. Demonstration of Strategy This strategy is demonstrated with simulated TDLAS signals for a highly nonuniform LOS. More generally, this strategy can be applied to any LOS nonuniformity as long as the linestrength varies linearly with temperature and the lineshape function accurately models the shape of the path-integrated absorbance spectrum. In this demonstration, the temperature and water mole fraction distributions across the LOS were generated to be representative of those in hydrogen-air diffusion flames and are shown in Fig. 6. The optical path length is 10 cm, the geometric path-average temperature is 1185 K, the water number-density-weighted path-average temperature, TnH2O , is 1390 K, and the path-average water mole fraction is 0.08. Across the simulated LOS the temperature varies between 900 and 1500 K, and the water mole fraction varies from 0 to 0.20.

7203.65 7203.8 7203.95 7204.10

0.02

0.04

0.06

Frequency, cm−1

Abso

rban

ce

Simulated Path−Integrated AbsorbanceSimulated Absorbance with Path−Averaged ConditionsVoigt Fit of Path−Integrated Absorbance

Uniform T = 1500 KUniform P = 1 atmNonuniform XH2O


Voigt−Fit MatchesPath−Integrated

Absorbance Lineshape


300 1200 2100 30000

0.25

0.5

0.75

1

Temperature, K

Ma

x−

No

rma

lize

d L

ine

str

en

gth

E"=500 cm−1

E"=2600 cm−1

Region of TIndependence

Regions of LinearT Dependence

Figure 6.2: Linestrength curves shown for H2O with pre-normalized units of cm�2/molecule-cm�1. The transition lower-state energy sets the temperature dependenceof transition linestrength at a given temperature. The linestrength curve is charac-terized by two regions of near-linear temperature dependence and one region of neartemperature independence.

This is particularly problematic at low temperatures where transitions with a smaller

lower-state energy and narrower linestrength peak are optimal. As a result of these

shortcomings, we recommend using two transitions with strengths that scale linearly

with temperature.

In this strategy, two transitions with a linear temperature dependence and a large

di↵erence in lower-state energy are used to measure Ni and T ni . A large di↵erence

in lower-state energy is needed to ensure that the two-color ratio is sensitive to tem-

perature [108], and a linear temperature dependence is needed to guarantee that the

measured temperature is equal to T ni . For optimal results, this corresponds to us-

ing one transition that linearly decreases in strength as temperature increases with

another transition that linearly increases in strength as temperature increases. For

example, Fig. 6.2 shows that H2O transitions with lower-state energies of 500 and

2600 cm�1 are appropriate choices for temperatures near 850 K. In this case, the

linestrengths of the two transitions are approximated by

S1(T ) = m1T + b2 and S2(T ) = m2T + b2 (6.7)


where m and b are constants that enable the linestrength of each color to be accu-

rately described as a linear function of temperature. It is important to note that

if m = 0, Eq. (6.7) represents the constant-linestrength approximation. As a re-

sult, the constant-linestrength approximation can be used in conjunction with the

linear-linestrength approximation; however, this case is suboptimal as the region of

temperature independence is small. The two-color ratio of integrated areas for tran-

sitions with linear linestrengths, R02�,A, is given by Eq. (6.8)

R0

2�,A ⌘ A2

A1=

R L

0 (m2T + b2)nidlR L

0 (m1T + b1)nidl=

m2

R L

0 Tnidl + b2R L

0 nidl

m1

R L

0 Tnidl + b1R L

0 nidl(6.8)

The absorbing-species number-density-weighted path-average temperature, T ni ,

is defined by Eq. (6.9)

T ni ⌘R L

0 TnidlR L

0 nidl(6.9)

and can be used to simplify Eq. (6.8) to Eq. (6.10).

R0

2�,A =m2T ni + b2

m1T ni + b1(6.10)

Since Eq. (6.10) analytically describes the two-color ratio of integrated areas across a

nonuniform LOS, the LOS temperature of the gas could be calculated by comparing

Eq. (6.10) to the simulated two-color ratio of linear linestrengths, R02�,S, given by Eq.

(6.11).

R0

2�,S ⌘ S2(T )

S1(T )=

m2T + b2m1T + b1

(6.11)

By comparing Eq. (6.10) to Eq. (6.11) it is clear that R02�,A is equal to the simu-

lated R02�,S when the temperature in Eq. (6.11) is equal to T ni . This simple analysis

is significant because it proves that the experimentally measured ratio of integrated

areas of two transitions that have linear-temperature-dependent linestrengths can be

used to measure the absorbing-species number-density-weighted path-average tem-

perature across a nonuniform LOS. Again, this same result holds when one transition


is independent of temperature (i.e., m1 = 0 or m2=0). Perhaps most significantly, it

can be shown that the column density along the nonuniform LOS can now be found

by using Eq. (6.12).

Ni ⌘Z L

0

nidl =A

S(T ni)=

A

S(Tmeasured)(6.12)

Eq. (6.12) is also relevant to lineshape-dependent TDLAS strategies as it states that

the integrated area of either transition can be simulated as a function of Ni and T ni

only. In this case, the integrated area observed across a LOS with nonuniform temper-

ature can be used to infer Ni and T ni without knowledge of the distribution function

describing the LOS evolution of temperature as long as the transition linestrength

scales linearly with temperature over the LOS. In Section 6.6, this analysis is repeated

for the pressure-normalized linestrength convention.

6.4.2 Optimized Line Selection

For a given temperature range and absorbing species, the accuracy of the linear-

linestrength approximation (i.e., linearity of the linestrength profile given by Eq.

(2.2) ) is primarily set by the lower-state energy of the transition. As a result,

transitions with appropriate values of lower-state energy must be used to ensure

a linear temperature dependence over a given range of temperature. It is worth

noting that the linecenter frequency also influences the linearity of the linestrength

profile, however, this is a small e↵ect. To optimize the line selection process, a

linear polynomial was fit to a temperature-specified region of the peak-normalized

linestrength profile for numerous values of lower-state energy. The corresponding

sum of squared error (SSE) normalized by the square of the mean linestrength was

used to rank the linearity of each linestrength profile within the specified temperature

domain. A more intuitive error metric, the maximum percent error associated with

each linear fit, is used hereafter to quantify linearity without significant compromise.

Fig. 6.3 shows that for the temperature range of 1000-1500 K, the maximum percent

error in the linear fit reaches a local minimum at two values of lower-state energy

labeled E”L and E”

H . These two values of lower-state energy represent the optimal


250 1500 2750 4000 52500

2

4

6

8

Lower State Energy (E"), cm−1

Ma

x E

rro

r in

Lin

ea

r F

it,

% o

f M

ea

n S

(10

00

−1

50

0 K

)

EC

"

E" for Most−Linear LinestrengthOver Simulated Temperature

Range

E" for Most−ConstantLinestrength Over Simluated

Temperature Range

Calculated Error for T = 1000−1500 K

EH

"

EL

"

Figure 6.3: The maximum error in the linear fit (i.e., linear-linestregth approximation)reaches a local minimum at two values of lower-state energy: E”

L and E”H . The error in

the linear-linestrength approximation is approximately 7 times smaller at E”L and E”

H

than at E”C (the location corresponding to the most-constant linestrength). Results

shown are for water vapor.

values for the temperature range shown because they correspond to the most-linear-

linestrength curves with a large di↵erence in lower-state energy. Fig. 6.3 also shows

that the linear-linestrength approximation is nearly seven times more accurate than

the constant-linestrength approximation with its most optimal lower-state energy

labeled E”C . The percent error shown in Fig. 6.3 is defined relative to the mean value

of linestrength over the temperature range (i.e., over the domain of the linear-fit).

If the temperature range of interest is shifted to larger values, the entire curve

in Fig. 6.3 shifts to smaller values of error (i.e. downward) and to higher values of

lower-state energy (i.e. to the right). The influence of the mean temperature on the

optimal lower-state energies (E”L and E”

H) for a temperature range of 500 K (i.e. ±250 K) is shown in Fig. 4. E”

L and E”H increase as the mean temperature increases,

and the maximum error in the linear fit decreases near exponentially as the mean

temperature increases.

The accuracy of the linear-linestrength approximation is discussed in greater detail

in Section 6.7. There, the linear-linestrength approximation is evaluated for various


temperature nonuniformities and compared with the constant-linestrength approxi-

mation. The influence of uncertainty in mean temperature for which the transitions

were chosen is also examined.

6.4.3 E↵ective Lineshape Function

The analysis presented in the previous section is all that is required for accurate

lineshape-independent measurements of Ni and T ni in nonuniform environments.

However, additional considerations are required when using lineshape-dependent strate-

gies (e.g. WMS) in nonuniform environments. When the gas conditions vary along

the LOS, the lineshape varies due to the varying collisional and Doppler widths. As

a result, without precise knowledge of how the gas conditions are distributed across

the optical path, it is not possible to accurately predict an analytical function that

e↵ectively describes the shape of the observed path-integrated absorbance spectrum.

While this e↵ective lineshape function cannot be predicted analytically in an un-

known environment, it can be inferred empirically and used to accurately model the

absorbance. Here we will define this e↵ective lineshape function and show that it

can be used to enable accurate lineshape-dependent measurements of Ni and T ni in

nonuniform environments. The e↵ective lineshape function, ⌫ , is defined such that

5000

2

4

6

Max E

rro

r in

Lin

ear−

Fit

, %

Mean

S(T

)

500 1000 1500 20000

500

1000

1500

2000

Mean Temperature, K

EL", cm

−1

Error

Size of Temperature Range = 500 K (+/− 250 K)

EL

"

5000

2

4

6

Max E

rro

r in

Lin

ear−

Fit

, %

of

Mean

S(T

)

500 1000 1500 20000

1600

3200

4800

6400

8000

Mean Temperature, K

EH", cm

−1

Error

Size of Temperature Range = 500 K (+/− 250 K)

EH

"

Figure 6.4: The maximum error in the linear-linestrength approximation decreasesnear exponentially as the mean temperature increases for H2O transitions with alower-state energy equal to E”

L (left) and E”H (right). The values of E”

L and E”H

increase with the mean temperature.


its integral over all ⌫ is unity and Eq. (6.13) holds.

↵(⌫) = A ⌫ (6.13)

It is important to note that Eq. (6.13) is always valid for a single transition and if

the gas is uniform along the LOS the e↵ective lineshape function ⌫ is equivalent to

the lineshape function �⌫ . Similarly, when Eq. (6.4) is valid, a WMS-2f/1f analog

to Eq. (6.13) is given by Eq. (6.14):

2f/1f ⇡ A

io⇡

Z ⇡

�⇡

⌫(⌫o + a cos ✓) cos(2✓)d✓ (6.14)

The e↵ective lineshape function can be determined by best-fitting simulated spec-

tra to measured scanned-wavelength spectra with the integrated area and lineshape

parameters as free variables or by using scanned-WMS techniques such as those pre-

sented in [21, 73]. It should be noted that this can also be done in partially blended

spectra as long as the spectral-fitting technique can resolve the contribution from

each transition. This is demonstrated in Section 6.5. When fitting simulated spectra

to scanned-wavelength direct-absorption spectra, the lineshape parameters dictate

the shape of the absorption lineshape and the integrated area scales the lineshape

function to match the observed spectrum. Since the integral of the e↵ective lineshape

function over all ⌫ is unity, the best-fit integrated area is equivalent to the numeri-

cally integrated area of the path-integrated spectrum; however, the best-fit lineshape

parameters are numerical artifacts of the fitting routine and no longer have a physical

interpretation. This technique is demonstrated in Fig. 6.5 for the path-integrated

absorbance spectrum shown in Fig. 6.1. In Fig. 6.5, the best-fit Voigt profile re-

covers the path-integrated absorbance and the integrated area to within 0.2%. Here,

the best-fit e↵ective lineshape is described by a Voigt profile with a collisional and

Doppler FWHM of 0.0555 and 0.0480 cm�1, respectively. The significance of this

methodology is that by determining the e↵ective lineshape function and its lineshape

parameters, the absorbance spectra can now be accurately modeled as a function of

the integrated area and empirically known lineshape function only. If lines with a


7203.65 7203.8 7203.95 7204.10

0.02

0.04

0.06

Frequency, cm−1

Ab

so

rba

nc

e

Simulated Path−Integrated Absorbance

Simulated Absorbance with Path−Averaged Conditions

Voigt Fit of Path−Integrated Absorbance

Uniform T = 1500 KUniform P = 1 atmNonuniform X

H2O


Voigt−Fit MatchesPath−Integrated

Absorbance Lineshape

Figure 6.5: Simulated absorbance spectrum for a single water vapor transition for aLOS with the nonuniform water mole fraction distribution shown in Fig. 6.1 (left).The best-fit Voigt profile accurately replicates the path-integrated absorbance spec-trum shown.

linearly-temperature-dependent linestrength are used in conjunction with this tech-

nique, the absorbance spectra and WMS signals observed across a nonuniform LOS

can be modeled as a function of the empirically determined lineshape function, Ni,

and T ni only.

6.5 Demonstration of Strategy

This strategy is demonstrated with simulated TDLAS signals for a highly nonuniform

LOS. More generally, this strategy can be applied to any LOS nonuniformity as

long as the linestrength varies linearly with temperature and the lineshape function

accurately models the shape of the path-integrated absorbance spectrum. In this

demonstration, the temperature and water mole fraction distributions across the LOS

were generated to be representative of those in hydrogen-air di↵usion flames and are

shown in Fig. 6.6. The optical path length is 10 cm, the geometric path-average

temperature is 1185 K, the water number-density-weighted path-average temperature,

T nH2O, is 1390 K, and the path-average water mole fraction is 0.08. Across the

6.5. DEMONSTRATION OF STRATEGY 89

00

400

800

1200

1600

Te

mp

era

ture

, K

0 2 4 6 8 100

0.06

0.12

0.18

0.24

Line−of−Sight Path, cm

H2O

Mo

le F

ract

ion

P = 1 atm, XH2O,PA

= 0.08, TPA

= 1185 K, TnH2O,PA

= 1390 K

Figure 6.6: Temperature and water mole fraction distributions across simulated LOS.The path-average water mole fraction is 0.08, the path-average temperature is 1185K, and T nH2O

is 1390 K.

simulated LOS the temperature varies between 900 and 1500 K, and the water mole

fraction varies from 0 to 0.20.

According to the new methodology presented in the previous section, transitions

with lower-state energies near 815 and 4025 cm�1 should be used for measuring NH2O

and T nH2Oalong the LOS shown in Fig. 6.6. These values of lower-state energy corre-

spond to the optimal values of E”L and E”

H for the temperature range shown in Fig. 6.6.

The HITEMP 2010 database [74] lists well-isolated transitions with comparable val-

ues of lower-state energy near 3565.7 and 4083.9 cm�1. For these transitions, Fig. 6.7

compares the simulated path-integrated absorbance spectra and corresponding best-

fit Voigt lineshapes with simulations performed using water number-density-weighted

path-average conditions and a uniform LOS. The simulated spectra shown in Fig. 6.7

include all neighboring transitions listed in HITEMP 2010 [74]. To account for the

influence of neighboring transitions, e↵ective lineshapes were inferred by least-squares

fitting a Voigt profile to each nearby transition as done in [65]. The best-fit Voigt

lineshapes model the path-integrated spectra to within 0.5 and 1.3% while spectra

simulated with water number-density-weighted path-average conditions overpredict

the peak absorbance by 17 and 18%, respectively. The temperature and column


density inferred from the integrated areas obtained from the best-fit Voigt lineshapes

recover NH2O and T nH2Oto within 0.5 and 0.1%. Similarly, when the Voigt-fit-derived

e↵ective lineshapes are used to model the absorbance spectrum, the column density

and temperature inferred from the ratio of peak-absorbances are also accurate to

within 0.5 and 0.1%. These small di↵erences result from the imperfect accuracy of

the linear-linestrength approximation and the best-fit Voigt lineshapes for these path-

integrated spectra. In contrast, when the e↵ective lineshapes are not used to model

the absorbance spectra, the ratio of peak-absorbances leads to errors of 1 and 16%

in temperature and column density. For these transitions, the error in temperature

is small without using the e↵ective lineshape because the air- and H2O-broadening

coe�cients for each transition are similar. The reader should note that this is

not guaranteed since the air-broadening coe�cients of H2O transitions span nearly

two orders of magnitude. As a result, lineshape-dependent thermometry techniques

can su↵er errors greater than 10% without using the e↵ective lineshape function.

The corresponding WMS-2f/1f spectra for these two transitions with a modula-

tion index, m, of 2.2 are shown in Fig. 6.8. Here the modulation index is defined as

the ratio of the modulation depth, a, and the transition half-width at half-maximum.

Similar to the raw absorbance spectra shown in Fig. 6.7, the WMS-2f/1f spectra

simulated with water number-density-weighted path-average conditions overpredicts

the path-integrated WMS-2f/1f spectra by approximately 20%. However, Fig. 6.8

shows that the WMS-2f/1f spectra simulated with water number-density-weighted

path-average conditions and e↵ective lineshapes agree with the path-integrated WMS-

2f/1f spectra to within 0.2 and 0.4% of the peak-2f/1f signal. For the WMS-2f/1f

spectra, the e↵ective lineshapes were inferred for the two dominant lines according to

the WMS-2f/1f spectral-fitting routine described in [21]. The two-color temperature

and H2O column density calculated from comparing the path-integrated 2f/1f signal

at linecenter with simulations performed using path-average conditions and e↵ective

lineshapes agree within 0.3% of T nH2Oand 0.4% of NH2O. It is important to note

that while eqs. (6.4), (6.5) and (6.14) were derived for an optically thin line-of-sight,

the results presented here prove that e↵ective lineshapes can be used to accurately

model WMS signals far outside the optically thin limit.

6.5. DEMONSTRATION OF STRATEGY 91

0

0.2

0.4

0.6

0.8

1

Ab

sorb

an

ce

3565.4 3565.6 3565.8 3566 3566.2−20

0

20

Optical Frequency [cm−1]

Re

sid

ua

l [%

]

Simulated Path−Integrated Abs.Simulated Abs. w/Path−AveConditionsSimulated Abs. w/Path−AveConditions and Effec. Lineshape

E" = 842 cm−1

0

0.05

0.1

0.15

Ab

sorb

an

ce

4083.6 4083.8 4084 4084.2−20

0

20


Re

sid

ua

l [%

]

E" = 4331 cm−1

Figure 6.7: Simulated absorbance spectra for two water vapor transitions chosen ac-cording to the new measurement strategy for nonuniform environments. Simulationswere performed with a uniform pressure of 1 atm and with the temperature and wa-ter mole fraction distributions shown in Fig. 6.6. The residual shown is betweenvarious simulation techniques and the path-integrated spectra. Simulations with wa-ter number-density-weighted path-average conditions overpredict peak absorbance bynearly 20%. Absorbance spectra simulated with path-average conditions and e↵ec-tive lineshapes (derived from Voigt profile fitting) matches path-integrated spectra towithin 0.5% (top) and 1.3% (bottom).


0

0.5

1

1.5

2

2.5W

MS

−2

f/1

f

Simulated Path−Integrated WMS

Simulated WMS w/Path−AveConditions

Simulated WMS w/Path−AveConditions and Effec. Lineshape

3565.5 3565.6 3565.7 3565.8 3565.9−20

0

20


Re

sid

ua

l [%

]E" = 842 cm−1

0

0.1

0.2

0.3

0.4

0.5

WM

S−

2f/

1f

4083.8 4083.85 4083.9 4083.95 4084−50

0

50


Re

sid

ua

l [%

]

E" = 4331 cm−1

Figure 6.8: Simulated WMS-2f/1f spectra for two water vapor transitions chosenaccording to the new measurement strategy for nonuniform environments. Simula-tions were performed with a uniform pressure of 1 atm and with the temperatureand water mole fraction distributions shown in Fig. 6.6. The residual shown is be-tween various simulation techniques and the path-integrated spectra. Simulationswith path-average conditions overpredict WMS-2f/1f signals by 20%. SimulatedWMS-2f/1f spectra with path-average conditions and e↵ective lineshape (derivedfrom scanned-WMS spectral fitting) matches path-integrated spectra to within 0.2%(top) and 0.4% (bottom).

6.6. EXTENSION TO PRESSURE-NORMALIZED LINESTRENGTH CONVENTION93

6.6 Extension to Pressure-Normalized Linestrength

Convention

In cases where the pressure and composition are uniform along the LOS, it is often

more convenient to define the transition linestrength on a per-unit pressure basis.

Fig. 6.9 shows that the linestrength of a given transition exhibits a temperature

dependence that depends on the linestrength convention. This is significant because

it implies that the lower-state energy necessary to achieve a particular temperature

dependence over a given range of temperature depends on the units of linestrength

and thus, the form of the relations describing absorbance and integrated absorbance.

If the pressure-normalized linestrength form is used and the linestrengths scale

linearly with temperature, the two-color ratio of integrated areas can be used to

measured the absorbing-species partial-pressure-weighted path-average temperature,

T Pi , defined by Eq. (6.15).

300 1200 2100 30000

0.25

0.5

0.75

1

Temperature, K

Ma

x−

No

rma

lize

d L

ine

str

en

gth

Pre−Normalized Units = cm−2/atm

Pre−Normalized Units = cm−1/molecule−cm−2

Max−Normalized S(T) for an H2O Transition with E" = 2000 cm−1

Figure 6.9: The linestrength normalization convention alters the temperature de-pendence of a given transition’s linestrength. The number density-normalizedlinestrength convention leads to a broader linestrength profile that peaks at a highertemperature.


T Pi ⌘R L

0 TPidlR L

0 Pidl(6.15)

If the gas pressure is uniform and ideal gas relations apply, Eq. (6.15) reduces

to the absorbing-species mole-fraction-weighted path-average temperature, T �i , given

by Eq. (6.16).

T �i ⌘R L

0 T�idlR L

0 �idl(6.16)

If the gas composition and pressure are uniform, Eq. (6.16) reduces to the geo-

metric path-average temperature, T , given by Eq. (6.17).

T ⌘R L

0 TdlR L

0 dl(6.17)

In all cases, it is clear that the physical meaning of a measured LOS temperature

depends on the lower-state energy of the chosen transitions, the linestrength conven-

tion, and the type of LOS nonuniformity. For the pressure-normalized linestrength

convention with linestrengths that scale linearly with temperature, the integrated

area and measured temperature can then be used to calculate column pressure, �i

[atm-cm], according to Eq. (6.18).

�i ⌘Z L

0

Pidl =A

S(T Pi)=

A

S(Tmeasured)(6.18)

6.7 Accuracy of the Linear-Linestrength Approx-

imation

When the temperature varies along the LOS, the accuracy of Eq. (6.12) depends

on the accuracy of the linear-linestrength approximation and on how the absorbing

species is distributed along the LOS. This is because the total integrated area e↵ec-

tively represents the sum of di↵erential integrated areas that originate within each

6.7. ACCURACY OF THE LINEAR-LINESTRENGTH APPROXIMATION 95

volumetric element along the LOS. The total integrated area is, therefore, biased to-

wards regions where the product of linestrength and absorbing species number density

is largest. As a result, Eq. (6.12) is accurate if the majority of the integrated area orig-

inates within locations along the LOS where the linear-linestrength approximation is

accurate. On the other hand, if the majority of the integrated area originates within

locations along the LOS where the linear-linestrength approximation is not accurate,

Eq. (6.12) is also not accurate. However, in the limit of perfectly linear linestrengths

Eq. (6.12) is always valid, and thus, only the accuracy of the linear-linestrength

approximation will be considered here. More specifically, the linear-linestrength ap-

proximation is evaluated here for various sized temperature nonuniformities and for

a ± 100 K uncertainty in the mean gas temperature for which the transitions were

chosen.

6.7.1 Influence of Size of Temperature Nonuniformity

As the size of the temperature range along the LOS is increased, the maximum error

in the linear fit increases. This is because the linestrength is actually a nonlinear

function of temperature. Fig. 6.10 shows lines of constant maximum percent error

for the most optimal transitions as a function of the mean temperature and the

size of the temperature range. The maximum error in the linear fit decreases as

the mean temperature increases and as the size of the temperature range decreases.

These figures show that the linear-linestrength approximation is accurate to within

2.5% of the corresponding mean linestrength for both transitions for nearly 70% of the

operating space shown. Most significantly, Fig. 6.10 shows that the linear-linestrength

approximation is accurate to within 5% of the corresponding mean linestrength over

large ranges of temperatures (500-700 K) for mean temperatures of 1000-2000 K.

6.7.2 Influence of Uncertainty in Mean Gas Temperature

In many practical applications, the precise mean temperature of the gas in a nonuni-

form environment is not known a priori. As a result, it is important to understand

and quantify how the error in the linear-linestrength approximation is a↵ected by


0.15625

0.15625

0.3125

0.3125

0.3125

0.625

0.625

0.625

1.25

1.25

2.5

2.5

510

Size of Temperature Range, K

Mean

Tem

pera

ture

, K

Contour Lines of Maximum Value of % Error in Linear−Fit of S(T) for Transitions with E" = E

L

"

200 300 400 500 600 700 800500

1000

1500

2000

0.15625

0.15625

0.3125

0.3125

0.625

0.625

1.25

1.25

1.25

2.5

2.5

2.5

5

5

10

10

Size of Temperature Range, K

Mean

Tem

pera

ture

, K

Contour Lines of Maximum Value of % Error in Linear−Fit of S(T) for Transitions with E" = EH

"

200 300 400 500 600 700 800500

1000

1500

2000

Figure 6.10: Contour lines of constant maximum percent error in the linear-linestrength approximation for H2O transitions with lower-state energy of E”

L (top)and E”

L (bottom) as a function of the mean temperature and size of the temper-ature range. The maximum percent error in the linear-linestrength approximationdecreases as the mean temperature increases and as the size of the temperature rangedecreases. The linear-linestrength approximation is accurate to within 2.5% of themean linestrength over the majority of temperature space shown.

6.7. ACCURACY OF THE LINEAR-LINESTRENGTH APPROXIMATION 97

0

5

10

15Size of Temperature Range = 500 K (+/− 250 K)

0

5

10

15

Ra

ng

e o

f %

Err

or

in L

ine

stre

ng

th A

pp

roxi

ma

tion

fo

r +

/−1

00

K U

nce

rta

inty

in M

ea

n T

em

pe

ratu

re

500 1000 1500 20000

20

40

60

Mean Temperature, K

Linear−Linestrength Approximation with E" = E"L(Mean T)

Linear−Linestrength Approximation with E" = E"H

(Mean T)

Constant−Linestrength Approximation with E" = E"C

(Mean T )

Figure 6.11: Range of percent error in linestrength approximations as a function ofmean temperature for a temperature range of 500 K and a ± 100 K uncertainty in themean temperature. Despite ± 100 K uncertainty in mean temperature, the linear-linestrength approximation using H2O transitions with E” = E”

L(Tmean) or E”H(Tmean)

remains accurate to within 2.5% of the corresponding mean linestrength for meantemperatures greater than 1000 K. For a temperature range of 500 K and a ± 100K uncertainty in the mean temperature, the linear-linestrength approximation withE” = E”

H(Tmean) is 3.5 to 6.25 times less sensitive to uncertainty in mean temperaturethan the constant-linestrength approximation with E” = E”

C(Tmean)

uncertainty in the mean temperature for which the transitions were selected. This

was done by evaluating the accuracy of the linear-linestrength approximation outside

the temperature domain for which it was optimized. For a given mean tempera-

ture, the linestrengths of transitions with lower-state energies equal to E”L(Tmean)

and E”H(Tmean) (as shown in Fig. 6.4) were calculated over ranges of temperature

that were centered 100 K above and below the mean temperature they were chosen

for. This simulates an uncertainty in mean temperature of ± 100 K. The maximum

error in the linear-linestrength approximation was then calculated for each value of

E”L(Tmean) and E”

H(Tmean) and for various mean temperatures. The same process was

also done to evaluate the constant-linestrength assumption. These results are shown

in Fig. 6.11 for a temperature range of 500 K.

For a given mean temperature, the bars in Fig. 6.11 represent the range of error

in a linestrength approximation that results from a ± 100 K uncertainty in the mean


temperature. Fig. 6.11 shows that the linear-linestrength approximation is accurate

for moderate uncertainties in mean temperature, especially at mean temperatures

above 1000 K. For a mean temperature of 1000 K, the maximum error in the linear-

linestrength approximation with an uncertainty in mean temperature of ± 100 K

is 1.2 and 2.5% of the mean linestrength for transitions with lower-state energies

of E”L(1000 K) and E”

H(1000 K), respectively. In comparison, the corresponding

maximum error in the constant-linestrength approximation is 11.8%. The accuracy

of the linear-linestrength approximation for transitions with lower-state energies equal

to E”L(Tmean) and E”

H(Tmean) is far less sensitive to uncertainty in mean temperature

than the constant-linestrength approximation. This is expected since the constant-

linestrength approximation breaks down rapidly on both sides of the linestrength

peak. Fig. 6.11 also shows that the accuracy of both linestrength approximations

become less sensitive to uncertainty in the mean temperature as the mean temperature

increases. This is also expected since the nonlinear behavior of the linestrength curve

is dampened as the optimal lower-state energy increases.

Chapter 7

NIR T and H2O Sensor for

High-Pressure and -Temperature

Environments

7.1 Introduction

Global demands for reduced consumption of fossil fuels have led to the development

of novel, high-pressure and -temperature energy systems (e.g., coal gasifiers, detona-

tion combustors, and homogenous-charge compression-ignition engines). As a result,

a variety of diagnostics are needed to study the complex physical processes (e.g.,

chemical kinetics, phase-change, turbulence, etc.) that govern these systems. Laser

absorption sensors have been used extensively to study a variety of practical energy

systems [1, 109] including scramjets [6], detonation combustors [10, 12], internal com-

bustion engines [4, 2, 5], coal gasifiers [17], and for 2D temperature measurements in

low-pressure combustion gases [110, 16]. However, while some work has been done

at high-pressures and -bandwidth [10, 12, 4, 2], a number of measurement challenges

including limited optical access, window fouling, particulate scattering, beamsteering,

and broad and blended absorbance spectra have limited the bandwidth and operating

domain of many of these sensors. As a result, more robust, high-bandwidth sensors

capable of providing temperature and concentration measurements over a broad range

99

100 CHAPTER 7. NIR T AND H2O SENSOR FOR HIGH-P AND -T

of temperatures and pressures are needed.

Here, the development, validation, and demonstration of a two-color TDLAS sen-

sor for gas temperature and H2O concentration in high-pressure and -temperature

environments are presented. This sensor simultaneously probes water vapor absorp-

tion transitions near 1391.7 and 1469.3 nm to enable use of telecommunications-grade

TDLs and fiber optics for a robust and portable sensor package. This sensor uses

WMS-2f/1f to account for emission and non-absorbing transmission losses encoun-

tered in harsh environments. The intensity and wavelength of the two lasers were

modulated at 160 and 200 kHz, respectively, to enable a maximum sensor bandwidth

of 30 kHz. This sensor was validated under low-absorbance (<0.05) conditions at

known conditions in shock-heated H2O-N2 mixtures at temperatures and pressures

from 700 to 2400 K and 2 to 25 atm. There, the sensor recovered the known tem-

perature and H2O mole fraction within 2.8 and 4.7% RMS (nominally) of known

conditions. In addition, this sensor is demonstrated with measurements acquired in

a reactive shock tube experiment.

To our knowledge, this work represents the first near-infrared WMS-2f/1f based

temperature and H2O sensor that has been (1) validated with measurements at well-

known temperatures and pressures greater than 1200 K and 10 atm and (2) that can

achieve a sensor bandwidth greater than 7.5 kHz (up to 30 kHz here). As a result,

this sensor provides several key improvements that enable study of a greater range of

practical applications.

7.2 Sensor Design and Architecture

7.2.1 Wavelength Selection

Selecting appropriate wavelengths is critical to the success of all laser absorption

sensors and line selection rules have been developed for low pressure applications with

uniform [108] and nonuniform gas conditions [111, 28]. This process largely consists of

selecting strong, well-isolated transitions with appropriate lower-state energies. While

many of these line selection rules are still relevant at high pressures, this strategy

7.2. SENSOR DESIGN AND ARCHITECTURE 101

is complicated by the influence of collisional broadening which leads to broad and

blended spectra. As a result, in this case it is more appropriate to select wavelengths

with an absorbance and/or WMS-2f/1f spectrum that change desirably with gas

properties. This fact has been addressed in other line selection strategies [112, 113].

For the work presented here, two wavelengths near 1391.7 nm (7185.59 cm�1) and

1469.3 nm (6806.03 cm�1) were used due to their strength, temperature- and pressure-

dependence, and relative isolation from strong neighboring transitions. However, since

the conclusion of this work, more rigorous selection rules for the laser wavelength and

modulation depth have been developed for high-pressure applications (see Ch. 8 or

[30] ) and are recommended. The pertinent spectroscopic parameters for the dominant

transitions are listed in Table 7.1, and Fig. 7.1 shows simulated H2O absorbance

spectra for the wavelengths used here.

7185.1 7185.3 7185.5 7185.7 7185.9 7186.10

0.01

0.02

0.03

0.04


Ab

sorb

an

ce

1 atm15 atm

6805.5 6805.75 6806 6806.25 6806.50

0.005

0.01

0.015

0.02


Ab

sorb

an

ce

1 atm15 atm

Figure 7.1: Simulated H2O absorbance spectra for transitions near 7185.59 cm�1 (left)and 6806.03 cm�1 (right) at 1 and 15 atm with a temperature, H2O mole fractionand path length of 1500 K, 3%, and 5 cm, respectively.

7.2.2 Experimental Setup

Fig. 7.2 shows the experimental setup used in shock tube experiments. A detailed

description of the Stanford High Pressure Shock Tube (HPST) is given by Petersen

and Hanson [82]. Briefly, the HPST has an inner diameter of 5 cm and is capable

of reaching reflected-shock pressures greater than 1000 atm. Initially, a diaphragm


divides the tube into two sections. The driven section is filled with the test gas

and the driver section is filled with helium until the diaphragm bursts. Once the

diaphragm bursts, a shock wave propagates into the test gas, thereby setting it into

motion and raising its temperature and pressure near instantaneously. Once the

shock wave reaches the tube endwall, it reflects and stagnates the oncoming test

gas, further raising its temperature and pressure. The temperature and pressure

behind the incident and reflected shocks are known within 1% from shock jump

relations [114] combined with measured shock speeds. The test gas conditions were

calculated assuming vibrational equilibrium, due to the large levels (1-5%) of H2O

in the test gas, and frozen chemistry. During each test, the pressure behind the

reflected shock was measured with a 120 kHz pressure transducer. Prior to each test,

the H2O concentration of the test gas was measured in situ via scanned-wavelength

direct-absorption experiments to account for adsorption losses to the tube walls. In

addition, the HPST was heated to 105 �C to prevent condensation on the tube walls

at high pressures.

Two TDLs (NEL America) near 1391.7 and 1469.3 nm were combined onto two

polarization-maintaining (PM) single-mode fibers (SMF). The laser near 1391.7 nm

was modulated at 160 kHz with a modulation depth of 0.32 cm�1 and the laser near

1469.3 nm was modulated at 200 kHz with a modulation depth of 0.20 cm�1. A

commercially available diode laser controller (ILX LDC-3900) was used to control the

nominal current and temperature of each laser. One SMF was directed to a measure-

ment port located approximately 93 cm from the HPST endwall for measurements

behind the incident shock wave. The other SMF was directed to a measurement port

located approximately 1 cm from the HPST endwall for measurements behind the

reflected shock wave. The output light was collimated (Thorlabs F240-APC) and

pitched across the shock tube. At each measurement location, the transmitted light

was collected by a 2 cm focal length lens with a 12.5 cm diameter and an InGaAs

detector (ScienceTech) with a 9 mm2 active area and a 3 MHz bandwidth. All de-

tector signals were sampled at 10 MHz (National Instruments PXI-6115) and lock-in

filters with a cut-o↵ frequency 15 or 30 kHz were used to extract the WMS-1f and

-2f signals during post-processing.

7.3. DEVELOPMENT OF SPECTROSCOPIC DATABASE 103

Reflected Shock

Spectral Filter

InGaAs Detector

Catch Lens

Shock Tube 1392 nm

f = 160 kHz PM

Multiplexer

End Wall

1469 nm f = 200 kHz

Figure 7.2: Schematic of experimental setup used for temperature and H2O measure-ments at two locations in the shock tube.

7.3 Development of Spectroscopic Database

7.3.1 Linestrength, H2O-broadening, and N2-pressure-shift

measurements at low pressures

Scanned-wavelength direct-absorption measurements were acquired in a heated static-

cell to measure the linestrength, H2O-broadening, and N2-pressure-shift parameters of

the two dominant transitions used by this sensor. These parameters are listed in Table

7.1 and were used to simulate the absorbance spectra incorporated in the WMS model.

An experimental setup similar to that shown in Fig. 7.2 was used and details regarding

the furnace and static cell are given in [68]. Measurements were acquired in pure

H2O and H2O-N2 mixtures at pressures and temperatures from 2 to 760 torr and 600

to 1325 K. Spectroscopic parameters were inferred from least-squares fitting a Voigt

profile to measured absorbance spectra as described in [27]. Each doublet was treated

as a single transition due to the small di↵erences in lower-state energy and linecenter

frequency (< 0.005 cm�1) as done in [27]. A reference temperature of 296 K was used

solely to enable comparisons with the HITEMP 2010 database. It is important to note

that broadening measurements were not acquired below 600 K, and therefore, caution

should be used when extrapolating these data to temperatures di↵erent than studied


Table 7.1: Spectroscopic parameters derived from direct-absorption experiments con-ducted at 600 to 1325 K.

vo [cm-1]

E” [cm-1]

S(296 K) [cm-2/atm]

γH2O(296 K) [cm-1/atm]

nH2O δN2(296 K) [cm-1/atm]

mN2

C. S. HT’10 C. S. HT’10 7185.59* 1045.1 1.96x10-2(1) 1.98x10-2(3) 0.198(2) 0.371/0.195(4) 0.53(2) -0.0162(2) 1.20(2) 6806.03* 3291.2 6.40x10-7(1) 6.54x10-2(3) 0.205(2) 0.195/0.12(4) 0.86(2) -0.0257(2) 1.51(2) Uncertainty Codes: (1)< 3%, (2)5-10%, (3)10-20%,(4)>20%, *Indicates a doublet transition. vo and E” taken from HITEMP 2010 [32]. C.S. indicates “Current Study” HT’10 indicates “HITEMP 2010”

Table 2. N2-broadening coefficients inferred from WMS-2f/1f signals at 2 to 25 atm and 700 to 2400 K.

vo [cm-1]

γN2(296 K) [cm-1/atm]

nN2

7185.59* 0.045(2) 0.51(2) 6806.03* 0.0105(4) -0.108(4)

Uncertainty Codes: (1)< 3%, (2)5-10%, (3)10-20%,(4)>20%, *Denotes a doublet transition

here. As expected, collisional narrowing was not observed in pure H2O; however,

pronounced collisional narrowing was observed in H2O-N2 mixtures as indicated by

the gull-wing residuals shown in Fig. 7.3. Failure to address this phenomena in the

development of collisional-broadening databases can lead to large errors in lineshape

modeling, particularly when extrapolating broadening coe�cients to high pressures

[27]. As a result, this complication was avoided by inferring N2-broadening coe�cients

from WMS-2f/1f signals acquired at high pressures (>10 atm) where collisional-

broadening dominates collisional-narrowing.

0

0.2

0.4

0.6

0.8

Ab

sorb

an

ce

Data

Voigt Fit

−0.7 −0.5 −0.3 −0.1−5

0

5

Relative Optical Frequency [cm−1]

Re

sid

ua

l [%

]

νo ~ 7185.59 cm−1

E" ~ 1045 cm−1

0

0.05

0.1

Ab

sorb

an

ce

DataVoigt Fit

−0.5 −0.4 −0.3 −0.2 −0.1−5

0

5

Relative Optical Frequency [cm−1]

Re

sid

ua

l [%

]

νo ~ 6806.03 cm−1

E" ~ 3291 cm−1

Figure 7.3: Measured absorbance spectra and best-fit Voigt profiles for transitionsnear 7185.59 cm�1 (left) and 6806.03 cm�1 (right) at 1000 K, 1 atm, and 3% H2Oin N2. Gull-wing residual indicates the presence of collisional narrowing.

7.3. DEVELOPMENT OF SPECTROSCOPIC DATABASE 105

7.3.2 N2-broadening measurements at high pressures

N2-broadening parameters were inferred from WMS-2f/1f measurements acquired

at high-pressures and -temperatures for several reasons. (1) By measuring collisional

broadening at high pressures the lineshape is dominated by collisional broadening. As

a result, measured signals are more sensitive to the collisional width and less sensitive

to collisional-narrowing e↵ects which act upon the Doppler width. Fig. 7.4 shows

the WMS-2f/1f signal’s sensitivity at linecenter to collisional width as a function of

the modulation index, m = a/HWHM , for a single absorption transition described

by a Voigt profile with a Lorentzian to Doppler width ratio, L/D, of 10. Sensitivity

is defined as a unit change in signal per unit change in the collisional width. For

a modulation index of one, the WMS-2f/1f signal at linecenter is nearly twice as

sensitive to the transition collisional width than to the integrated absorbance (i.e.,

absorbing species mole fraction). As a result, by operating in a regime with large L/D

and small m (m near 1 for experiments presented in this work), the WMS-2f/1f

signal at linecenter is a robust and sensitive indicator of the transition collisional

width. (2) By measuring broadening coe�cients at higher temperatures (i.e., 1000-

2400 K), the broadening model is less susceptible to extrapolation errors resulting

from the temperature dependence of n. (3) By using WMS-2f/1f , measured signals

are immune to non-absorbing transmission losses (e.g., resulting from beamsteering)

that can compromise the accuracy of direct-absorption techniques, particularly in

cases of low absorbance and broad spectra. For example, a 0.25% error in the incident

laser intensity leads to a 20% error in the collisional width inferred from fitting a Voigt

profile to an absorbance profile with a peak absorbance of 2.5%, a FWHM of 0.64

cm�1, and a L/D of 13. While smaller uncertainties in the incident light intensity

can be achieved to reduce such errors, this requires exceptional optical engineering

which can be extremely di�cult to achieve.

N2-broadening parameters were inferred from measured WMS-2f/1f signals as

follows. For a given shock tube experiment, the WMS-2f/1f signal at known wave-

length, temperature, pressure, and composition was used to solve for the collisional

width of the transition using the WMS model given by Rieker et al. [25]. The N2-

broadening coe�cient was then calculated from the inferred collisional width using


0 1 2 3

1

2

3

Modulation Index (m=a/HWHM)

WM

S−

2f/1f S

ensi

tivity

to ∆

νC

WMS−2f/1fSensitivity to

IntegratedAbsorbance(i.e., X

H2O)

Figure 7.4: Sensitivity of the WMS-2f/1f signal at linecenter to collisional width asa function of modulation index (i.e., a) for a H2O transition with a L/D = 10 and aVoigt FWHM of 0.48 cm�1.

Eq. (2.16) with the H2O-broadening coe�cient given by the parameters listed in Ta-

ble 7.1. Results for the complete dataset are shown in Fig. 7.5, however, a truncated

and randomized set of experiments was used to infer the best-fit N2-broadening pa-

rameters given in Table 7.2. Several important trends regarding these data are worth

noting. (1) For both transitions, the N2-broadening coe�cients appear to be inde-

pendent of pressure. This suggests that measurements were acquired in a collisional

regime where the Voigt profile is accurate and that weaker nearby transitions are ap-

propriately accounted for in the WMS simulations. (2) The N2-broadening coe�cient

for the transition near 6806.03 cm�1 increases with temperature. This is predicted

by theory [32] and has been observed by others for some high-rotational quantum

number H2O transitions in air and N2 [34, 27, 94]. In addition, the N2-broadening

power-law parameters listed in Table 7.2 are similar to those given in Ch. 5 and [27]

for H2O transitions with similar rotational quantum numbers.

7.4. SENSOR VALIDATION 107

500 1000 1500 2000 25000

0.01

0.02

0.03

0.04

Temperature [K]

γ N2 [

cm−

1/a

tm]

For νo ~ 7185.59 cm−1

500 1000 1500 2000 25000

0.01

0.02

0.03

0.04

Temperature [K]

γ N2 [

cm−

1/a

tm]

Power−Law Fit2−5 atm5−10 atm10−15 atm15−20 atm20−25 atm

For νo ~ 6806.03 cm−1

Figure 7.5: N2-broadening coe�cients inferred from WMS-2f/1f signals at knownconditions for the transitions near 7185.59 cm�1 (left ) and 6806.03 cm�1 (right). Asexpected, the N2-broadening coe�cients appear to be independent of pressure.

Table 7.2: N2-broadening coe�cients inferred from WMS-2f/1f signals at 2 to 25atm and 700 to 2400 K.

vo [cm-1]

E” [cm-1]

S(296 K) [cm-2/atm]

γH2O(296 K) [cm-1/atm]

nH2O δN2(296 K) [cm-1/atm]

mN2

C. S. HT’10 C. S. HT’10 7185.59* 1045.1 1.96x10-2(1) 1.98x10-2(3) 0.198(2) 0.371/0.195(4) 0.53(2) -0.0162(2) 1.20(2) 6806.03* 3291.2 6.40x10-7(1) 6.54x10-2(3) 0.205(2) 0.195/0.12(4) 0.86(2) -0.0257(2) 1.51(2) Uncertainty Codes: (1)< 3%, (2)5-10%, (3)10-20%,(4)>20%, *Indicates a doublet transition. vo and E” taken from HITEMP 2010 [32]. C.S. indicates “Current Study” HT’10 indicates “HITEMP 2010”

Table 2. N2-broadening coefficients inferred from WMS-2f/1f signals at 2 to 25 atm and 700 to 2400 K.

vo [cm-1]

γN2(296 K) [cm-1/atm]

nN2

7185.59* 0.045(2) 0.51(2) 6806.03* 0.0105(4) -0.108(4)

Uncertainty Codes: (1)< 3%, (2)5-10%, (3)10-20%,(4)>20%, *Denotes a doublet transition

7.4 Sensor Validation

After obtaining an accurate spectroscopic database, WMS-2f/1f signals were then

used to convert measured signals to time-resolved gas properties in shock tube ex-

periments. Fig. 7.6 shows measured temperature, pressure, and H2O time-histories

acquired behind the incident shock (left) and reflected shock (right) for a single test

with a sensor bandwidth of 30 kHz. The temperature and H2O mole fraction decrease

behind the incident shock after 0.6 ms due to the arrival of the helium driver gas. For

both lines-of-sight, the measured temperature and H2O mole fraction are accurate

to within 2.5% of known values throughout the steady-state test time. These results

demonstrate the time-response and large operating range of this sensor.

Fig. 7.7 shows a summary of the temperature and H2O sensors performance at

temperatures and pressures from 700 to 2400 K and 2 to 25 atm with a bandwidth of


15 kHz. The error bars indicate the measurement precision denoted by one standard

deviation of the measurement over the steady-state test time. The sensor recovered

the known steady-state temperature with a nominal accuracy and precision of 2.8%

and 2.4% of known values, respectively. The sensor recovered the known H2O mole

fraction with a nominal accuracy and precision of 4.7 and 3.5%, respectively. This

sensor’s ability to measure temperature and H2O accurately over such a broad range

of temperatures and pressures supports the methodology used to infer N2-broadening

coe�cients.

0

400

800

1200

1600

Te

mp

era

ture

[K

]

0

4

8

12

16

Pre

ssu

re [

atm

]

0 0.6 1.2 1.80

0.03

0.06

0.09

XH

2O

Time [ms]

Arrival of He Driver Gas

Measurements Behind Incident Shock

0

400

800

1200

1600

Te

mp

era

ture

[K

]

0

4

8

12

16

Pre

ssu

re [

atm

]

0 0.6 1.2 1.80

0.03

0.06

0.09

Time [ms]

XH

2O

Measurements Behind Reflected Shock

Figure 7.6: Temperature, pressure, and H2O time histories acquired behind incidentshock (left) and reflected shock (right) for a single experiment. Dashed lines indicateknown values. For both measurement locations, the WMS-2f/1f sensor recoveredthe known temperature and H2O mole fraction within 2.5% with a bandwidth of 30kHz. The temperature and H2O decrease behind the incident shock near 0.6 ms dueto the arrival of the helium driver gas.

7.5. SENSOR DEMONSTRATION 109

500 1000 1500 2000 2500500

1000

1500

2000

2500

Known Temperature [K]

Me

asu

red

Te

mp

era

ture

[K

]

Ideal

2−5 atm

5−10 atm

10−15 atm

15−20 atm

20−25 atm

500 1000 1500 2000 25000.7

0.8

0.9

1

1.1

1.2

1.3

Known Temperature [K]

Xm

easu

red/X

know

n

Figure 7.7: Accuracy and precision of temperature (left) and H2O (right) sensor forshock tube experiments at temperatures and pressures from 700 to 2400 K and 2 to25 atm with a sensor bandwidth of 15 kHz. The nominal accuracy of the temperatureand H2O sensor is 2.8 and 4.7%, respectively, for the conditions shown.

7.5 Sensor Demonstration

The high bandwidth and large operating range of this sensor enables study of a wide

range of dynamic systems. Here, this sensor is demonstrated in a reactive shock tube

experiment. This sensor was also used to study a pulse-detonation combustor which

is discussed in Ch. 10.

Fig. 7.8 shows measured temperature, pressure, and H2O mole fraction time-

histories acquired in a shock-heated, stoichiometric H2O-H2-O2-Ar mixture within the

HPST. Measurements were acquired 1.1 cm from the HPST endwall along a single

line-of-sight. An independent dataset was used to infer Ar-broadening coe�cients

using the same methodology as described in Section 7.3.2. The sensor recovered

the initial H2O mole fraction and the known temperature behind both the incident

(TIS) and reflected shocks (TRS) within 1.5% of known values. In addition, the

sensor resolved the ignition event that begins at approximately 0.4 ms. The H2O

mole fraction measured post-combustion agrees within 2% of that predicted assuming

thermochemical equilibrium. In addition, the measured temperature post-combustion

falls between those predicted by Chemkin simulations performed assuming constant-

pressure (TCP ) and constant-volume (TCV ) combustion. Chemkin simulations were

performed using the H2-O2 mechanism given by Hong et al. [115]. The success of this


demonstration confirms the great potential of this sensor for studying high-pressure

combustion systems.

0

400

800

1200

1600

Tem

pera

ture

[K

]

0

5

10

15

20

Pre

ssure

[atm

]

0 0.5 1 1.5 20

0.03

0.06

0.09

Time [ms]

XH

2O

TCP P

CV

Post−Combustion

Pre−Combustion

TRS

TIS

Ignition

TCV

Figure 7.8: Measured temperature, pressure, and H2O mole fraction time-historiesfor a shock-heated, stoichiometric H2O-H2-O2-Ar mixture. Temperature and H2Oresults are shown with a 30 kHz bandwidth. Dashed lines indicate expected values.

Chapter 8

MIR T and H2O Sensor for

High-Pressure and -Temperature

Environments

8.1 Introduction

Here, the design and validation of a mid-infrared, two-color wavelength-modulation

spectroscopy sensor for measurements of temperature and H2O at temperatures and

pressures up to 3000 K and 50 bar are presented. This sensor uses two TDLs near

2474 and 2482 nm that were fiber-coupled in free-space and frequency multiplexed

to enable measurements along a single line-of-sight. Furthermore, this sensor op-

erates in the fundamental vibration bands of H2O near 2.5 µm to achieve 5 to 10

times larger signals than comparable near-infrared sensors. WMS-2f/1f was used

for three primary reasons: (1) the WMS-2f/1f signal is immune to emission and

non-absorbing transmission losses that vary at frequencies much less than the mod-

ulation frequency and/or outside the passband (9 kHz here) centered at the 1st and

2nd harmonics of each laser’s modulation frequency, (2) WMS-2f/1f is a di↵erential

absorbance technique that does not require knowledge of the absolute absorbance,

and (3) WMS-2f/1f is insensitive to non-Lorentzian e↵ects that can compromise

111

112 CHAPTER 8. MIR T AND H2O SENSOR FOR HIGH-P AND -T

other absorption methods at high pressures [116]. An experimentally-derived and -

validated spectroscopic database (presented in Ch. 5) and a new method for selecting

optimal wavelengths and modulation depths were used to enable accurate measure-

ments over a large range of temperatures and pressures. The performance of this

sensor was validated behind reflected shock waves at temperatures and pressures up

to 2700 K and 50 bar. On average, the sensor recovered the known steady-state

temperature and H2O mole fraction within the measurement precision (3.2 and 2.6%

RMS, respectively).

To the best of our knowledge, the novelty of this work is fourfold. This work rep-

resents (1) the first mid-infrared TDL temperature and H2O sensor for high-pressure

(> 10 bar) gases and (2) the first calibration-free WMS-based temperature and H2O

sensor that has been validated at pressures up to 50 bar. In addition, this work

introduces (3) a new strategy for selecting the wavelength and modulation depth of

each laser.

8.2 High-Pressure and -Temperature Measurement

Challenges and Solutions

8.2.1 Challenges

Broad and Blended Spectra

As pressure increases, the corresponding increase in collisional broadening leads to

broad, overlapping transitions. This e↵ect is shown in Fig. 8.1 (top) with simulated

H2O spectra at 6 kPa, 25 bar, and 50 bar. At 6 kPa, the absorbance spectrum is de-

fined by many discrete transitions; however, at 25 bar the spectrum is continuous and

characterized by comparatively broad structure. At 50 bar, there is little evidence

of the underlying transitions and the spectrum appears to consist of two broadband

absorption features superimposed upon an absorbing baseline. Broad and blended

spectra complicate quantitative absorption measurements for three primary reasons:

8.2. HIGH-P AND -T MEASUREMENT CHALLENGES AND SOLUTIONS 113

(1) the absorbing baseline complicates the determination of the incident laser inten-

sity, (2) overlapping transitions complicate the relationship between the absorbance

spectrum and gas conditions, and (3) the broad spectrum leads to smaller WMS-2f

signals.

0

0.5

1

Abso

rbance

6 kPa

25 bar

50 bar

4025 4030 4035 4040 40450

0.05

0.1

0.15

0.2


WM

S−

2f/1f

25 bar

50 bara = 0.35 cm−1

T = 2000 K, XH2O

= 0.10, L = 5 cm

Figure 8.1: Simulated high-pressure absorbance (top) and WMS-2f/1f spectra (bot-tom) near 2474 and 2482 nm. Higher pressure leads to increased collisional broadeningand overlapping transitions. The WMS-2f/1f signal is largest in regions with largeabsorbance curvature.

Breakdown of the Impact Approximation

The Lorentzian, and therefore, Voigt and Galatry lineshape models all rely on the

accuracy of the impact approximation. This approximation assumes that collisions

are instantaneous and, therefore, neglects energy level perturbations resulting from

intermolecular forces. At number densities above approximately 5 amagat (i.e., 5

atm at 273 K), this approximation begins to break down for H2O [52]. As this

approximation breaks down, absorption is distributed di↵erently in the wings of the

transitions, and the primary net result is an o↵set in the absorbance spectrum [116],

compared to that modeled by Lorentzian-based profiles.


Beamsteering, Birefringence, and Emission

At high-pressures and -temperatures, beam-steering, birefringence, and emission all

pose formidable challenges, particularly in unsteady systems. All three of these ef-

fects alter the intensity of the collected light, and can therefore, significantly compro-

mise the accuracy and precision of conventional direct-absorption techniques. Beam-

steering results from density gradients in the gas and this e↵ect strengthens with in-

creasing pressure. Stress-induced birefringence alters the polarization and trajectory

of light passing through the windows. This e↵ect also strengthens with pressure and

can be extremely problematic when polarization sensitive optics are used. Emission

from gaseous molecules increases with temperature and pressure, the latter result is

from the corresponding increase in number density. Emission at high temperatures is

particularly problematic in the mid-infrared due to the strong fundamental vibration

bands of various molecules (e.g., H2O, CO2, CO, NO).

8.2.2 Solutions

The sensor used here overcomes all of these challenges via three design components:

(1) WMS-2f/1f , (2) stronger MIR absorption, and (3) optical engineering. By using

WMS-2f/1f the sensor presented here is immune to emission and non-absorbing

losses (e.g., from beam-steering and window fouling) that vary at frequencies that

are much less than f and/or outside the passband (9 kHz here) around the 1f and

2f of each laser. WMS-2f/1f does not require knowledge of the absolute absorbance

magnitude. This method is a di↵erential absorption technique that detects relative

changes in absorbance that occur across the modulation period. This is illustrated

in Fig. 8.1 where the WMS-2f/1f signal is large in regions of curvature (e.g., 4030

and 4040 cm�1) and near zero in regions with a flat absorbance spectrum (e.g., 4035

cm�1). Similarly, WMS techniques are less sensitive to non-Lorentzian e↵ects [116].

As a result, WMS-2f/1f is well suited for high-pressure environments where the

absolute absorbance magnitude cannot be easily determined.

The sensor used here exploits stronger MIR absorption bands to overcome the

increased noise encountered in high-pressure environments. By using lasers near 2.5

8.3. WAVELENGTH AND MODULATION DEPTH SELECTION 115

µm, this sensor achieves 5 to 10 times larger signals compared to near-infrared H2O

sensors [29, 73, 117].

All absorption sensors require sound optical engineering to minimize the noise and

interference encountered in harsh environments. For the work presented here, beam-

steering and emission were the primary challenges faced. To reduce beam-steering, a

linear-catch system [118] was used with a large-area (3.14 mm2) detector. To reduce

emission, a neutral-density filter (80% attenuation) and two narrow band-pass filters

(2470 +/- 50 nm) were used. The WMS-2f/1f signals were also found to be immune

to the remaining emission signals (5-10% of detector’s dynamic range).

8.3 Wavelength and Modulation Depth Selection

When the absorption spectrum is heavily blended, it changes with gas properties ac-

cording to how the ensemble of transitions sum together. As a result, the absorbance

and WMS-2f/1f signal at a given wavelength exhibit a complex dependence upon

gas properties. Most significantly, the gas pressure alters the magnitude and shape

of the spectrum due to collisional broadening (Fig. 8.1), the temperature alters the

magnitude and shape of the spectrum due to its influence upon line broadening and

the strength of each transition (Fig. 8.2), and the center wavelength and modulation

depth specify which portion of the spectrum is interrogated by each laser (Fig. 8.3).

Due to these complexities, conventional line selection rules [108] are not appropriate

for designing high-pressure WMS sensors. Here, a brute-force optimization routine

was developed to select the center wavelength and modulation depth of each laser.

This routine was designed to minimize uncertainty in the measurement targets (tem-

perature and H2O mole fraction) over a broad range of temperatures and pressures.

8.3.1 Optimization Routine

This section describes how the wavelength and modulation depth of each laser were

chosen to enable sensitive measurements of temperature and H2O over a broad range

of temperatures and pressures. For shock tube experiments, this sensor was optimized


3750 3850 3950 4050 41500

0.5

1

1.5

2


Abso

rbance

2 kPa, 2000 K

25 bar, 1500 K

25 bar, 2500 K

Wavelengths of Interest

0

0.5

1

Abso

rbance

1500 K

2000 K

2500 K

4025 4030 4035 4040 40450

0.05

0.1

0.15

0.2


WM

S−

2f/1f a = 0.35 cm−1

P = 25 bar, XH2O

= 10%, L = 5 cm

Figure 8.2: Simulated H2O absorbance spectra at various temperatures for H2O vi-bration band (top) and wavelengths studied (bottom). Optical frequencies greaterthan 4025 cm�1 are less crowded and are dominated by high-rotational-energy transi-tions. Changing temperature alters the shape and magnitude of the absorbance andWMS-2f/1f spectra (bottom).


4025 4030 4035 4040 40450

0.05

0.1

0.15

0.2


WM

S−

2f/1f

25 bar, 2000 K, 10% H2O, L = 5 cm

a=0.25 cm−1

a=0.50 cm−1

Figure 8.3: E↵ect of modulation depth, a, on high-pressure WMS-2f/1f spectra.Changing the modulation depth alters the WMS-2f/1f spectrum according to thelocal curvature of the absorbance spectrum.

for temperatures and pressures from 1000 to 2500 K and 10 to 50 bar with 3% H2O by

mole and a 5 cm path length. The optimization routine was restricted to wavelengths

between 4025 and 4100 cm�1 for two primary reasons: (1) the H2O spectrum in

this region is considerably less dense than at smaller optical frequencies (i.e., 3750-

4025 cm�1) (see Fig. 8.2) and (2) the transitions in this region are primarily high-J

transitions with smaller collisional-broadening coe�cients. As a result, by probing

wavelengths in this regime, a smaller spectroscopic database is required and larger 2f

signals can be obtained due to the narrower absorbance features. This optimization

routine consists of the following steps:

1. Prescribe a modulation depth for laser A and laser B and simulate the WMS-

2f/1f spectrum over the temperature and pressure range of interest (for each

laser).

2. Impose a minimum WMS-2f signal requirement for each laser to ensure high


SNR over the operating domain. This removes wavelengths with large WMS-

2f/1f signal due to a small WMS-1f signal.

3. For all wavelength pairs, calculate the two-color ratio of WMS-2f/1f signals,

R, for the entire temperature and pressure domain. For a given two-color pair,

R is defined according to Eq. (8.1),

R =(2f/1f)�B

(2f/1f)�A

(8.1)

where �A denotes the wavelength of laser A and �B denotes the wavelength of

laser B.

4. For all wavelength pairs, calculate the corresponding uncertainty in tempera-

ture, �T , using Eq. (8.2) [119, 120] for the entire temperature and pressure

domain.

�T (T, P ) ⇡=�2f/1f

dR(T, P )/dT

p1 +R(T, P )2

(2f/1f)�A(T, P )(8.2)

�2f/1f is the expected uncertainty (i.e., noise level) in the WMS-2f/1f signal

for both wavelengths.

5. For all wavelength pairs, calculate the thermometry performance metric, M ,

given by Eq. (8.3).

M =q[�T (T, P )]2 + �[�T (T, P )]2 (8.3)

[�T (T, P )] and �[�T (T, P )] represent the mean and standard deviation, respec-

tively, in temperature uncertainty over the temperature and pressure domain of

interest. M represents a temperature sensor’s deviation from perfection marked

by (i.e., [�T (T, P )] = �[�T (T, P )] = 0). This is illustrated in Fig. 8.4. M


accounts for [�T (T, P )] and �[�T (T, P )] to achieve a relatively smooth perfor-

mance map in temperature- and pressure-space (i.e., to avoid wavelength pairs

with a large range of temperature uncertainty despite a small average tempera-

ture uncertainty). It should be noted that the definition of M is dependent on

the specific goals of the user and, as a result, Eq. (8.3) is application and user

specific. Furthermore, if there is large uncertainty in the pressure of the gas, the

user should confirm that the chosen wavelength pairs yield pressure-insensitive

thermometry performance.

6. Rank wavelength pairs by values of M . The most optimal wavelength pair for

a given pair of modulation depths is that with the smallest value of M .

7. Repeat steps 1-6 using di↵erent modulation depths for each laser. The e↵ect of

di↵erent modulation depths uponM is shown in Fig. 8.4. Once all combinations

have been evaluated, the optimal combination of wavelengths and modulation

depths is that which yields the smallest value of M .

As a starting point, this routine was initially performed using simulations per-

formed with the HITEMP 2010 database. This iteration suggested that optical fre-

quencies near 4030 cm�1 should be paired with optical frequencies near 4042 or 4044

cm�1, with only minor di↵erences between the pairs. As a result, optical frequen-

cies near 4030 cm�1 were paired with optical frequencies near 4042 cm�1 due to the

reduced number of strong transitions nearby. After developing the hybrid database

discussed in Chapter 5 and characterizing the modulation performance of each laser,

the optimization routine was repeated for the measurement environment of interest.

8.3.2 Projected Sensor Performance

The performance of this sensor is simulated for a high-pressure hydrocarbon-fueled

combustor with a H2O mole fraction of 0.10 and temperatures and pressures from

1000 to 2500 K and 10 to 50 bar, respectively. The tuning limitations of each laser

limited the range of potential optical frequencies from 4028 to 4030 and 4038 to


4042 cm�1. Seven modulation depths from 0.04 to 0.28 cm�1 and 0.07 to 0.50 cm�1

were considered for the lasers near 4030 and 4042 cm�1, respectively. An uncertainty

in the 2f/1f signal of 0.001 was used to provide realistic uncertainty estimates for

harsh environments. This uncertainty is approximately 10 times larger than the

noise floor quoted for quiescent environments in [120]. According to the optimization

routine, the lasers should be centered at 4029.76 and 4041.96 cm�1 and modulated

with the maximum possible modulation depth (0.28 and 0.5 cm�1 for the modulation

frequencies used here). Fig. 8.5 shows simulated absorbance spectra at 2000 K and

25 bar with the recommended center wavelength and modulation bounds of each laser

indicated.

Fig. 8.6 shows the corresponding contour lines of 2f/1f signal for the recom-

mended laser setpoints as a function of temperature and pressure. For a 2f/1f noise

level of 0.001, a SNR of 20 to 200 is expected over the operating domain. Fig. 8.7

shows contour lines of temperature sensitivity (left) and temperature uncertainty

0 10 20 30 40 500

10

20

30

40

50

σ(∆T(T,P)), K

me

an

(∆T(T

,P))

, K

Modulation Depth Pair 1

Modulation Depth Pair 2

M = distance a point lies from origin

M for Optimal Wavelengthand Modulation Depth

Each point represents a different wavelength pair

Figure 8.4: Thermometry performance of several wavelength pairs near 4030 and4042 cm�1 grouped by their mean and standard deviation in temperature uncertainty(calculated over the temperature and pressure domain of interest). Groups are shownfor two pairs of modulation depths. The optimal pair of wavelengths and modulationdepths is that which is closest to the origin (i.e., smallest M).


4026 4028 4030 40320

0.25

0.5

0.75


Ab

sorb

an

ce

4038 4040 4042 4044

25 bar, 2000 K, 10% H2O, L = 5 cm

Bounds ofModulation

Bounds ofModulation

Center v

Center v

Figure 8.5: Simulated H2O absorbance spectra for transitions near 4030 and 4042cm�1. The center wavelengths and modulation bounds recommended by the opti-mization routine for WMS-2f/1f sensing are shown.

(right). Here, temperature sensitivity is defined as the unit change in the two-color

ratio of WMS-2f/1f signals per unit change in temperature. The temperature sensi-

tivity is lowest at low temperatures and pressures and highest at high temperatures

and pressures. This relationship compensates for the lower signals at high tempera-

tures and pressures, and indicates that this sensor exploits the interaction between

multiple lines to achieve large temperature sensitivity. The expected temperature

uncertainty ranges from 5 to 50 K (i.e., 0.5 to 2%) and the results presented in Sect.

8.4.3 support the accuracy of these projections. Thus, this sensor is expected to yield

excellent mole fraction and temperature sensing performance in high-pressure and

-temperature combustion environments.


0.025

0.05

0.1

0.1

0.15

0.2

Contour Lines of 2f/1f for 4029.76 cm−1 with a = 0.28 cm−1

Pressure, bar

Tem

pera

ture

, K

10 20 30 40 501000

1500

2000

2500

0.04

0.06

0.08

0.08

0.1

0.1

0.12

0.12

0.14

0.14

0.16

Contour Lines of 2f/1f for 4041.96 cm−1 with a = 0.50 cm−1

Pressure, bar

Tem

pera

ture

, K

10 20 30 40 501000

1500

2000

2500

Figure 8.6: Contour lines of 2f/1f signal as a function of temperature and pressurefor 4029.76 cm�1 (top) and 4041.96 cm�1 (bottom). Simulations were performedwith a path length and H2O mole fraction of 5 cm and 0.10, respectively. Modulationdepths are indicated above each figure. For a noise level of 0.001, an SNR of 20-200is expected.


0.5 0.51 1

1.5

1.5

2

2

2.5

3

3.5

4

Contour Lines of Temperature Sensitivity

Pressure, bar

Tem

pera

ture

, K

10 20 30 40 501000

1500

2000

2500

Contour Lines of Expected Temperature Uncertainty (K) for ∆2f/1f

= 0.001

Pressure, bar

Tem

pera

ture

, K

10 20 30 40 501000

1500

2000

2500

15

20

30

4050

5

10

Figure 8.7: Contour lines of temperature sensitivity (top) and predicted temperatureuncertainty (bottom) for 4029.76 and 4041.96 cm�1 pair with an uncertainty in 2f/1fof 0.001. Simulations were performed with a path length and H2O mole fraction of5 cm and 0.10, respectively. Over the temperature and pressure domain shown, theestimated uncertainty in temperature ranges from approximately 0.5 to 2%.


8.4 Experimental Method and Sensor Validation

8.4.1 Optical Setup

Fig. 8.8 shows a schematic of the experimental setup used for shock tube experiments.

Measurements of temperature and H2O were acquired at two locations within the

Stanford HPST using two di↵erent TDL sensors. Two fiber-coupled TDLs (NEL

America) near 1392 and 1469 nm were used to measure the temperature and H2O

behind the incident shock. In addition, prior to the shock arrival, the TDL near 1392

nm was used to measure the H2O mole fraction in the low-pressure (< 1 bar) test-gas

via scanned-wavelength direct absorption. These lasers were multiplexed onto a single

polarization maintaining fiber and the light was collimated (Thorlabs F240APC-C)

and pitched across the shock tube approximately 92 cm from the end wall. The

transmitted light was focused onto a 3 mm diameter InGaAs detector (ScienceTech)

with a 3 MHz bandwidth. More information regarding this sensor can be found in

Ch. 7 or [29].

Two narrow-linewidth (less than 3 MHz [84]) TDLs (Nanoplus GmbH) near 2.5

µm were used to measure temperature and H2O behind the reflected shock. The

nominal temperature and current of each laser were controlled (ILX-LDC 3900) and

the signals used to modulate the injection current of each laser were generated by a

conventional desktop computer running LabView software. The output of each laser

was collimated (Thorlabs C036TME-D) and the two beams were combined using

a 50/50 beamsplitter (Thorlabs BSW23). A 6 mm focal length lens (Innovation

Photonics) was used to focus the combined beam into a 400 µm ZBLAN multimode-

fiber (Fiber-Labs). The fiber output was collimated with a 20 mm focal length zinc-

selenide lens to a near-Gaussian FWHM of approximately 3 mm. The collimated

light was pitched across the shock tube and collected with a 12.5 mm diameter, 20

mm focal length calcium fluoride lens (Thorlabs LA5315-D). Two band-pass filters

(Spectrogon NB-2470-050 nm) and a neutral density filter (80% attenuation) were

used to reduce collected emission levels. The transmitted light was detected with a

MCT detector (Vigo Systems PVI-2TE-4) with a 2 mm diameter active area and 10

MHz bandwidth. The raw detector signal was anti-aliased to 1 MHz with a low-pass

8.4. EXPERIMENTAL METHOD AND SENSOR VALIDATION 125

Beam Splitter Collimating Lens

5-axis Fiber-Mount

400 µm MMF

Diode Lasers near 2.5 µm

Spectral Filters

MCT Detector

Catch Lens

Pitch Lens

Reflected Shock

Spectral Filter

InGaAs Detector

Catch Lens

Shock Tube

Diode Lasers near 1.4 µm

PM SMF

End Wall

Figure 8.8: Experimental setup used in shock tube experiments.

filter (Kronhite) prior to acquisition at 10 MHz (National Instruments PXI-6115).

8.4.2 Experimental Method

For all tests, the shock tube was heated to 105 �C to prevent condensation behind

the reflected shock. 30 minutes prior to testing, H2O-N2 mixtures were prepared in a

magnetically-stirred, heated mixing tank. All gas lines between the mixing tank and

shock tube were also heated to prevent condensation while filling the shock tube. The

shock tube was evacuated to 4 Pa and all WMS and direct-absorption background

signals were acquired. The tube was filled to the desired pressure, and the test gas was

allowed to thermodynamically equilibrate with the shock tube walls (⇡15 minutes).

The H2O in the test-gas was then measured via scanned-wavelength direct absorption.

All lasers were then set to the temperature and current required to achieve a given

center wavelength during modulation. These laser set points were derived as done in

[64]. Multiple center wavelengths were used for each laser to confirm the accuracy

of the spectroscopic model. More specifically, tests were conducted with each laser


at: 4029.42 and 4041.91 cm�1, 4029.46 and 4041.91 cm�1, 4029.57 and 4042.04 cm�1,

and 4029.65 and 4041.99 cm�1. For all tests, the lasers near 4030 and 4042 cm�1

were modulated at 35 and 45.5 kHz with a modulation depth of 0.28 and 0.50 cm�1,

respectively. During post-processing, the WMS signals were frequency demultiplexed

with 9 kHz low-pass filters to achieve a sensor bandwidth of 9 kHz.

8.4.3 Shock Tube Results

Fig. 8.9 shows measured time-histories of temperature, H2O mole fraction, and pres-

sure for a representative test. The gas pressure was measured independently with a

high-speed transducer. The known steady-state temperature, pressure, and H2O mole

fraction of the test gas are 1870 K, 25.9 bar, and 4%, respectively. The measured

temperature and H2O mole fraction rise to within 1.5% of the known values within

approximately 80 µs and remain relatively steady throughout the 0.5 ms steady-state

test-time. The temperature and pressure begin to rise at approximately 0.55 ms due

to slight attenuation of the incident shock speed. Despite this rise in temperature and

pressure, the H2O mole fraction remains constant as expected. This demonstrates the

sensors ability to resolve transient gas conditions with high accuracy.

To validate this sensor’s accuracy over a broad range of temperatures and pressures

relevant to combustion environments, experiments were performed at temperatures

and pressures from 1000 to 2700 K and 8 to 50 bar. Fig. 8.10 summarizes the accuracy

of the temperature (left) and H2O (right) sensing performed in the HPST. Error bars

represent one standard deviation of the measurement over the steady-state test-time

(i.e., the measurement precision). On average, the sensor recovered the known steady-

state temperature and H2O mole fraction within 3.2 and 2.6% RMS of known values,

respectively (i.e., within measurement precision). For 75% of the experiments, the

sensor recovered the temperature and H2O to within less than 2% of known values.

These results suggest that the accuracy of this sensor is independent of temperature,

pressure, and the center wavelength of each laser (of those studied) and indicate that

the spectroscopic model used here is highly accurate.

8.4. EXPERIMENTAL METHOD AND SENSOR VALIDATION 127

500

1000

1500

2000

2500

Tem

pera

ture

, K

0

5

10

15

20

25

30

Pre

ssure

, bar

0 0.2 0.4 0.6 0.80

0.02

0.04

0.06

Time, ms

XH

2O

Arrival of Incident Shock

Arrival of Reflected Shock

Arrival ofCompression

Waves

Figure 8.9: Measured temperature and H2O mole fraction time-histories acquired be-hind reflected shock wave. The sensor recovered the known steady-state temperatureand H2O to within 1.5% of known values.


1000 1500 2000 2500 30001000

1500

2000

2500

3000

Known Temperature, K

Measu

red T

em

pera

ture

, K

Ideal

5−15 bar

15−20 bar

20−30 bar

30−40 bar

40−50 bar

1000 1500 2000 2500 30000.8

0.9

1

1.1

1.2

Known Temperature, K

Xm

easu

red/X

know

n

Ideal

5−15 bar

15−20 bar

20−30 bar

30−40 bar

40−50 bar

5% Error Boundary

Figure 8.10: Accuracy of temperature (top) and H2O mole fraction (bottom) sensingin shock tube experiments. On average, the sensor recovered the known steady-statetemperature and H2Omole fraction within 3.2 and 2.6% RMS of known values, respec-tively. Error bars represent measurement precision given by the standard deviationof the measurement over the steady-state test-time.

Chapter 9

Temperature and H2O Sensing in a

Model Scramjet Combustor

9.1 Introduction

Here, temperature and H2O measurements acquired in the University of Virginia’s

dual-mode scramjet combustor are presented. This work was conducted as part of

the NCHCCP’s (National Center for Hypersonic Combined Cycle Propulsion) e↵ort

to characterize and model several scramjet combustor configurations. Although the

basic principles of a scramjet engine are simple, a number of complex phenomena

(e.g., shock-boundary-layer interactions, turbulence, and chemical kinetics) continue

to hinder scramjet development. Hydrocarbon-fueled systems pose even greater chal-

lenges due to their complex and comparatively slow chemistry. As a result, tunable

diode laser (TDL) sensors continue to play a vital role in providing critical infor-

mation regarding the combustion and flow physics governing these devices. While

considerable sensing of H2O has been conducted in scramjets [6, 7, 69, 121, 8], all

of that work was conducted using the weaker near-infrared (NIR) overtone and com-

bination bands (2⌫1 and ⌫1+⌫3). By using the H2O fundamental vibration band,

the sensor reported here realizes three primary benefits: (1) access to lines that are

up to 20 times stronger than overtone and combination band lines, (2) access to

strong lines with larger lower-state energy for increased temperature sensitivity and

129

130 CHAPTER 9. T AND H2O SENSING IN A SCRAMJET COMBUSTOR

improved measurement fidelity in high-temperature nonuniform flows [28], and (3)

reduced Doppler broadening due to the longer wavelengths used which leads to larger

peak-absorbance and -WMS signals. These three benefits improve the accuracy, pre-

cision, and sensitivity of TDLAS sensors, and therefore, enable study of a greater

range of applications. We present the design and demonstration of a two-color TD-

LAS sensor for highly-sensitive measurements of temperature and H2O near 2.5 µm.

The sensor was designed and validated at Stanford University and then deployed

at the University of Virginia’s Supersonic Combustion Facility (UVaSCF). Measure-

ments were acquired along more than 35 lines-of-sight (LOS) within the combustor

to characterize the combustion process. This sensor used two frequency-multiplexed

fiber-coupled TDLs near 2551 and 2482 nm to probe three H2O transitions with

lower-state energies of 704, 2660, and 4889 cm�1. Two design measures enabled high-

fidelity measurements in the nonuniform reaction zone: (1) the scanned-WMS-2f/1f

spectral-fitting strategy (discussed in Ch. 4) was used to infer the integrated ab-

sorbance of each transition without prior knowledge of the transition linewidths and

(2) transitions with strengths that scale near-linearly with temperature were used to

accurately determine the H2O column density and the H2O-weighted path-averaged

temperature from the integrated absorbance of two transitions [28].

9.2 Experimental Setup

9.2.1 University of Virginia Supersonic Combustion Facility

(UVaSCF)

The UVaSCF, shown in Fig. 9.1, is an electrically heated, continuous-flow wind tunnel

designed to produce flow conditions encountered by hypersonic aircraft. In the current

study, the total temperature, total pressure and Mach number at the combustor inlet

were 1200 K, 330 kPa, and 2, respectively. This configuration consists of four main

sections: (1) isolator, (2) combustor, (3) constant area section, and (4) extender. The

isolator is 3.81 cm deep (z-direction) and 2.54 cm wide (y-direction). The combustor

flow path is 3.81 cm deep and diverges at 2.9 degrees along the cavity flameholder

9.2. EXPERIMENTAL SETUP 131

wall. The cavity is 0.9 cm wide and 4.73 cm long. Ethylene was injected 2.46 cm

upstream of the cavity at five coplanar injection sites that span the depth of the

combustor. Downstream of the combustor, the flow path consisted of a 14.9 cm long

constant area section and a 18 cm long extender that was open to the atmosphere.

Y

X

Fuel Injection

Reaction Zone

Cavity

Plane I

Plane II

Free-Stream

Recirculation Zone

Flow Direction

Z

Combustor

Isolator

Figure 9.1: Photo of UVaSCF (left) and cartoon of combustor with labeled mea-surement planes (right). Line-of-sight measurements were acquired in the z-directionthrough the large windows shown in the photo.

9.2.2 Optical Setup

A schematic of the optical setup used for temperature and H2O measurements in the

UVaSCF is shown in Fig. 9.2. Two frequency-multiplexed TDLs (Nanoplus GmbH)

near 2551 and 2482 nm were used to probe H2O transitions near 3920, 4029.5, and

4030.7 cm�1. During a given experiment, the transition near 3920 cm�1 was probed

simultaneously with either the transition near 4029.5 or the transition near 4030.7

cm�1. Each laser produced a nominal power output of 1-5 mW and a linewidth

less than 3 MHz [84]. The lasers were injection-current tuned with a scanning si-

nusoid at 250 Hz (giving a measurement repetition rate of 500 Hz) and a modu-

lation sinusoid at 75 or 100 kHz. A modulation depth of 0.16 to 0.20 cm�1 and


0.031 to 0.038 cm�1 was used for the lasers at 2551 and 2482 nm, respectively. For

both lasers, the modulation index, defined as the ratio of the modulation depth

and transition half-width at half-maximum (HWHM), was between 3 and 3.5 to

reduce sensitivity to potential lineshape modeling errors as recommended in [21].

A 4 mm focal length anti-reflection coated aspheric lens (Thorlabs C036TME-D)

was used to collimate the output beam of each laser. The two lasers were oriented

orthogonal to one another and a 50/50 beamsplitter (Thorlabs BSW23) was used

to combine the laser beams. One of the combined beam paths was directed into a

400 µm ZBLAN multi-mode fiber (Fiber-Labs) using a 6 mm focal length lens (In-

novation Photonics). The fiber-coupled light was directed to the flow facility, colli-

mated with a 20 mm focal length zinc-selenide lens, and pitched across the combustor

with a near-Gaussian full-width at half-maximum (FWHM) of approximately 3 mm.

A single set of fused silica windows, shown in Fig. 9.1, enabled optical access

throughout the combustor. Three optical filters were used to reduce detected emis-

sion. A broad band-pass filter (Spectrogon BBP-2200-2600c nm) and a long-pass filter

(Spectrogon LP-2440 nm) were used to create a band-pass filter from 2440-2600 nm.

In addition, a neutral density filter was used to further reduce power levels by 80%.

A 12.5 mm diameter, 20 mm focal length calcium fluoride lens (Thorlabs LA5315-

D) was used to focus the collected light onto a mercury cadmium telluride (MCT)

detector (Vigo Systems PVI-2TE-4) with a 2 mm diameter active area and 10 MHz

bandwidth. The pitch and catch optics were mounted to a set of computer-controlled

translation stages to traverse the measurement LOS in the x- and y-direction. More

information regarding the arrangement of the translation stages can be found in [121].

Measurements were acquired at two axial planes (shown in Fig. 9.1) spaced 7.6 cm

apart. The upstream-most plane was located 4.62 cm downstream of fuel injection.

At each axial plane, 250 measurements (0.5 seconds of data) were acquired at up to

26 di↵erent locations spaced 1.5 mm apart in the y-direction. During all experiments,

the raw detector signal was anti-aliased to 1 MHz with a low-pass filter (Kronhite)

and sampled at 5 MHz (National Instruments PXI-6115). The WMS signals of each

laser were frequency demultiplexed during post-processing with 5 kHz Butterworth

filters.

9.3. LINE SELECTION AND EVALUATION 133

Beam Splitter

Collimating Lens

5-axis Fiber-Mount

Purged with N2

400 µm MMF

Diode Laser

Model Scramjet Combustor

YZ

X-Direction (Flow-Direction) = Out of Page Pitch & Catch Optics Translated X-Y

Spectral Filters

MCT Detector

Catch Lens

Pitch Lens

Figure 9.2: Schematic of optical setup used in measurements conducted at theUVaSCF.

9.3 Line Selection and Evaluation

9.3.1 Line Selection

To provide high signal-to-noise ratio (SNR) over the measurement domain, three

water vapor transitions in the stronger fundamental vibration bands near 2.5 µm

were used to measure the gas temperature and H2O column-density throughout the

scramjet combustor. The pertinent spectroscopic parameters for these lines, labeled

A, B, and C, are given in Table 9.1. In addition, Fig. 9.3 (left) shows simulated

absorbance spectra for these lines at 0.8 bar, 1500 K and 10% H2O by mole with a

path length of 3.81 cm. Lines A and B (line pair 1 ) were used to characterize the

free-stream and Lines A and C (line pair 2 ) were used to characterize the nonuniform

reaction zone (shown in Fig. 9.1). Line B was chosen according to conventional

line-selection techniques [108], since the gas in the free-stream is expected to be

near uniform along the LOS. However, Lines A and C were chosen according to the

methodology put forth in Ch. 6 and [28] since the temperature and composition

of the gas in the reaction zone are expected to be nonuniform along the LOS. In

addition to incorporating conventional line selection rules [108], this method uses two

transitions with strengths that scale near-linearly with temperature over the domain

of the temperature nonuniformity to enable accurate determination of T ni and Ni


Table 9.1: Relevant spectroscopic parameters for the H2O transitions used in UVaSCFcombustor sensor.

Table 1. Relevant spectroscopic parameters for the H2O transitions used.

Line vo [cm-1] E” [cm-1] S(296 K) [cm-1/molecule-cm-2] Measured/(Uncertainty) HITEMP ’10/(Uncertainty) A 3920.089 704.214 2.56 x 10-20/(2.1%) 2.58 x 10-20 / (5-10%) B 4029.524 2660.945 4.44 x 10-24 /(2.3%) 4.27 x10-24 / (5-10%) C 4030.729 4889.488 1.08 x 10-28/(2.5%) 1.16 x 10-28/ (10-20%) *Denotes a doublet transition. Linestrengths quoted for doublet transitions are quoted as the sum of the doublet. The linestrength of Lines A and C were measured as done by Goldenstein et al. [35]. vo and E” were taken from [37].

from the integrated absorbance of two transitions.

9.3.2 Evaluation of Chosen Lines

Signal Strength

To achieve su�cient SNR in harsh environments, strong absorption transitions must

be used. The fundamental vibration band transitions used here are 1.5 to 20 times

stronger, depending on temperature, than the combination- and overtone-band tran-

sitions used in other scramjet sensors [69, 8, 6, 7, 121]. In addition, the reduction in

Doppler width associated with using lines near 2.5 µm (as opposed to 1.4 µm) leads to

an increase in peak absorbance on the order of 20% for typical atmospheric pressure

flame conditions. As a result, using lines in the fundamental H2O bands near 2.5 µm

provides large gains in signal strength, and thereby, sensor accuracy and precision.

Temperature Sensitivity

Large temperature sensitivity is critical to the success of all thermometry techniques.

Since the temperature is inferred from the two-color ratio of integrated absorbance,

R, temperature sensitivity is defined here as the unit change in R per unit change in

temperature. Fig. 9.3 (right) shows the temperature sensitivity of line pairs 1 and 2

as a function of temperature. It is well known that the temperature sensitivity scales

with the di↵erence in lower-state energies, �E” [83]. As a result, the temperature

sensitivity of line pair 2 (�E” = 4185 cm�1) is always greater than that of line

pair 1 (�E” = 1956 cm�1). Furthermore, from 1000 to 2500 K, the temperature

sensitivity of line pairs 1 and 2 decrease from 2.8 to 1.1 and 6 to 2.4, respectively.

9.3. LINE SELECTION AND EVALUATION 135

3919.5 3920 3920.50

0.1

0.2

0.3

0.4

Optical Frequency (cm−1)

Ab

sorb

an

ce

4029 4030 40310

0.06

0.12

0.18

0.24

Line B

E" ~ 2660 cm−1

Line C

E" ~ 4889 cm−1

Line A

E" ~ 704 cm−1

500 1000 1500 2000 25000

3

6

9

12

Temperature (K)

Te

mp

era

ture

Se

nsi

tivity

(a

.u.)

Line Pair 1: ∆E" ~ 1956 cm−1

Line Pair 2: ∆E" ~ 4185 cm−1

Figure 9.3: Simulated absorbance spectra (left) for Lines A, B, and C at 0.8 bar, 1500K, and 10% H2O with a path length of 3.8 cm. Temperature sensitivity (right) forline pairs 1 and 2 as a function of temperature. Line Pair 1 = Lines A and B, LinePair 2 = Lines A and C.

The temperature sensitivity decreases with increasing temperature due to Boltzmann

statistics. In general, a temperature sensitivity greater than one is recommended

[108]. That said, both line pairs used here are expected to yield excellent thermometry

performance over the experimental domain.

Linearity of Linestrength

Using lines with strengths that scale linearly with temperature enables the determi-

nation of T ni and Ni in a nonuniform gas [28]. However, in reality, the transition

linestrength is a nonlinear function of temperature as shown in Eq. (2.2). As a re-

sult, it is important to evaluate the accuracy of the linear-linestrength approximation

of the chosen transitions for the expected range of temperatures. This was done by

least-squares fitting a line to temperature-specified regions of the linestrength curves

given by Eq. (2.2). To remove the influence of the value of S(To), all linestrength pro-

files were normalized to a maximum of 1. Figure 9.4 shows the maximum error in the

linear-linestrength approximation, quantified in terms of percent of the linestrength

at the mean temperature, for Lines A and C as a function of the mean temperature.

For mean temperatures between 1300 and 2000 K and a 500 K wide temperature

range, the linear-linestrength approximation is accurate to within 1.2-2.6% of the


1200 1400 1600 1800 20000

1

2

3

4

5

Mean Temperature (K)

Err

or

in L

inear

S(T

) A

ppro

x. (

% o

f S

(Tm

ean))

Line ALine C

Results Shown for T = Mean T +/− 250 K

Figure 9.4: Maximum error in linear-linestrength approximation for Lines A and Cas a function of mean temperature for a temperature range of 500 K (i.e., ± 250 K).The linear-linestrength approximation for Lines A and C is accurate to within 1.2and 2.6% of S(Tmean) for mean temperatures between 1300 and 2000 K.

mean linestrength for Lines A and C. While this error cannot be directly translated

to errors in T ni and Ni without knowing how the gas conditions vary along the LOS,

the results shown in Fig. 9.4 suggest that the linear-linestrength approximation is

accurate for Lines A and C in the nonuniform reaction zone.

Projected Performance in Nonuniform Reaction Zone

A scanned-WMS-2f/1f measurement was simulated for a nonuniform LOS to esti-

mate the accuracy of this sensor in a nonuniform combustor. Fig. 9.5 (left) shows

an example distribution of temperature and H2O along a simulated optical path.

The temperature and H2O mole fraction vary from 1100 to 1625 K and 0 to 0.13,

respectively, and T nH2Oequals 1450 K. These distribution functions were designed

to simulate a case where the measurement LOS passes through two distinct zones

of combustion. Fig. 9.5 (right) shows simulated path-integrated WMS-2f/1f spec-

tra and corresponding best-fit for Lines A and C. The path-integrated WMS-2f/1f

spectra represent a simulated measurement for the LOS shown in Fig. 9.5 (left) with


0

500

1000

1500

2000

Te

mp

era

ture

(K

)

0 1 2 3 40

0.05

0.1

0.15

Optical Path (cm)

XH

2O

3919.9 3920.1 3920.30

0.15

0.3

0.45


WM

S−

2f/

1f

4030.6 4030.75 4030.90

0.02

0.04

0.06Path−Integrated Simulation

Best−Fit

Line A

Line C

Figure 9.5: Example of temperature and H2O mole fraction distributions used tosimulate WMS-2f/1f measurements in a nonuniform reaction zone (left). Simulatedpath-integrated WMS-2f/1f spectra and corresponding best-fit for Lines A and C(right). Best-fit spectra recover measured spectra within less than 0.5% of peakvalues, and T nH2O

and NH2O to within 1.5 and 0.3%, respectively.

a uniform pressure of 0.8 bar. In this example, the best-fit spectra match the path-

integrated spectra to within less than 0.5% of the peak signal. The temperature and

H2O column density inferred from the best-fit integrated absorbance of Lines A and

C agree within 1.5% of T nH2Oand 0.3% of NH2O, respectively. To quantify how the

accuracy of this sensor varies with mean temperature, these simulations were repeated

with ranging from 1200 to 1900 K in increments of 100 K. The corresponding error in

temperature and H2O column density varied from 0.3 to 3.3% and 0.1% to 2.6%, re-

spectively. As a result, these simulations indicate that the sensor and data processing

methods used are accurate in nonuniform combustion environments with the range of

temperatures expected here. More details describing how these measurements were

simulated can be found in Ch. 6 or [28].


Scanned-WMS-2f/1f measurements were conducted in air-H2O mixtures within a

heated static cell to validate the accuracy of the temperature and H2O sensor. An


experimental setup similar to that shown in Fig. 9.2 was used in static-cell experi-

ments and more information regarding the furnace and the static cell can be found in

[27]. Measurements were conducted with line pair 1 from 600 to 1325 K and with line

pair 2 from 1050 to 1325 K. The gas pressure was 1 bar and the water mole fraction

ranged from 1 to 7% depending on the experiment. The temperature was calculated

from the two-color ratio of integrated absorbances inferred from fitting simulated

WMS-2f/1f spectra to measured WMS-2f/1f spectra. Fig. 9.6 (left) shows an ex-

ample of a measured WMS-2f/1f spectrum and corresponding best-fit for Line B.

The best-fit spectrum recovered the measured WMS-2f/1f spectrum to within 2% of

the peak signal for all lines. In addition, the 95% confidence interval (obtained from

the fitting routine) in the integrated absorbance was less than ± 0.5% of its best-fit

value. Fig. 9.6 (right) shows the temperature sensing performance of both line pairs.

Line pairs 1 and 2 recovered the known temperature, measured with thermocouples,

to within 2% and 1.25%, respectively. In addition, the H2O mole fraction calculated

from the integrated absorbance of Line A inferred from scanned-WMS-2f/1f spec-

tral fitting agrees within 2.8% of that determined from scanned-wavelength direct-

absorption measurements. These small di↵erences could result from optical distortion

(e.g., etalon reflections) or from di↵erences in the models (e.g., Voigt profile fitting

vs. scanned-WMS-2f/1f model) used to convert measured signals to gas properties.

9.5 Measurements in Scramjet Combustor

This section presents example temperature and H2O results for Planes I and II (see

Fig. 9.1) of the UVaSCF operating at a global equivalence ratio of 0.15. A more com-

plete discussion of these results and a comparison with LOS absorption measurements

of CO and CO2 conducted in the same facility are given in [122].

Fig. 9.7 shows scanned-WMS-2f/1f time-histories for Lines A and C collected

inside the cavity flameholder (Plane I, y = 34.5 mm). The WMS-2f/1f signal di↵ers

(for identical gas conditions) for the up-scan and down-scan since the phase-shift

between the laser intensity and optical frequency is greater than ⇡. For each half-

scan (up-scan or down-scan), a simulated WMS-2f/1f spectrum was least-squares fit

9.5. MEASUREMENTS IN SCRAMJET COMBUSTOR 139

4029.45 4029.5 4029.55 4029.60

0.25

0.5

0.75

1


WM

S−

2f/

1f

(a.u

.)

Data

Fit

Line B

500 1000 1500500

1000

1500

Known Temperature (K)

Me

asu

red

Te

mp

era

ture

(K

)

Ideal

Line Pair 1

Line Pair 2

Figure 9.6: Scanned-WMS-2f/1f spectrum and corresponding best-fit (left) for LineB in a static-cell experiment conducted at 1 bar and 1000 K with ⇡7% H2O bymole. Accuracy of scanned-WMS-2f/1f temperature sensor (right) using line pairs1 and 2 as a function of temperature for static-cell experiments. Line pairs 1 and 2recover the known temperature to within 2 and 1.25%, respectively. Error bars aretoo small to be seen. The known temperature was determined from thermocouplemeasurements.

to a measured WMS-2f/1f spectrum to determine the integrated absorbance of each

transition. Fig. 9.8 shows examples of measured and corresponding best-fit WMS-

2f/1f spectra for Lines A and C. The WMS-2f/1f spectrum for Line A is asymmetric

due to its large absorbance, and thus asymmetric 1f signal [62]. For both lines, the

best-fit spectra match the measured spectra to within less than 2% of the peak signal,

which indicates that the fitting routine produced an accurate representation of the

experiment. Furthermore, the 95% confidence interval (obtained from the fitting

routine) in the integrated absorbance was less than ± 2.5% of the best-fit value.

T nH2Owas calculated by comparing the two-color ratio of integrated absorbances

with the two-color ratio of linestrengths. NH2O was calculated according to (6) us-

ing the integrated absorbance of Line A. Fig. 9.9 shows a 0.5 second time-history

(acquired uninterrupted) of T nH2Oand NH2O ⇥ T nH2O

for y = 28.5 mm at Plane I.

NH2O was scaled by T nH2Oto highlight oscillations in composition. Fig. 9.9 indicates

that the gas conditions are nominally steady, however, some low-frequency (O(100

Hz)) oscillations exist, particularly between 0 and 0.3 seconds. These oscillations in


0 2 4 6 8 100

0.5

1

1.5

WM

S−

2f/1f Lin

e A

0 2 4 6 8 100

0.1

0.2

Time (ms)

WM

S−

2f/1f Lin

e C

Up−scan

E" = 4889 cm−1

E" = 704 cm−1Down−scan

Peak−SNR ~ 30

Peak−SNR ~ 125

Figure 9.7: Example scanned-WMS-2f/1f time-histories for Lines A (top) and C(bottom) acquired in the UVaSCF cavity flameholder (y=34.5 mm on Plane I). Eachscanned-WMS-2f/1f spectrum yields a measured temperature and H2O column den-sity. A total of 500 ms of data were collected at each measurement location.

3919.9 3920 3920.1 3920.2 3920.30

0.5

1

1.5

2


WM

S−

2f/

1f

(a.u

.)

Data

Fit

Line A

4030.65 4030.7 4030.75 4030.80

0.025

0.05

0.075

0.1


WM

S−

2f/

1f

(a.u

.)

Line C

Figure 9.8: Examples of measured and best-fit scanned-WMS-2f/1f spectra for LinesA (left) and C (right) acquired in the UVaSCF. The best-fit spectra match the mea-sured spectra to within 2% of the peak signals.


0 0.1 0.2 0.3 0.4 0.5500

1000

1500

2000

2500

Te

mp

era

ture

(K

)

0 0.1 0.2 0.3 0.4 0.510

20

30

40

Time (s)

NH

2O

x T

H2O

(m

ole

−K

/m2)

Results Shown for Line Pair 2

Figure 9.9: Example temperature and H2O column density time-histories acquiredin UVaSCF at y = 28.5 mm on Plane I. H2O column density is scaled by tempera-ture to highlight oscillations due to composition only (assuming constant pressure).Smoothed data highlights low-frequency oscillations in temperature and H2O.

temperature and H2O are correlated which suggests that the oscillations reflect fluctu-

ations in either the combustion progress or in the transport of combustion products to

the measurement location. Similar oscillations were observed throughout the reaction

zone.

Fig. 9.10 shows the mean temperature and H2O column density as a function

of y for Planes I and II (see Fig. 9.1). All measurements were acquired without

shutting down the UVaSCF. The bars indicate the temporal variation (1 standard

deviation). The measurement uncertainty, obtained from the 95% confidence interval

in the integrated absorbance of each transition, is typically five times smaller than

the temporal variation. While pressure measurements are not needed to determine

TNH2Oor NH2O, it is worth noting that the static pressure at Planes I and II was

approximately 0.73 and 0.83 bar. Fig. 9.10 (top) shows results spanning the entire

flow path for Plane I. The temperature first rises away from the cavity wall and then

falls monotonically outside the cavity before plateauing at the free-stream tempera-

ture near 1000 K. The H2O column density, however, falls near monotonically away

from the cavity wall before reaching the expected free-stream value corresponding

to 0.8% H2O by mole. This immediate drop in column density cannot be explained


by the density decrease associated with the rising temperature. As a result, these

results suggest that combustion is most complete near the cavity wall and that the

lower temperatures could result from three potential sources: (1) heat transfer to the

cooled walls, (2) increased dilution with cooler gases, and (3) thermal stratification

in the unburnt gas entering the cavity.

Several interesting conclusions can be made by comparing temperature and H2O

results between Planes I and II. (1) Combustion products penetrate into the free-

stream a greater distance as the flow moves downstream. Similar results were ob-

served in [121] for a di↵erent combustor configuration. (2) Along the expansion wall,

the temperature decreases in the flow direction. This could result from heat transfer

to the combustor wall. (3) For y =21-27 mm, the H2O column density increases a

large amount from Plane I to II, however, the temperature exhibits a slight decrease.

While larger values of H2O column density suggest greater combustion progress, the

minor drop in temperature suggests that the associated heat-release is o↵set by ther-

mal dilution with the free-stream. More discussion regarding these results and the

performance of the model scramjet combustor can be found in [122].


0 5 10 15 20 25 30 35 40500

1000

1500

2000

2500

Tem

pera

ture

(K

)

Wall

Line Pair 2

Line Pair 1

0 5 10 15 20 25 30 35 400

0.01

0.02

0.03

Y (mm)

NH

2O

(m

ole

/m2)

Results Shown for Plane I

Cavity

Cavity

Expected Ambient H2O

~0.8% by mole

0 5 10 15 20 25 30 35 40500

1000

1500

2000

2500

Tem

pera

ture

(K

)

Plane I

Plane II

0 5 10 15 20 25 30 35 400

0.01

0.02

0.03

0.04

Y (mm)

NH

2O

(m

ole

/m2)

Wall

Cavity

Cavity

Wall

Results Shown for Line Pair 2

Figure 9.10: Time-averaged temperature and H2O column density measured with linepairs 1 and 2 on Plane I (top) and for Planes I and II (bottom). Results are shown forthe UVaSCF operating with a global ethylene-air equivalence ratio of 0.17. Outside ofthe reaction zone, the WMS sensor recovers the expected H2O concentration. Insidethe reaction zone the H2O column density increases between Planes I and II whichindicates that combustion progresses in the flow direction.

Chapter 10

Temperature, Composition, and

Enthalpy Sensing in a Pulse

Detonation Combustor

10.1 Introduction

Since the late 1950s [123], numerous researchers have studied pulse detonation com-

bustors and engines (PDC/E) in hopes of achieving large e�ciency gains (O(10%)).

In particular, PDEs have received considerable attention in the propulsion commu-

nity due to their mechanical simplicity and large specific impulse [124]. However,

while these devices are both conceptually and mechanically simple, many complex

phenomena (e.g., deflagration-to-detonation transition (DDT), turbulence, chemical

kinetics, and heat transfer) present formidable design challenges. As a result, a vari-

ety of robust, high-speed diagnostics (e.g., pressure, temperature, and composition)

are needed to study these systems.

Over the last two decades, laser absorption sensors have matured into robust and

practical tools for providing non-intrusive, in situ measurements of temperature, com-

position, and velocity in harsh environments [109, 1]. While less sensing has been done

in high-pressure environments, absorption sensors have been developed for coal gasi-

fiers [17], internal combustion engines [2, 4] and pulse detonation engines/combustors

144

10.1. INTRODUCTION 145

[10, 125, 11, 12]. Regarding PDCs, Sanders et al. [10, 125, 11] developed near-

infrared (NIR) diagnostics for temperature, composition, and soot [10] and utilized

absorption of seeded atomic Cs for temperature and pressure [125], and velocity [11].

More recently, Caswell et al. [12] used NIR absorption of H2O to measure temper-

ature, H2O, velocity and pressure for tracking the enthalpy exiting a PDC. While

these sensors have provided invaluable information, all previous sensing of combus-

tion products has been limited to the near-infrared, with most sensing done in the

weaker overtone and combination absorption bands of H2O near 1.4 µm. In addition,

extreme mechanical vibration, limited optical access, beamsteering, window fouling,

and emission continue to limit the fidelity and applicability of absorption sensors in

PDCs. Furthermore, the extreme temperatures (up to 4000 K) and pressures (up to

100 atm) of detonation gases require use of spectroscopic databases that have been

validated at extreme conditions. As a result, a new generation of sensors is needed

to provide: (1) measurements of additional combustion products and (2) improved

measurement accuracy and precision in detonation environments.

Here, time-resolved laser absorption measurements of temperature, H2O, CO2,

and CO in an ethylene-fueled PDC located at the Naval Postgraduate School (NPS)

in Monterey, CA are presented. Measurements were acquired in the PDC combustion

chamber and the throat of a converging-diverging nozzle located at the exit of the

PDC. The time-resolved enthalpy flow rate was calculated in the PDC throat using

the measured temperature, pressure, and composition with a choked flow assumption.

The measurement of CO and CO2 enables accurate enthalpy measurements and eval-

uation of combustion e�ciency in hydrocarbon-fueled combustors. Here, strong MIR

absorption and WMS-2f/1f were used to overcome the harsh measurement environ-

ment. Each sensor was validated at high-pressures (up to 50 atm) and -temperatures

(up to 2700 K) in non-reactive shock tube experiments to assess the accuracy of each

sensor at conditions representative of detonation environments. For the first time,

this work presents, describes, and analyzes the first: (1) use of MIR-H2O, -CO, and

-CO2 laser absorption for improved temperature and species sensing in a field engine,

(2) use of simultaneous multi-species measurements to evaluate PDC performance,

and (3) use of temperature and multi-species composition measurements in a choked

146 CHAPTER 10. T, �, AND H SENSING IN A PDC

throat for determining time-resolved enthalpy flow rate in a hydrocarbon-fueled com-

bustor.

10.2 Sensor Design and Architecture

10.2.1 Diagnostic Strategy

The WMS-2f/1f sensors used here realize four primary benefits. (1) Multiple col-

ors are frequency-multiplexed and -demultiplexed along a single LOS avoiding the

need for wavelength-dispersion-based demultiplexing. (2) The WMS-2f/1f signal is

immune to emission and non-absorbing transmission losses that vary at frequencies

outside the passband around the 1f and 2f signals [20, 25, 56]. (3) WMS-2f/1f is

a di↵erential absorbance technique that does not require knowledge of the absolute

absorbance, and therefore, the incident light intensity. (4) WMS-2f/1f is insen-

sitive to non-Lorentzian e↵ects that can compromise other absorption methods at

high-pressures [116]. As a result, WMS-2f/1f enables high-fidelity measurements in

detonation environments where non-absorbing transmission losses and mid-infrared

emission can be pronounced.

10.2.2 Wavelength Selection

The mid-infrared absorption transitions used for H2O near 2.5 µm, CO2 near 2.7

µm, and CO near 4.8 µm provide enhanced measurement sensitivity and precision

since they are 10-104 times stronger than those accessible in the near-infrared. In

addition, near-infrared transitions near 1.4 µm were also used for temperature and

H2O sensing to utilize robust telecommunications-grade fiber-optics. The wavelengths

for CO, CO2, and NIR H2O absorption were selected for their strength, temperature

sensitivity, and relative isolation from neighboring transitions [30, 118, 126]. MIR

wavelengths for H2O were selected according to a recently developed optimization

routine that enables sensitive measurements of temperature and H2O over a broad

range of temperatures and pressures [30]. The dominant transitions used by each

sensor are listed in Table 10.1. However, it should be noted that the absorbance

10.2. SENSOR DESIGN AND ARCHITECTURE 147

2059 2060 20610

0.06

0.12

0.18

Abso

rban

ce

1 atm20 atm

CO Spectra near 4854 nm

3733 3733.5 37340

0.06

0.12

0.18

1 atm5 atm

CO2 Spectra Near 2678 nm

��

7185 7185.5 7186

1 atm20 atm

6805.5 6806 6806.50

0.03

0.06

0.09

Abso

rban

ce

H2O Spectra Near 1392 and 1469 nm

4028 4029 40300

0.1

0.2

0.3

Abso

rban

ce

4041 4042 4043

1 atm20 atm

H2O Spectra Near 2474 and 2482 nm

Figure 10.1: Simulated absorbance spectra for H2O (top), CO (bottom left) and CO2

(bottom right) sensors at 1800 K with 5% H2O, 10% CO2, 0.5% CO and a 4 cmpath length. Simulations were performed using the hybrid databases described in[29, 30, 118, 126].

spectra of all species used here are blended at high pressure. As a result, simulations

used to convert measured signals to gas properties were performed with all transitions,

listed by HITEMP 2010 [74], located within ± 5 cm�1 of the wavelengths of interest.

Simulated H2O, CO2, and CO absorbance spectra for the wavelengths of interest are

shown in Fig. 10.1.


10.2.3 Optical Setup

In the interest of brevity, only the most critical hardware is discussed here. More

information regarding each of these sensors can be found in [29, 30, 118, 126]. All

lasers were fiber-coupled to enable remote light delivery to the PDC. Wedged 6.35

mm diameter sapphire windows mounted flush with the inner diameter of the PDC

provided optical access. For the results presented in Section 10.5, the MIR tem-

perature and H2O sensor and the CO sensor were directed across two orthogonal

lines-of-sight (LOS) in the PDC combustion chamber. Similarly, the NIR H2O and

temperature sensor and the CO2 sensor were directed across two orthogonal LOS

in the PDC throat. A schematic of each sensor and its interface with the PDC are

shown in Fig. 10.2. The MIR H2O and temperature sensor consists of two distributed

feedback (DFB) tunable diode lasers (TDLs) (Nanoplus GmbH) near 2474 and 2482

nm that were fiber-coupled in free-space into a 400 µm ZBLAN multi-mode fiber

(MMF) (FiberLabs). The CO sensor used a distributed-feedback quantum cascade

laser (Alpes) near 4854 nm that was fiber-coupled in free-space into a 17 µm InF3

single-mode fiber (SMF) (IR-Photonics). The near-infrared H2O and temperature

sensor used two fiber-coupled DFB TDLs (NEL America) near 1392 and 1469 nm.

The CO2 sensor used a single DFB TDL (Nanoplus GmbH) near 2678 nm that was

fiber-coupled in free-space into a 9 µm ZBLAN SMF (IR-Photonics). The modula-

tion parameters for each laser and the low-pass filter cuto↵ frequency used to extract

the WMS-1f and -2f signals for each laser are listed in Table 10.2. The modula-

tion depth and optical frequency of the lasers used for H2O and temperature sensing

were chosen according to the methodology presented in [30]. This method considers

the temperature- and pressure-dependence of the absorption spectra to determine

the modulation depth and center wavelength of each laser that provides the optimal

combination of signal strength and temperature sensitivity across the range of gas

conditions produced by the PDC. Laser light was collected by photo-voltaic detec-

tors that were mounted directly to the PDC. The detector signals were all sampled

at 5 MHz (National Instruments PXI-6115). For the MIR sensors, spectral filters

were used to reduce collected emission levels. In addition, raw emission signals were

acquired to confirm that the WMS-2f/1f signal of each laser was immune to any

10.3. CALCULATION OF GAS PROPERTIES 149

Table 10.1: Pertinent spectroscopic parameters for the dominant transitions used byeach sensor.

1

Table 1 Pertinent spectroscopic parameters for the dominant transitions used by each sensor. Linecenter [cm-1]

[nm]

Lower state energy (E”) [cm-1]

Sensor/Location in PDC

7185.59 1391.7 1045 T & H2O/Throat 6806.03 1469.3 3291 T & H2O/Throat 4041.92 2474.1 2981.4 T & H2O/Chamber 4029.52 2481.7 2660.9 T & H2O/Chamber 3733.47 2678.5 273.8 CO2/Throat 2059.91 4854.6 806.4 CO/Chamber

Table 2 Laser modulation parameters and low-pass filter cutoff frequency.

vlaser [cm-1]

f [kHz]

a [cm-1]

Filter [kHz]

7185.30 160 0.32 10 6806.08 200 0.24 10 4041.99 45.5 0.50 9 4029.65 35 0.28 9 3733.48 60 0.19 2 2059.91 50 0.23 20

remaining emission signal.

10.3 Calculation of Gas Properties

10.3.1 Calculation of Temperature and Composition

All absorption sensors rely on an accurate spectroscopic database and model to con-

vert measured signals to gas properties. Here, spectroscopic databases combining the

HITEMP 2010 database [74] with measured linestrength, lineshift, and collisional-

broadening parameters were used to enable highly accurate measurements of H2O,

CO, and CO2. For the H2O sensors, measured parameters given by Goldenstein et al.

[27, 29, 30] were used to simulate H2O absorbance spectra. For the CO2 and CO sen-

sors, measured collisional-broadening parameters given by Spearrin et al. [118, 126]

were used to simulate the absorbance spectra.

The calibration-free WMS model given by Rieker et al. [25] was used to simulate

WMS signals as a function of gas properites. In this method a Fourier expansion

is performed upon the time-varying transmitted laser intensity to calculate WMS

signals as a function of the simulated absorbance spectrum (i.e., gas properties) and

known laser parameters. For each data point comprising a measured WMS-2f/1f

time-history, the gas temperature and composition were calculated according to the


Table 10.2: Laser modulation parameters and low-pass filter cuto↵ frequency.

1

Table 1 Pertinent spectroscopic parameters for the dominant transitions used by each sensor. Linecenter [cm-1]

[nm]

Lower state energy (E”) [cm-1]

Sensor/Location in PDC



vlaser [cm-1]

f [kHz]

a [cm-1]

Filter [kHz]

7185.30 160 0.32 10 6806.08 200 0.24 10 4041.99 45.5 0.50 9 4029.65 35 0.28 9 3733.48 60 0.19 2 2059.91 50 0.23 20

10.3. CALCULATION OF GAS PROPERTIES 151

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

� ��

��

��

��

��

��

��

��

� ��

��

Figure 10.2: Schematic of optical setup (left) and sensor interface with PDC (right).

methods outlined by Rieker et at. [25]. The gas temperature at each point in time was

then determined from the two-color ratio of WMS-2f/1f signals at the independently

measured pressure. With temperature and pressure known, the mole fraction of the

absorbing species (e.g., H2O, CO2, or CO) was calculated from the WMS-2f/1f

signal of a given laser. Prior to calculating gas properties, the filter-induced time-lag

of the WMS signals was removed to synchronize the absorption measurements with

the pressure measurement.

10.3.2 Calculation of Enthalpy

The measurement of temperature, pressure, and composition in a choked throat en-

ables the calculation of the stagnation enthalpy flow rate, H, given by Eq. (10.1).

The H2O and CO2 mole fractions were measured directly in the throat and the mole

fraction of CO was assumed to be constant between the combustion chamber and

nozzle throat. The remainder of the gas was approximated as N2. Since CO only

exists in small quantities (<4.5%) and the thermodynamic and collisional-broadening

properties of CO are comparable to N2, any plausible change in CO mole fraction


between the chamber and throat introduces negligible uncertainty (<<1%) in the en-

thalpy calculation.The mass flow rate, m, was calculated using the local gas density

and the sound speed, u. The density was determined from the ideal gas law and the

sound speed was given by the temperature, mixture gas constant, and specific heat

ratio of the mixture. The specific heat ratio and sensible enthalpy of the mixture,

hsensible,mix, were calculated using the Burcat polynomials [127] with ideal mixture

relations.

H = m

✓hsensible,mix +

1

2u2

◆(10.1)


The accuracy of each sensor was validated via high-pressure and -temperature shock-

tube experiments. Experimental setups similar to those shown in Fig. 10.2 were

used and experiments were conducted using the Stanford High Pressure Shock Tube

(HPST). The HPST is 8.4 m long with an inner diameter of 5 cm and is capable

of reaching reflected-shock pressures greater than 1000 atm. More details regarding

the HPST are given by Petersen and Hanson [82]. Absorption measurements were

acquired behind the reflected shock approximately 1 cm from the shock tube endwall.

The temperature behind the reflected shock is known within ± 1% from shock-jump

relations [114] together with measured shock speeds. Tests were conducted using 1-

5% H2O in N2, 0.5% CO in N2, and 6-9% CO2 in air. Prior to each test, the mixture

composition was measured in situ prior to the shock arrival using scanned-wavelength

direct absorption to account for adsorption to the shock tube walls. In addition,

the HPST was heated to 105 C to prevent condensation on the tube walls. During

testing, the N2-broadening coe�cients for CO and NIR H2O transitions were refined at

extreme temperatures (>1300 K) to account for the slight temperature dependence of

the broadening-coe�cient temperature exponent [50]. Fig. 10.3 shows the accuracy

and precision of each sensor for various temperatures and pressures. Accuracy is

defined as the percent error between measured and known values and precision is

quoted as one standard deviation over the steady-state test time. The MIR H2O and


��

��

��

��

�� MIR H2O T Sensor Results ��

�

�

��

��

��

��

��

��

�� NIR H2O T Sensor Results

� ��

�

�

��

1000 1500 2000 2500 30000.80.9

11.11.2

MIR H2O Sensor Results

X mea

sure

d/Xkn

own

500 1000 1500 2000 2500 30000.80.9

11.11.2

NIR H2O Sensor Results

X mea

sure

d/Xkn

own

1000 1500 2000 2500 30000.80.9

11.11.2

CO Sensor Results

X mea

sure

d/Xkn

own

Known Temperature [K]500 1000 1500 2000 2500 30000.8

0.91

1.11.2

CO2 Sensor Results

Known Temperature [K]X mea

sure

d/Xkn

own

Nominal Precision = ± 0.03

Nominal Precision = ± 0.03 Nominal Precision = ± 0.045

Nominal Precision = ± 0.05

Figure 10.3: Accuracy of PDC sensors used in shock tube experiments. Each legendapplies to its own panel and those below it. Error bars indicate one standard deviationof the measurement over the steady-state test time. The MIR temperature, H2O, andCO sensors are nominally accurate to within less than 3% of known values. The CO2

and NIR temperature and H2O sensors are nominally accurate to within 5% of knownvalues.

temperature sensor and the CO sensor exhibit excellent accuracy (± ⇡3%) up to 50

atm and 2700 K. The NIR H2O and temperature sensor performs well (± ⇡1-10%

accuracy) in HPST tests up to 25 atm, however, higher pressures could not be tested

in the HPST with this sensor due to condensation that prevented the study of higher

H2O concentrations (i.e., higher SNR). The CO2 sensor is limited to pressures below

20 atm due to its reduced signal strength at higher pressures.


10.5 Pulse Detonation Combustor and Results

10.5.1 Pulse Detonation Combustor

The NPS PDC is 1.3 m long with a 7.6 cm diameter combustion chamber and a

converging-diverging nozzle attached to the combustor exit. Six detonation obstacles

were placed within the combustor to promote detonation formation. The nozzle

throat is 2.54 cm wide to enable optical access and has a diameter of 3.54 cm. The

measurement ports in the combustion chamber and nozzle throat (shown in Fig. 10.2)

were located 94 and 113 cm downstream of ignition, respectively, and a high-speed

(500 kHz) pressure transducer (Kistler 603B1, accuracy of ± 0.14 atm) was used

to monitor pressure at each location. Compressed air at 560 K and 5.75 atm was

continuously fed into the combustor and ethylene was intermittently injected into

the 3.8 cm diameter intake manifold 45 cm upstream of the PDC. The air and fuel

were convectively mixed at Mach 0.3 to achieve a near-homogeneous mixture with

an equivalence ratio near 1. Ignition was initiated with an automotive-grade spark

ignition source (MSD) at 20 Hz.

10.5.2 Results

Time-resolved measurements of temperature, pressure, H2O, CO, and CO2 for a single

PDC cycle are shown in Fig. 10.4. For the SNRs observed in the PDC, the detection

limits of the MIR-H2O, -CO, -CO2, and NIR-H2O sensors varied from 0.083-0.5%,

0.05-0.6%, 0.4-5%, and 1-4% by mole, respectively, across the PDC cycle. The detec-

tion limit for all sensors is largest at the highest pressures. Several interesting points

regarding these data are worth noting. (1) In general, the trends in temperature and

pressure are correlated. (2) For this particular cycle, the temperature and pressure

are higher in the throat than in the combustion chamber. This was observed inter-

mittently and suggests that a detonation propagated through the throat. (3) The

magnitude and trends in the H2O time-history are consistent between both sensors,

however, the larger MIR H2O absorption in the combustion chamber led to 5-10 times

smaller measurement precision. The rise and fall of H2O between 1 and 3 ms (in the

10.5. PULSE DETONATION COMBUSTOR AND RESULTS 155

500

1500

2500

3500

Tem

pera

ture

[K]

0

25

50

75

Pres

sure

[atm

]

00.05

0.10.15

X H2O

� ��

500

1500

2500

3500

Tem

pera

ture

[K]

0

20

40

60

Pres

sure

[atm

]

00.05

0.10.15

X H2O

� ��

0 5 10 150

0.05

Time [ms]

X CO

0 5 10 1500.05

0.10.15

Time [ms]

X CO

2Figure 10.4: Time-resolved temperature, H2O, CO, and CO2 results for a single PDCcycle. Data shown were acquired in the combustion chamber (left) and nozzle throat(right). In all plots, time = 0 refers to the arrival of the detonation front at thecombustion chamber measurement plane.

combustion chamber) is consistent with that expected due to the time-varying equi-

librium state of the gas; however, this may also result from stratified fuel loading.

(4) While the H2O levels indicate nearly complete combustion, the relatively large

levels of CO and small levels of CO2 indicate incomplete combustion at early times

(<5 ms), and (5) the sensors indicate a clear inverse relationship between the CO and

CO2 mole fractions as expected.

Fig. 10.5 shows the stagnation enthalpy flow rate as a function of time for three

consecutive PDC cycles. These results indicate that the enthalpy flow rate is highly

transient, but repeatable with peak values consistently near 25 MW. While the en-

thalpy flow rate is greatest during the primary blow-down event (0-3 ms), this event

only accounts for approximately 35% of the total enthalpy tracked. The tracked

cycle-integrated enthalpy was consistently near 70% of that injected (air + fuel) into

the PDC each cycle.

According to CFD simulations [128], the expected temperature and composition


0

10

20

30

Enth

alpy

Out

[MW

]

0 10 20 0 10 20Time [ms]

0 10 20

Results for 3 Consecutive Cycles Pulsed at 20 Hz

Figure 10.5: Time-resolved enthalpy flow rate for 3 consecutive cycles. Enthalpywas calculated assuming choked flow with the measured temperature, pressure, andcomposition.

time-histories are dominated by frequency-content below 2 kHz with some high-

frequency components due to the step-change behind the detonation wave. The tem-

perature, H2O, and CO sensors have su�cient bandwidth to resolve the gas conditions

behind the detonation front with a rise-time of 20-30 µs and an accuracy of 2.5%

thereafter. The CO2 sensor exhibits a rise time of 250 µs and is able to recover the

transients of interest within 3% at times where pressure is below 12 atm.

10.5.3 Uncertainty Analysis

In data processing we approximate the mixture composition to be the measured

species with a balance of N2. This approximation introduces uncertainty in collisional

broadening and the thermodynamic properties of the mixture. The former introduces

uncertainty in WMS-derived gas properties and the latter introduces uncertainty in

the enthalpy calculation. These e↵ects, however, are small for several reasons: (1)

CFD simulations [128] indicate that the measured species and N2 make up >95% of

the mixture by mole and the additional species exhibit similar properties to N2, (2)

the wavelength and modulation depth of each laser were chosen to reduce sensitivity

10.5. PULSE DETONATION COMBUSTOR AND RESULTS 157

Table 10.3: Uncertainty in reported PDC quantities.

15

Table 1 Pertinent spectroscopic parameters for the dominant transitions used by each sensor. Linecenter

[cm-1]

[nm] Lower state energy (E”)

[cm-1] Sensor/Location in PDC



vlaser [cm-1]

f [kHz]

a [cm-1]

Filter [kHz]

7185.30 160 0.32 10 6806.08 200 0.24 10 4041.99 45.5 0.50 9 4029.65 35 0.28 9 3733.48 60 0.19 2 2059.91 50 0.23 20 Table 3 Uncertainty in reported quantities.

T, K χi,, % P, atm Mt t<125 µs/cycle averaged

±90/75 ±2-20/2-3 ±2/0.2 -0.17/0.02 Contribution to Uncertainty in H, %

t<125 µs /cycle integrated ±2.4/2 ±3/2.5 ±3/2.2 -14/4 to uncertainty in collisional broadening (i.e., pressure and composition) [30], and (3)

the enthalpy calculation is dominated by temperature (given the small uncertainty in

composition).

The choked-flow assumption introduces uncertainty in the calculated enthalpy flow

rate due to its a↵ect on mass flow rate. CFD simulations [128] suggest that near-sonic

flow is established approximately ⇡125 µs after the detonation wave passes through

the throat. Prior to this time, the Mach number in the throat, Mt, is near 0.83.

Afterwards, Mt is expected to be near 0.98 due to boundary-layer e↵ects.

Considering the aforementioned sources of uncertainty and the time-response and

precision of each sensor, the root-sum-squared error in the enthalpy flow rate during

the first 125 µs and in the cycle-integrated enthalpy are 15% and 6%, respectively.

Table 10.3 shows the uncertainty of each variable and its contribution to uncertainty

in enthalpy.

Chapter 11

Summary and Future Work

11.1 Spectroscopic Database for H2O Near 2474

and 2482 nm

Linestrength measurements for 17 H2O transitions near 4029.52 and 4041.923 cm�1

have been reported. Measurements were performed with two DFB diode lasers at

pressures ranging from 2-22 Torr in neat H2O at temperatures ranging from 650-1325

K. It was found that the Voigt profile adequately described the measured absorbance

spectra of all transitions in neat H2O. Nearly all measured linestrengths agree within

uncertainty with the values reported by HITEMP 2010; however, we recommend

the use of our measured values due to the relatively large error bounds reported in

HITEMP 2010 (up to 20% for the transitions studied here). High-resolution absorp-

tion lineshapes were also presented for doublet transitions near 4029.52 and 4041.92

cm�1 in H2O, CO2, and N2. The collisional narrowing observed in neat H2O was found

to be negligible and the self-broadening coe�cients of several doublet pairs were found

to agree within uncertainty with the linestrength-weighted average of self-broadening

coe�cients predicted by HITEMP 2010. Moderate collisional narrowing was seen

in CO2 for the doublet near 4029.52 cm�1, and significant collisional narrowing was

seen in N2 for both doublets. For several high-J doublets, the N2-broadening coe�-

cients inferred from both Voigt and Galatry profile fits were found to increase with

158

11.2. SENSOR DESIGN FOR NONUNIFORM ENVIRONMENTS 159

temperature while those for H2O and CO2 perturbers were found to decrease with

temperature with similar temperature exponents. The reported collisional-narrowing

coe�cients at 296 K inferred from data agreed within uncertainty with the dynamic

friction coe�cient at 296 K predicted by power-law fits to theoretical values, and the

collisional-narrowing coe�cients of several doublets were found to decrease with tem-

perature according to temperature exponents that fall within the values predicted

by two theoretical approaches. Lastly, measurements conducted at high pressures

exhibit good agreement with simulations performed using the Galatry profile and

N2-broadening and -narrowing parameters derived from Galatry profile fits to low-

pressure spectra.

11.2 Sensor Design for Nonuniform Environments

A two-color absorption spectroscopy strategy has been developed for determining

the absorbing-species column density (Ni) and absorbing-species number-density-

weighted path-average temperature (TNi) in nonuniform gases. It was shown that

by using two absorption transitions with strengths that scale linearly with tempera-

ture over the domain of the temperature nonuniformity, Ni and TNi can be calculated

from the integrated areas of two transitions. Furthermore, the absorbance spectra

observed across a nonuniform LOS can be accurately compared with simulations

performed with a uniform LOS, e↵ective lineshapes, and absorbing-species number-

density-weighted path-average gas conditions (temperature, pressure, and absorbing

species column density). As a result, measured FWDA and WMS signals can also

be directly translated to the absorbing-species number-density-weighted path-average

gas conditions without knowing how the gas conditions vary along the LOS. It was

shown that this strategy can be used in highly-nonuniform environments where the

temperature varies along the LOS by up to 700 K.

This strategy was demonstrated for three common absorption spectroscopy tech-

niques: scanned-wavelength direct absorption, fixed-wavelength direct absorption,

and wavelength-modulation spectroscopy. In this demonstration, the gas tempera-

ture and water mole fraction varied from 900 to 1500 K and 0 to 20% by mole, with

160 CHAPTER 11. SUMMARY AND FUTURE WORK

LOS distribution functions that were chosen to be representative of the naturally

occurring gradients in hydrogen-air di↵usion flames. For this case, it was shown that

the strategy presented here measured NH2O and TNH2O to within 0.5% for all diag-

nostic techniques (SWDA, FDA, and WMS), while other more conventional methods

lead to errors of up to 20%. As a result, this strategy shows great promise for accu-

rate absorption measurements of Ni and TNi in a wide range of applications where

significant LOS nonuniformities in gas conditions exist.

11.3 NIR T and H2O Sensor for High-Pressure and

-Temperature Environments

A two-color TDLAS sensor for measurements of temperature and H2O in high-

pressure and -temperature gases has been developed, validated, and demonstrated.

Telecommunications-grade TDLs and fiber-optics were used to provide a robust and

portable sensor package capable of operating in harsh environments. WMS-2f/1f

was used to account for non-absorbing transmission losses and emission that are

commonly encountered in high-pressure and -temperature systems. In addition, an

experimentally-developed spectroscopic database for the two dominant transitions

was developed to improve the accuracy of this sensor. The linestrength and self-

broadening parameters were measured using scanned-wavelength direct absorption

in a heated static cell. However, N2-broadening parameters were measured at 2 to

25 atm and 700 to 2400 K to reduce errors introduced by (1) collisional narrowing

and (2) extrapolating broadening coe�cients to higher temperatures. This sensor

was then validated under known conditions in shock-heated gases. There, this sensor

recovered the known temperature and H2O mole fraction with a nominal accuracy

of 2.8% and 4.7% RMS, respectively. This sensor demonstrated exceptional range

and bandwidth during shock tube experiments. By using multiple lines-of-sight, this

sensor measured the temperature and H2O mole fraction behind the incident ( 800

K and 3 atm) and reflected shocks ( 1350 K and 14 atm) with a bandwidth of 30

11.4. MIR T AND H2O SENSOR FOR HIGH-P AND -T 161

kHz in a single experiment. In addition, using a single line-of-sight this sensor ac-

curately resolved the H2O mole fraction and temperature behind the incident and

reflected shocks and during an H2-O2 combustion event. Lastly, this sensor was used

to measure temperature and H2O in a pulse detonation combustor. As a result, this

sensor shows great potential for use in a number of harsh, real-world environments

with extreme vibrations and highly-transient gas conditions (e.g., internal combustion

engines, gas turbines, chemical reformers, etc.).

11.4 MIR T and H2O Sensor for High-Pressure

and -Temperature Environments

A two-color diode laser sensor for temperature and H2O mole fraction in high-pressure

and -temperature gases has been developed, validated, and demonstrated. High-

fidelity measurements are enabled through the use of: (1) strong H2O fundamental-

band absorption near 2.5 µm, (2) WMS-2f/1f , (3) an experimentally-derived and

-validated spectroscopic database, and (4) a new approach to selecting the optimal

wavelength and modulation depth of each laser. By using wavelengths in the fun-

damental vibration band of H2O, this sensor achieves 5 to 10 times larger signals

compared to near-infrared sensors. Furthermore, by using WMS-2f/1f , this sensor

is insensitive to emission, non-absorbing transmission losses, and non-Lorentzian ef-

fects. An experimentally-derived spectroscopic database was developed to provide

highly-accurate measurements and a new method for selecting the wavelength and

modulation depth of each laser was developed to ensure high sensitivity and SNR

over a broad range of temperatures and pressures.

This sensor was validated behind reflected shock waves at temperatures and pres-

sures up to 2700 K and 50 bar. On average, the sensor recovered the known steady-

state temperature and H2O mole fraction within 3.2 and 2.6% RMS of known values,

respectively (i.e., within typical measurement precision). Furthermore, the sensor

resolved transients with a rise time near 80 µs. The performance of this sensor was

estimated for a combustor with a path length of 5 cm, H2O mole fraction of 0.10, and


temperatures and pressures from 1000 to 2500 K and 10 to 50 bar, respectively. For

a 2f/1f noise level of 0.001, an SNR of 20 to 200 is expected and the corresponding

temperature uncertainty ranges from 5 to 50 K (i.e., 0.5 to 2%). The shock tube

measurements presented in Sect. 8.4.3 support the accuracy of these projections. As

a result, this sensor is well-suited for a number of high-pressure and -temperature

applications with any of the following: transient gas conditions (i.e., internal com-

bustion or gas turbine engines, new-concept detonation combustors, coal gasifiers),

mechanical vibration, particulates, or short path length.

11.5 Temperature and H2O Sensing in a Scramjet

The design and demonstration of a two-color tunable diode laser sensor for tem-

perature and H2O in an ethylene-fueled scramjet combustor were presented. This

sensor used three H2O transitions in the fundamental vibration bands near 2.5 µm

to enable high-SNR measurements in the non-reacting free-stream and the ethylene-

air reaction zone. The use of fundamental band transitions enabled three primary

advancements over previously used near-infrared based sensors: (1) up to 20 times

larger signals, (2) nearly a factor of two increase in temperature sensitivity, and (3)

use of lines with higher lower-state energy for improved measurement fidelity in high-

temperature nonuniform flows. In addition, this sensor used a recently developed

scanned-WMS-2f/1f spectral-fitting strategy to infer the integrated absorbance of

each transition without needing to model the transition linewidths beforehand. This

technique enabled accurate line-of-sight WMS absorption measurements of tempera-

ture and H2O in the nonuniform reaction zone. Temperature and H2O measurements

were presented for more than 35 locations within the UVaSCF combustor. Outside

of the reaction zone the measured H2O agrees with the expected free-stream value of

0.8% by mole. Within the reaction zone, low-frequency oscillations in temperature

and H2O were observed. These oscillations indicate fluctuations in either combus-

tion process or transport of combustion products to the measurement location. The

measured temperatures were greatest in the middle of the cavity (O(2100 K)) and

decreased away from the cavity before plateauing in the free-stream. At a given

11.6. TEMPERATURE, COMPOSITION, AND ENTHALPYSENSING IN A PDC163

y-coordinate, the temperature did not change significantly between planes I and II,

however, the H2O column-density rose significantly at all locations. These results

suggest that the heat-release associated with greater combustion progress is o↵set by

dilution with the cooler free-stream.

11.6 Temperature, Composition, and Enthalpy

Sensing in a PDC

Laser absorption sensors for temperature, H2O, CO2, and CO have been designed,

validated, and deployed in a pulse detonation combustor. These sensors used WMS-

2f/1f to account for non-absorbing transmission losses (e.g., from beamsteering,

soot, and window fouling) and emission. Strong mid-infrared absorption was used for

greater accuracy, precision, and improved detection limits. Each sensor was validated

in non-reactive shock-tube experiments at temperatures and pressures up to 2700 K

and 50 atm, where each sensor exhibited a nominal accuracy from 3 to 5% of known

values with bandwidths from 9 to 20 kHz.

During PDC experiments, measurements were acquired simultaneously along two

orthogonal lines-of-sight (LOS) in both the PDC combustion chamber and the throat

of a converging-diverging nozzle located at the PDC exit. Measurements at two

axial locations enabled detection of the detonation intermittently propagating into

the throat. In addition, temperature, pressure, and composition measurements in

the nozzle throat combined with a choked-flow assumption enabled calculation of the

time-resolved enthalpy flow rate exiting the PDC. As expected, the enthalpy flow rate

was highly transient, but repeatable with peak flow rates near 25 MW. As a result,

these sensors show great potential for aiding in the design of work extraction devices

(e.g., gas turbine) integrated downstream of PDCs.


11.7 Future Work

11.7.1 Scanned-WMS Spectral-Fitting at High-Pressures

In Chapter 4 it was shown how to use scanned-WMS spectral-fitting for simulta-

neous measurements of gas temperature, composition, pressure, and velocity in a

low-pressure supersonic flow. Furthermore, this technique has been used extensively

in environments with isolated or partially blended transitions [21, 9]. Some work has

been done at elevated pressures [129], however, this technique has not been rigorously

developed for heavily blended-spectra. As a result, future research is needed to es-

tablish the performance and operating bounds of this method over a broad range of

pressures or for species with absorption spectra characterized by dense, overlapping

rotational structure.

11.7.2 E↵ect of Harmonic Sidebands in Scanned-WMS

In Section 3.3.3 it was shown that when a modulated laser is scanned across the

majority of an absorption transition the WMS-nf signal is distributed in Fourier

space across a large number of sidebands. Preliminary studies indicate that the

information contained in these sidebands influences the accuracy of scanned-WMS

spectral-fitting techniques when lineshape modeling errors exist (e.g., in a highly-

nonuniform line-of-sight). In addition, the large bandwidth these sidebands occupy

complicates frequency-multiplexing of multiple lasers and the prevention of cross-

talk. As a result, it may be beneficial to selectively reject specific sidebands during

the filtering process used to extract the WMS-nf signals from the detector signal.

The analytical scanned-WMS model developed by Strand [130] should be helpful in

identifying which sidebands can/should be rejected.

11.7.3 “Multi-a WMS”

Since the strength of WMS-nf signals depend on the modulation index, “Multi-a

WMS” (i.e., multi-modulation-depth WMS) strategies could be used to maintain

a high signal-to-noise ratio in transient environments (i.e., environments where the

11.7. FUTURE WORK 165

transition linewidth varies in time). This design feature could be extremely valuable

and plausible in cases where the gas conditions vary periodically at a known frequency

(e.g., in an internal combustion engine operating at a fixed speed). However, research

is needed to overcome a number of design challenges. For example, it is unclear how

fast the modulation depth can be changed, how this limit varies with modulation

frequency, and in what fashion the modulation depth should be varied (e.g., stepped,

ramped, sinusoidally). Furthermore, this may introduce a number of complications

regarding laser dynamics and signal processing.

Appendix A

Procedure for Scanned-WMS

Spectral Fitting

This purpose of this section is to present a procedure for least-squares fitting simulated

scanned-WMS spectra to measured scanned-WMS spectra.

1. Extract the measured WMS-nf/1f signals of interest from a measured detector

signal using the method presented in Rieker et. al [25].

2. Isolate a single WMS-nf/1f spectrum from the measured time-history, noting

if the spectrum corresponds to a laser intensity up-scan or down-scan.

3. Begin least-squares fitting routine

4. Simulate the laser’s optical-frequency time-history, ⌫(t), using eqs. (3.4) to (3.6)

5. Measure the laser’s incident intensity, Io(t) while scanning and modulating the

laser’s intensity and optical frequency. The detector o↵set (e.g., due to back-

ground emission) must be subtracted from the measured Io(t) during this char-

acterization experiment, however, changes in emission that occur in the test-

data of interest do NOT need to be accounted for.

166

167

NOTE: Steps 4-5 must be performed such that the laser’s simulated ⌫(t) and

measured or simulated Io(t) are synchronized with the test-data. This requires

the test data to be triggered at the same phase of the laser’s scan and modulation

as the data used to characterize the laser’s ⌫(t) and Io(t).

6. Simulate the absorbance spectrum of the transition(s) of interest corresponding

to the free-parameters (e.g., ⌫o, A, �⌫c) of the current iteration. The absorbance

spectrum should be simulated over an optical-frequency range slightly larger

than that spanned by the laser’s simulated ⌫(t) to enable e�cient computing of

It(t) via interpolation.

7. Simulate the laser’s transmitted light-intensity time-history, It(t). This can be

executed a number of ways, but computational cost must be considered. One

simple and e�cient approach is to use interpolation to calculate an absorbance

time-history ↵(⌫(t)) from the simulated ⌫(t) and simulated absorbance spec-

trum. After computing ↵(⌫(t)), It(t) can be calculated easily using Eq. (3.7).

8. Extract the simulated WMS-nf/1f time-history from the simulated It(t) using

the same lock-in filter that was applied to the raw detector signal in Step 1.

9. Isolate a single simulated WMS-nf/1f spectrum from the simulated time-

history and calculate the sum-of-squared errors (SSE) between it and the mea-

sured WMS-nf/1f spectrum. NOTE: the simulated and measured WMS-

nf/1f spectra must both correspond to either an intensity up-scan or down-

scan.

10. Repeat steps 6-8 until the SSE is minimized.

Appendix B

Solutions to Common

Experimental Problems

The purpose of this section is to present solutions to a few commonly encountered

experimental problems. The solutions presented here should be treated as a starting

point and not as an all-inclusive solution manual.

1. Beam-steering

“Beam-steering” refers to the angular deflection (i.e., steering) of light rays

passing through a material with a spatially varying index of refraction (e.g.,

due to density gradients in a gas). When time-varying (e.g., due to a turbulent

flow field), this can lead to fluctuations in the transmitted laser intensity which

manifests as “noise” in the measured signal. Since a thorough discussion of

beam-steering is provided by Petersen [131], here only a few of the most common

methods designed to reduce the e↵ects of beam-steering are discussed. All of

these methods are designed to improve collection e�ciency and to minimize the

impact of deflected rays on your measured signal.

(a) Maximize the clear aperture of your collection optics to prevent deflected

rays from being blocked prior to reaching the detector.

(b) Minimize the distance between the beam-steering source (e.g., test gas) and

168

169

your collection optics. In doing so, you will reduce the o↵-axis displacement

of the steered rays. In other words, don’t let a small angular deflection

turn into a large displacement. If a large displacement is unavoidable, use

optics with a large clear aperture.

(c) Use a detector with the largest active-area possible. In other words, maxi-

mize the size of your target. An active-area of 3 mm2 is usually su�cient,

but bigger is better if you can tolerate the associated decrease in detector

bandwidth.

(d) Use WMS-nf/1f if you can. 1f -normalized WMS signals are much less

sensitive to beam-steering if the frequency of the beam-steering is much

less than the harmonics of interest or outside the passband of the lock-in

filter used to extract the WMS-nf/1f signals.

2. Emission

Emission from high-temperature gases and facilities can ruin a laser absorption

experiment if the proper steps aren’t taken. Emission strengthens with increas-

ing temperature and, for gaseous molecules, also with increasing pressure. The

latter relationship results from the corresponding increase in number density.

Furthermore, like absorption, emission from gaseous molecules is stronger at

wavelengths corresponding to the fundamental vibration bands of the emitter

due to Boltzmann statistics. In practice, the emission collected by a given exper-

imental setup also depends on the exact spectral window that a given detector

or camera “sees” and their wavelength response. In my field measurement ex-

perience, I have never observed pronounced emission in the near-infrared using

InGaAs detectors (only 0.2 V on a Thorlabs PDC-10C were observed in the NPS

PDC at 3500 K and 50 atm). In the mid-infrared (e.g., 2550 nm), however,

I have observed strong emission (O(2-3V)) in PDC and scramjet combustor

sensing applications. Several solutions to this problem are listed below.

(a) Use spectral filters to reject emission at wavelengths outside the passband

170 APPENDIX B. SOLUTIONS TO COMMON EXPERIMENTAL PROBLEMS

of the filter. In my opinion this the best optical engineering approach since

it does not increase susceptibility to beam-steering.

(b) Use WMS-nf/1f if you can. 1f -normalized WMS signals are immune to

emission if the frequency of the emission is much less than the harmonics

of interest or outside the passband of the lock-in filter used to extract

the WMS-nf/1f signals. In systems with transient emission (e.g., pulse-

detonation combustor), 1f -normalized WMS is a truly fantastic method

for rejecting emission (as long as the detector is not saturated).

(c) Reduce the clear aperture of your collection optics, or use an aperture

(i.e., iris) to reduce the clear aperture, and displace collection optics from

emission source. In doing so, you will reduce the intensity of collected emis-

sion, however, this can easily come at the cost of increased susceptibility

to beam-steering. As a result, this should only be done as a last-resort.

3. Extinction

Here, ”extinction” refers to any non-absorbing optical transmission loss result-

ing from particulate scattering or window fouling.

(a) Use di↵erential absorbance or 1f -normalized WMS techniques. In doing

so, you can either determine the extinction in-situ or, in the case of 1f -

normalized WMS, become independent of it.

(b) Measure the extinction via o↵-line techniques. These methods operate

by tuning a laser’s wavelength to be “o↵-line” or “non-resonant” such

that none of the light is absorbed by the test gas. In this case, all of

the attenuation in optical power results from extinction. The measured

extinction can then be used to correct the measured absorbance in the

measurement of interest, however, it is important to note that this method

assumes the extinction is independent of wavelength which may not be

true.

171

4. Etalon Reflections

“Etalon reflections” occur when light passes through a medium with two parallel

faces (e.g., a window). Since a portion of the light is reflected at each bound-

ary, an interference pattern is established between the incident and reflected

rays/electromagnetic waves. If the wavelength of the light is held constant, this

e↵ect goes unnoticed. However, if the wavelength of light varies in time, the

interference of the incident and reflected rays also varies in time which leads to

oscillations in the intensity of light. In practice, this can be problematic since

the period and/or amplitude of the oscillation can be time-varying due to ther-

mal and mechanical stresses in windows. As a result, this oscillation manifests

itself as distortion in the measured signal.

(a) Avoid using optics with parallel faces. By using optics (e.g., windows,

beam-splitters etc.) with a 2-3 degree wedge on one face, etalon reflections

can usually be avoided entirely.

(b) If wedged optics cannot be used, use thick optics and angle the light source

such that the incident ray enters the material at an angle. However, this

method can be problematic since reflected rays only diverge away from the

incident ray over the course of the internal reflection (i.e., the incident and

reflected rays exit the material displaced, but parallel to one another). As

a result, an accurate ray trace is required to establish the viability of this

method and an aperture/iris may be needed on the collection side to block

the unwanted reflected rays.

5. Wavelength Jitter

“Wavelength Jitter” refers to a high-frequency (O(1-100 kHz)), small-amplitude

fluctuation in a laser’s wavelength. In modern semi-conductor lasers this usu-

ally results from laser light reflecting back into the laser cavity or from “noise”

in the current passed to the laser (the latter of which is far less likely is using a

current controller). In my experience with low-power (2-20 mW) diode lasers,

172 APPENDIX B. SOLUTIONS TO COMMON EXPERIMENTAL PROBLEMS

back-reflection-induced wavelength jitter is typically 0.001-0.005 cm�1) and is

observed best by tuning the laser across a narrow absorption feature where small

variations in the laser wavelength correspond to large variations in absorbance

and, thus, transmitted light-intensity. Wavelength jitter can be minor, appear-

ing as small “staircasing” across an absorption transition resembling fiber-mode

noise or as severe as causing an absorption profile to look like a rectangle. In

either case, wavelength jitter should be minimized whenever possible.

(a) Use an optical isolator. Optical isolators act as a one-way light valve and

prevent light from re-entering the laser cavity. The telecommunication

grade NIR TDLs (e.g., from NEL America) often come with isolators built

in to reduce back reflections by 40 dB. Unfortunately, optical isolators are

often expensive or commercially unavailable at less mature wavlengths.

(b) Attenuate the laser power (e.g., using a neutral density filter). This is

the simplest and one of the most e↵ective methods at reducing wavelength

jitter. By placing a neutral density filter in front of the laser, the laser

power that re-enters the laser cavity is attenuated twice (once per pass).

The lower the power re-entering the cavity, the less problematic the wave-

length jitter is.

6. Use anti-reflection coated optics, avoid using optics with parallel faces, and

misalign optics if necessary to minimize the amount of reflected power that

re-enters the laser cavity.

7. Wavelength Drift

“Wavelength drift” refers to a slow (< 1 Hz) variation in a laser’s wavelength.

This could result from poor thermal contact, changing ambient conditions, im-

proper laser temperature controlling, or laser “aging.” In my experience, mod-

ern semiconductor lasers can exhibit wavelength drift up to 0.01 cm�1 when the

ambient temperature changes by ⇡ 5-10 C.

173

(a) Avoid exposing the laser to di↵erent ambient temperatures since the last

time its wavelength was characterized with a wavemeter.

(b) Avoid remounting the laser to its heat sink (this can cause the thermal

resistance between the laser and heat sink to change) since the last time

its wavelength was characterized with a wavemeter.

(c) Measure the laser’s wavelength with a wavemeter when any of the above

cannot be avoided.

(d) Use scanned-wavelength techniques that do not require precise knowledge

of the laser’s wavelength or to infer the laser’s wavelength during the ex-

periment.

Bibliography

[1] R. K. Hanson, “Applications of quantitative laser sensors to kinetics, propulsion

and practical energy systems,” Proceedings of the Combustion Institute 33, 1–

40 (2011).

[2] L. A. Kranendonk, J. W. Walewski, T. Kim, and S. T. Sanders, “Wavelength-

agile sensor applied for HCCI engine measurements,” Proceedings of the Com-

bustion Institute 30, 1619–1627 (2005).

[3] D. Mattison, J. Je↵ries, R. Hanson, R. Steeper, S. De Zilwa, J. Dec, M. Sjoberg,

and W. Hwang, “In-cylinder gas temperature and water concentration mea-

surements in HCCI engines using a multiplexed-wavelength diode-laser system:

Sensor development and initial demonstration,” Proceedings of the Combustion

Institute 31, 791–798 (2007).

[4] G. Rieker, H. Li, X. Liu, J. Liu, J. Je↵ries, R. Hanson, M. Allen, S. Wehe,

P. Mulhall, H. Kindle, A. Kakuho, K. Sholes, T. Matsuura, and S. Takatani,

“Rapid measurements of temperature and H2O concentration in IC engines

with a spark plug-mounted diode laser sensor,” Proceedings of the Combustion

Institute 31, 3041–3049 (2007).

[5] O. Witzel, A. Klein, C. Me↵ert, S. Wagner, S. Kaiser, C. Schulz, and V. Ebert,

“VCSEL-based, high-speed, in situ TDLAS for in-cylinder water vapor mea-

surements in IC engines,” Optics Express 21, 8057–8067 (2013).

174

BIBLIOGRAPHY 175

[6] J. T. C. Liu, G. B. Rieker, J. B. Je↵ries, M. R. Gruber, C. D. Carter, T. Mathur,

and R. K. Hanson, “Near-infrared diode laser absorption diagnostic for temper-

ature and water vapor in a scramjet combustor.” Applied Optics 44, 6701–11

(2005).

[7] A. D. Gri�ths and A. F. P. Houwing, “Diode laser absorption spectroscopy of

water vapor in a scramjet combustor.” Applied optics 44, 6653–9 (2005).

[8] F. Li, X. Yu, W. Cai, and L. Ma, “Uncertainty in velocity measurement based

on diode-laser absorption in nonuniform flows.” Applied Optics 51, 4788–97

(2012).

[9] C. S. Goldenstein, I. A. Schultz, R. M. Spearrin, J. B. Je↵ries, and R. K.

Hanson, “Scanned-wavelength-modulation spectroscopy near 2.5 µm for H2O

and temperature in a hydrocarbon-fueled scramjet combustor,” Applied Physics

B DOI:10.1007/s00340-013-5755-0 (2014).

[10] S. T. Sanders, J. A. Baldwin, T. P. Jenkins, D. S. Baer, and R. K. Hanson,

“Diode-laser sensor for monitoring multiple combustion parameters in pulse det-

onation engines,” Proceedings of the Combustion Institute 28, 587–594 (2000).

[11] S. T. Sanders, D. W. Mattison, J. B. Je↵ries, and R. K. Hanson, “Time-of-flight

diode-laser velocimeter using a locally seeded atomic absorber: Application in

a pulse detonation engine,” Shock Waves 12, 435–441 (2003).

[12] A. W. Caswell, S. Roy, X. An, S. T. Sanders, F. R. Schauer, and J. R. Gord,

“Measurements of multiple gas parameters in a pulsed-detonation combustor

using time-mode-locked lasers,” Applied optics 52, 2893–2904 (2013).

[13] C. S. Goldenstein, R. M. Spearrin, J. B. Je↵ries, and R. K. Hanson, “Mid-

infrared laser absorption sensors for multiple performance parameters in a det-

onation combustor,” Proceedings of the Combustion Institute In Press, 1–13

(2014).

176 BIBLIOGRAPHY

[14] K. H. Lyle, J. B. Je↵ries, R. K. Hanson, and M. Winter, “Diode-laser sensor

for air-mass flux 2: Non-uniform flow modeling and aeroengine tests,” AIAA

Journal 45, 2213–2223 (2007).

[15] H. Li, S. D. Wehe, and K. R. McManus, “Real-time equivalence ratio mea-

surements in gas turbine combustors with a near-infrared diode laser sensor,”

Proceedings of the Combustion Institute 33, 717–724 (2011).

[16] L. Ma, X. Li, S. T. Sanders, A. W. Caswell, S. Roy, D. H. Plemmons, and J. R.

Gord, “50-kHz-rate 2D imaging of temperature and H2O concentration at the

exhaust plane of a J85 engine using hyperspectral tomography.” Optics express

21, 1152–62 (2013).

[17] K. Sun, R. Sur, X. Chao, J. B. Je↵ries, R. K. Hanson, R. J. Pummill, and

K. J. Whitty, “TDL absorption sensors for gas temperature and concentrations

in a high-pressure entrained-flow coal gasifier,” Proceedings of the Combustion

Institute 34, 3593–3601 (2013).

[18] J. A. Silver, “Frequency-modulation spectroscopy for trace species detection:

theory and comparison among experimental methods,” Applied optics 31, 707–

717 (1992).

[19] D. S. Bomse, A. C. Stanton, and J. A. Silver, “Frequency modulation and

wavelength modulation spectroscopies: comparison of experimental methods

using a lead-salt diode laser.” Applied Optics 31, 718–31 (1992).

[20] D. T. Cassidy and J. Reid, “Atmospheric pressure monitoring of trace gases

using tunable diode lasers,” Applied optics 21, 1185–90 (1982).

[21] C. S. Goldenstein, C. L. Strand, I. A. Schultz, K. Sun, J. B. Je↵ries, and

R. K. Hanson, “Fitting of calibration-free scanned-wavelength-modulation spec-

troscopy spectra for determination of gas properties and absorption lineshapes,”

Applied Optics 53, 356–367 (2014).

BIBLIOGRAPHY 177

[22] L. C. Philippe and R. K. Hanson, “Laser diode wavelength-modulation spec-

troscopy for simultaneous measurement of temperature, pressure, and velocity

in shock-heated oxygen flows.” Applied optics 32, 6090–103 (1993).

[23] R. Wainner, B. Green, M. Allen, M. White, J. Sta↵ord-Evans, and R. Naper,

“Handheld, battery-powered near-IR TDL sensor for stand-o↵ detection of gas

and vapor plumes,” Applied Physics B: Lasers and Optics 75, 249–254 (2002).

[24] G. B. Rieker, J. T. C. Liu, J. B. Je↵ries, R. K. Hanson, T. Mathur, M. R. Gru-

ber, and C. D. Carter, “Diode laser sensor for gas temperature and H2O con-

centration in a scramjet combustor using wavelength modulation spectroscopy,”

in “41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit,”

(2005), AIAA 2005-3710.

[25] G. B. Rieker, J. B. Je↵ries, and R. K. Hanson, “Calibration-free wavelength-

modulation spectroscopy for measurements of gas temperature and concentra-

tion in harsh environments.” Applied Optics 48, 5546–60 (2009).

[26] J. R. P. Bain, W. Johnstone, K. Ruxton, G. Stewart, M. Lengden, and K. Duf-

fin, “Recovery of absolute gas absorption line shapes using tunable diode laser

spectroscopy with wavelength modulation Part 2 : Experimental investiga-

tion,” Journal of Lightwave Technology 29, 987–996 (2011).

[27] C. S. Goldenstein, J. B. Je↵ries, and R. K. Hanson, “Diode laser measurements

of linestrength and temperature-dependent lineshape parameters of H2O-, CO2-,

and N2-perturbed H2O transitions near 2474 and 2482 nm,” Journal of Quan-

titative Spectroscopy and Radiative Transfer 130, 100–111 (2013).

[28] C. S. Goldenstein, I. A. Schultz, J. B. Je↵ries, and R. K. Hanson, “Two-color

absorption spectroscopy strategy for measuring the column density and path

average temperature of the absorbing species in nonuniform gases,” Applied

Optics 52, 7950 (2013).

[29] C. S. Goldenstein, R. M. Spearrin, I. A. Schultz, J. B. Je↵ries, and R. K. Han-

son, “Wavelength-modulation spectroscopy near 1.4 µm for measurements of

178 BIBLIOGRAPHY

H2O and temperature in high-pressure and -temperature gases,” Measurement

Science and Technology 25, 055101 (2014).

[30] C. S. Goldenstein, R. M. Spearrin, J. B. Je↵ries, and R. K. Hanson,

“Wavelength-modulation spectroscopy near 2.5 µm for H2O and tempera-

ture in high-pressure and -temperature gases,” Applied Physics B DOI:

10.1007/s00340-013-5754-1 (2014).

[31] J. Fischer, R. R. Gamache, A. Goldman, L. S. Rothman, and A. Perrin, “Total

internal partition sums for molecular species in the 2000 edition of the HITRAN

database,” Journal of Quantitative Spectroscopy and Radiative Transfer 82,

401–412 (2003).

[32] J. M. Hartmann, J. Taine, J. Bonamy, B. Labani, and D. Robert, “Collisional

broadening of rotation-vibration lines for asymmetric-top molecules. II. H2O

diode laser measurements in the 400-900 K range; calculations in the 300-2000

K range,” The Journal of Chemical Physics 86, 144 (1987).

[33] R. R. Gamache and A. L. Laraia, “N2-, O2-, and air-broadened half-widths,

their temperature dependence, and line shifts for the rotation band of H216O,”

Journal of Molecular Spectroscopy 257, 116–127 (2009).

[34] G. Wagner, M. Birk, R. Gamache, and J.-M. Hartmann, “Collisional parame-

ters of lines: e↵ect of temperature,” Journal of Quantitative Spectroscopy and

Radiative Transfer 92, 211–230 (2005).

[35] R. Dicke, “The e↵ect of collisions upon the doppler width of spectral lines,”

Physical Review 89, 472–473 (1953).

[36] J.-M. Hartmann, C. Boulet, and D. Robert, Collisional e↵ects on molecular

spectra (Elsevier Inc., 2008).

[37] J. Humlicek, “Optimized computation of the Voigt and complex probability

functions,” Journal of Quantitative Spectroscopy and Radiative Transfer 27,

437–444 (1982).

BIBLIOGRAPHY 179

[38] M. Kuntz, “A new implementation of the Humlicek algorithm for the calcula-

tion of the Voigt profile function,” Journal of Quantitative Spectroscopy and


[39] W. Ruyten, “Comment on “A new implementation of the Humlicek algorithm

for the calculation of the Voigt profile function by M. Kuntz [JQSRT 57(6)

(1997) 819-824],” Journal of Quantitative Spectroscopy and Radiative Transfer

86, 231–233 (2004).

[40] L. Galatry, “Simultaneous e↵ect of doppler and foreign gas broadening on spec-

tral lines,” Physical Review 122, 1218–1223 (1961).

[41] X. Ouyang and P. L. Varghese, “Reliable and e�cient program for fitting Gala-

try and Voigt profiles to spectral data on multiple lines.” Applied Optics 28,

1538–45 (1989).

[42] P. L. Varghese and R. K. Hanson, “Collisional narrowing e↵ects on spectral line

shapes measured at high resolution.” Applied Optics 23, 2376–2385 (1984).

[43] J. Hirschfelder, C. Curtiss, and R. Bird, Molecular theory of gases and liquids

(Wiley, New York, 1954).

[44] M. Lepere, A. Henry, A. Valentin, and C. Camy-Peyret, “Diode-laser spec-

troscopy: line profiles of H2O in the region of 1.39 µm,” Journal of molecular

spectroscopy 208, 25–31 (2001).

[45] P. L. Varghese, “Tunable infrared diode laser measurements of spectral pa-

rameters of carbon monoxide and hydrogen cyanide.” Ph.D. thesis, Stanford

University (1983).

[46] S. Rautian and I. Sobel’man, “The e↵ect of collisions on the Doppler broadening

of spectral lines.” Sov Phys Uspekhi 9, 701–716 (1967).

[47] N. H. Ngo, D. Lisak, H. Tran, and J. Hartmann, “An isolated line-shape model

to go beyond the Voigt profile in spectroscopic databases and radiative transfer

180 BIBLIOGRAPHY

codes,” Journal of Quantitative Spectroscopy and Radiative Transfer 129, 89–

100 (2013).

[48] C. D. Rodgers, “Collisional narrowing: its e↵ect on the equivalent widths of

spectral lines.” Applied Optics 15, 714–6 (1976).

[49] C. D. Boone, K. A. Walker, and P. F. Bernath, “Speed-dependent Voigt profile

for water vapor in infrared remote sensing applications,” Journal of Quantitative

Spectroscopy and Radiative Transfer 105, 525–532 (2007).

[50] J. Bonamy, D. Robert, and C. Boulet, “Simplified models for the tempera-

ture dependence of linewidths at elevated temperatures and applications to CO

broadened by Ar and N2,” JQSRT 31, 23–34 (1984).

[51] H. Cybulski, A. Bielski, R. Ciuryo, J. Szudy, and R. S. Trawiski, “Power-

law temperature dependence of collision broadening and shift of atomic and

molecular rovibronic lines,” Journal of Quantitative Spectroscopy and Radiative

Transfer 120, 90–103 (2013).

[52] J. Hartmann, M. Y. Perrin, Q. Ma, and R. H. Tipping, “The infrared continuum

of pure water vapor: calculations and high-temperature measurements,” Jour-

nal of Quantitative Spectroscopy and Radiative Transfer 49, 675–691 (1993).

[53] V. Nagali, “Diode laser study of high-pressure water-vapor spectroscopy,” Ph.D.

thesis, Stanford University (1998).

[54] J. Reid and D. Labrie, “Second-harmonic detection with tunable diode lasers -

Comparison of experiment and theory*,” Applied Physics B 26, 203–210 (1981).

[55] D. T. Cassidy and L. J. Bonnell, “Trace gas detection with short-external-cavity

InGaAsP diode laser transmitter modules operating at 1.58 µm.” Applied optics

27, 2688–93 (1988).

[56] T. Fernholz, H. Teichert, and V. Ebert, “Digital, phase-sensitive detection for in

situ diode-laser spectroscopy under rapidly changing transmission conditions,”

Applied Physics B: Lasers and Optics 75, 229–236 (2002).

BIBLIOGRAPHY 181

[57] R. Arndt, “Analytical line shapes for Lorentzian signals broadened by modula-

tion,” Journal of Applied Physics 36, 2522 (1965).

[58] P. Kluczynski and O. Axner, “Theoretical description based on Fourier analysis

of wavelength-modulation spectrometry in terms of analytical and background

signals,” Applied Optics 38, 5803–5815 (1999).

[59] P. Kluczynski, A. M. Lindberg, and O. Axner, “Wavelength modulation diode

laser absorption signals from Doppler broadened absorption profiles,” Journal

of Quantitative Spectroscopy and Radiative Transfer 83, 345–360 (2004).

[60] H. Li, G. B. Rieker, X. Liu, J. B. Je↵ries, and R. K. Hanson, “Extension of

wavelength-modulation spectroscopy to large modulation depth for diode laser

absorption measurements in high-pressure gases,” Applied Optics 45, 1052–

1061 (2006).

[61] K. Du�n, A. J. McGettrick, W. Johnstone, G. Stewart, and D. G. Moodie,

“Tunable diode-laser spectroscopy with wavelength modulation: A calibration-

free approach to the recovery of absolute gas absorption line shapes,” Journal

of Lightwave Technology 25, 3114–3125 (2007).

[62] K. Sun, X. Chao, R. Sur, C. S. Goldenstein, J. B. Je↵ries, and R. K. Hanson,

“Analysis of calibration-free wavelength-scanned modulation spectroscopy for

practical gas sensing using tunable diode lasers,” Measurement Science and

Technology 24, 12 (2013).

[63] P. Kluczynski, A. M. Lindberg, and O. Axner, “Background signals in

wavelength-modulation spectrometry with frequency-doubled diode-laser light.

I. Theory,” Applied Optics 40, 783–793 (2001).

[64] A. Farooq, J. B. Je↵ries, and R. K. Hanson, “Measurements of CO2 concentra-

tion and temperature at high pressures using 1f -normalized wavelength modu-

lation spectroscopy with second harmonic detection near 2.7 micron.” Applied

optics 48, 6740–53 (2009).

182 BIBLIOGRAPHY

[65] X. Liu, J. B. Je↵ries, and R. K. Hanson, “Measurements of spectral parameters

of water-vapour transitions near 1388 and 1345 nm for accurate simulation of

high-pressure absorption spectra,” Measurement Science and Technology 18,

1185–1194 (2007).

[66] K. H. Lyle, J. B. Je↵ries, and R. K. Hanson, “Diode-laser sensor for air-mass

flux 1: design and wind tunnel validation,” AIAA Journal 45, 2204–2212 (2007).

[67] H. Li, A. Farooq, J. B. Je↵ries, and R. K. Hanson, “Diode laser measurements of

temperature-dependent collisional-narrowing and broadening parameters of Ar-

perturbed H2O transitions at 1391.7 and 1397.8 nm,” Journal of Quantitative


[68] G. B. Rieker, “Wavelength-modulation spectroscopy for measurements of gas

temperature and concentration in harsh environments,” Ph.D. thesis, Stanford

University (2009).

[69] C. L. Strand and R. K. Hanson, “Thermometry and velocimetry in super-

sonic flows via scanned wavelength-modulation absorption spectroscopy,” in

“47th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit,” (San

Diego, 2011), August.

[70] W. N. Heltsley, J. A. Snyder, A. J. Houle, D. F. Davidson, M. G. Mungal,

and R. K. Hanson, “Design and characterization of the Stanford 6 inch expan-

sion tube,” in “42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference &

Exhibit,” (Sacramento, 2006), AIAA 2006-4443.

[71] R. L. Trimpi, “A preliminary theoretical study of the expansion tube, a new

device for producing high-enthalpy short-duration hypersonic gas flows,” Tech.

rep., NASA (1962).

[72] V. A. Miller, M. Gamba, M. G. Mungal, and R. K. Hanson, “E↵ects of sec-

ondary diaphragm thickness and transducer type on pressure measurements in

an expansion tube,” AIAA Journal 52, 451–456 (2014).

BIBLIOGRAPHY 183

[73] K. Sun, X. Chao, R. Sur, J. B. Je↵ries, and R. K. Hanson, “Wavelength modula-

tion diode laser absorption spectroscopy for high-pressure gas sensing,” Applied

Physics B 110, 497–508 (2012).

[74] L. Rothman, I. Gordon, R. Barber, H. Dothe, R. Gamache, A. Goldman,

V. Perevalov, S. Tashkun, and J. Tennyson, “HITEMP, the high-temperature

molecular spectroscopic database,” Journal of Quantitative Spectroscopy and


[75] C. Claveau, A. Henry, M. Lepere, A. Valentin, and D. Hurtmans, “Narrowing

and broadening parameters for H2O lines in the ⌫2 band perturbed by nitro-

gen from Fourier transform and tunable diode laser spectroscopy,” Journal of

Molecular Spectroscopy 212, 171–185 (2002).

[76] X. Liu, X. Zhou, J. B. Je↵ries, and R. K. Hanson, “Experimental study of

H2O spectroscopic parameters in the near-IR (6940-7440 cm1) for gas sensing

applications at elevated temperature,” Journal of Quantitative Spectroscopy

and Radiative Transfer 103, 565–577 (2007).

[77] A. Pine, “Collisional narrowing of HF fundamental band spectral lines by neon

and argon,” Journal of Molecular Spectroscopy 82, 435–448 (1980).

[78] D. R. Rao and T. Oka, “Dicke narrowing and pressure broadening in the infrared

fundamental band of HCl perturbed by Ar,” Journal of Molecular Spectroscopy

122, 16–27 (1987).

[79] J. F. D’Eu, B. Lemoine, and F. Rohart, “Infrared HCN lineshapes as a test

of Galatry and speed-dependent Voigt profiles,” Journal of Molecular Spec-

troscopy 212, 96–110 (2002).

[80] N. Ngo, N. Ibrahim, X. Landsheere, H. Tran, P. Chelin, M. Schwell, and J.-M.

Hartmann, “Intensities and shapes of H2O lines in the near-infrared by tunable

diode laser spectroscopy,” Journal of Quantitative Spectroscopy and Radiative

Transfer 113, 870–877 (2012).

184 BIBLIOGRAPHY

[81] M. Nelkin and A. Ghatak, “Simple binary collision model for Van Hove’s

Gs(r, t),” Physical Review 135, A4 (1964).

[82] E. L. Petersen and R. K. Hanson, “Nonideal e↵ects behind reflected shock waves

in a high-pressure shock tube,” Shock Waves 10, 405–420 (2001).

[83] A. Farooq, J. B. Je↵ries, and R. K. Hanson, “In situ combustion measurements

of H2O and temperature near 2.5 µm using tunable diode laser absorption,”

Measurement Science and Technology 19 (2008).

[84] L. Hildebrandt, R. Knispel, S. Stry, J. R. Sacher, and F. Schael, “Antireflection-

coated blue GaN laser diodes in an external cavity and Doppler-free indium

absorption spectroscopy.” Applied Optics 42, 2110–8 (2003).

[85] S. Adachi, “Model dielectric constants of Si and Ge.” Physical review. B, Con-

densed matter 38, 12966–12976 (1988).

[86] A. McLean, C. Mitchell, and D. Swanston, “Implementation of an e�cient an-

alytical approximation to the Voigt function for photoemission lineshape anal-

ysis,” Journal of Electron Spectroscopy and Related Phenomena 69, 125–132

(1994).

[87] V. Nagali, S. Chou, D. Baer, and R. Hanson, “Diode-laser measurements

of temperature-dependent half-widths of H2O transitions in the 1.4 µm re-

gion,” Journal of Quantitative Spectroscopy and Radiative Transfer 57, 795–809

(1997).

[88] V. Nagali and R. K. Hanson, “Design of a diode-laser sensor to monitor water

vapor in high-pressure combustion gases.” Applied Optics 36, 9518–27 (1997).

[89] S. Chou, D. Baer, and R. Hanson, “Diode-laser measurements of He-, Ar-, and

N2-broadened HF lineshapes in the first overtone band.” Journal of molecular

spectroscopy 196, 70–76 (1999).

BIBLIOGRAPHY 185

[90] D. Lisak, J. Hodges, and R. Ciuryo, “Comparison of semiclassical line-shape

models to rovibrational H2O spectra measured by frequency-stabilized cavity

ring-down spectroscopy,” Physical Review A 73, 1–13 (2006).

[91] L. Rothman, I. Gordon, A. Barbe, D. C. Benner, P. Bernath, M. Birk,

V. Boudon, L. Brown, A. Campargue, J.-P. Champion, K. Chance, L. Coud-

ert, V. Dana, V. Devi, S. Fally, J.-M. Flaud, R. Gamache, A. Goldman,

D. Jacquemart, I. Kleiner, N. Lacome, W. La↵erty, J.-Y. Mandin, S. Massie,

S. Mikhailenko, C. Miller, N. Moazzen-Ahmadi, O. Naumenko, A. Nikitin,

J. Orphal, V. Perevalov, A. Perrin, A. Predoi-Cross, C. Rinsland, M. Rot-

ger, M. Simeckova, M. Smith, K. Sung, S. Tashkun, J. Tennyson, R. Toth,

A. Vandaele, and J. Vander Auwera, “The HITRAN 2008 molecular spectro-

scopic database,” Journal of Quantitative Spectroscopy and Radiative Transfer

110, 533–572 (2009).

[92] Q. Ma, R. Tipping, and N. Lavrentieva, “Pair identity and smooth variation

rules applicable for the spectroscopic parameters of H2O transitions involving

high-J states,” Molecular Physics 109, 1925–1941 (2011).

[93] Q. Ma, R. H. Tipping, and N. N. Lavrentieva, “Theoretical studies of N2-

broadened half-widths of H2O lines involving high j states,” Molecular Physics:

An International Journal at the Interface Between Chemistry and Physics 110,

307–331 (2012).

[94] R. A. Toth, L. Brown, M. Smith, V. Malathy Devi, D. Chris Benner, and

M. Dulick, “Air-broadening of H2O as a function of temperature: 696-2163

cm�1,” Journal of Quantitative Spectroscopy and Radiative Transfer 101, 339–

366 (2006).

[95] R. Gamache, J. Hartmann, and L. Rosenmann, “Collisional broadening of wa-

ter vapor lines-I. A survey of experimental results,” Journal of Quantitative


186 BIBLIOGRAPHY

[96] V. Nagali, J. T. Herbon, D. C. Horning, D. F. Davidson, and R. K. Han-

son, “Shock-tube study of high-pressure H2O spectroscopy.” Applied Optics

38, 6942–50 (1999).

[97] M. Schoenung and R. K. Hanson, “CO and temperature measurements in a

flat flame by laser absorption spectroscopy and probe techniques,” Combustion

Science and Technology 24, 227–237 (1980).

[98] I. A. Schultz, C. S. Goldenstein, J. B. Je↵ries, and R. K. Hanson, “TDL absorp-

tion sensor for in situ determination of combustion progress in scramjet ground

testing,” in “28th Aerodynamic Measurement Technology, Ground Testing, and

Flight Testing Conference,” (New Orleans, 2012), June.

[99] L. S. Chang, C. L. Strand, J. B. Je↵ries, R. K. Hanson, G. S. Diskin, R. L.

Ga↵ney, and D. P. Capriotti, “Supersonic mass flux measurements via tun-

able diode laser absorption and non-uniform flow modeling,” in “49th AIAA

Aerospace Sciences Meeting,” (Orlando, FL, 2011), January.

[100] J. M. Seitzman and B. T. Scully, “Broadband infrared absorption sensor for

high-pressure combustor control,” Journal of Propulsion and Power 16, 994–

1001 (2000).

[101] J. Wang, M. Maiorov, J. B. Je↵ries, D. Z. Garbuzov, J. C. Connolly, and R. K.

Hanson, “A potential remote sensor of CO in vehicle exhausts using 2.3 µm

diode lasers,” Measurement Science and Technology 11, 1576–1584 (2000).

[102] X. Ouyang and P. L. Varghese, “Line-of-sight absorption measurements of high

temperature gases with thermal and concentration boundary layers,” Applied

Optics 28, 3979–3984 (1989).

[103] E. R. Furlong, R. M. Mihalcea, M. E. Webber, D. S. Baer, and R. K. Hanson,

“Diode-laser sensors for real-time control of pulsed combustion systems,” AIAA

Journal 37, 732–737 (1999).

BIBLIOGRAPHY 187

[104] T. I. Palaghita and J. M. Seitzman, “Control of temperature nonuniformity

based on line-of-sight absorption,” in “40th AIAA/ASME/SAE/ASEE Joint

Propulsion Conference,” (Ft. Lauderdale, FL, 2004), AIAA 2004-4163.

[105] S. T. Sanders, J. Wang, J. B. Je↵ries, and R. K. Hanson, “Diode-laser ab-

sorption sensor for line-of-sight temperature distributions,” Applied Optics 40,

4404–4415 (2001).

[106] X. Liu, J. B. Je↵ries, and R. K. Hanson, “Measurement of non-uniform temper-

ature distributions using line-of-sight absorption spectroscopy,” AIAA Journal

45, 411–419 (2007).

[107] M. R. Gruber, C. D. Carter, M. Ryan, G. B. Rieker, J. B. Je↵ries, R. K. Hanson,

J. T. C. Liu, and T. Mathur, “Laser-based measurements of OH, temperature,

and water vapor concentration in a hydrocarbon-fueled scramjet,” in “44th

AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit,” AIAA

2008-5070.

[108] X. Zhou, J. Je↵ries, and R. Hanson, “Development of a fast temperature sensor

for combustion gases using a single tunable diode laser,” Applied Physics B 81,

711–722 (2005).

[109] J. Wolfrum, “Lasers in combustion: from basic theory to practical devices,”

Proceedings of the Combustion Institute pp. 1–41 (1998).

[110] X. An, T. Kraetschmer, K. Takami, S. T. Sanders, L. Ma, W. Cai, X. Li, S. Roy,

and J. R. Gord, “Validation of temperature imaging by H2O absorption spec-

troscopy using hyperspectral tomography in controlled experiments.” Applied

optics 50, A29–37 (2011).

[111] L. Ma, X. Li, W. Cai, S. Roy, J. R. Gord, and S. T. Sanders, “Selection of

multiple optimal absorption transitions for nonuniform temperature sensing.”

Applied spectroscopy 64, 1274–82 (2010).

188 BIBLIOGRAPHY

[112] X. An, A. W. Caswell, and S. T. Sanders, “Quantifying the temperature sen-

sitivity of practical spectra using a new spectroscopic quantity: Frequency-

dependent lower-state energy,” Journal of Quantitative Spectroscopy and Ra-

diative Transfer 112, 779–785 (2011).

[113] X. An, A. W. Caswell, J. J. Lipor, and S. T. Sanders, “Determining the optimum

wavelength pairs to use for molecular absorption thermometry based on the

continuous-spectral lower-state energy,” Journal of Quantitative Spectroscopy

and Radiative Transfer 112, 2355–2362 (2011).

[114] G. Ben-Dor, O. Igra, and T. Elperin, 2001 Handbook of Shock Waves (San

Diego, CA, 2001).

[115] Z. Hong, D. F. Davidson, and R. K. Hanson, “An improved H2/O2 mechanism

based on recent shock tube/laser absorption measurements,” Combustion and

Flame 158, 633–644 (2011).

[116] G. Rieker, X. Liu, H. Li, J. Je↵ries, and R. Hanson, “Measurements of near-IR

water vapor absorption at high pressure and temperature,” Applied Physics B

87, 169–178 (2006).

[117] G. B. Rieker, H. Li, X. Liu, J. B. Je↵ries, R. K. Hanson, M. G. Allen, S. D.

Wehe, P. A. Mulhall, and H. S. Kindle, “A diode laser sensor for rapid, sensitive

measurements of gas temperature and water vapour concentration at high tem-

peratures and pressures,” Measurement Science and Technology 18, 1195–1204

(2007).

[118] R. M. Spearrin, C. S. Goldenstein, J. B. Je↵ries, and R. K. Hanson, “Fiber-

coupled 2.7 µm laser absorption sensor for CO2 in harsh combustion environ-

ments,” Measurement Science and Technology 24, 055107 (2013).

[119] P. R. Bevington and D. K. Robinson, Data reduction and error analysis for the

physical sciences (McGraw-Hill, New York, 1992).

BIBLIOGRAPHY 189

[120] X. Zhou, X. Liu, J. B. Je↵ries, and R. K. Hanson, “Selection of NIR H2O ab-

sorption transitions for in-cylinder measurement of temperature in IC engines,”

Measurement Science and Technology 16, 2437–2445 (2005).

[121] I. A. Schultz, C. S. Goldenstein, J. B. Je↵ries, R. K. Hanson, R. D. Rock-

well, and C. P. Goyne, “Spatially-resolved water measurements in a scramjet

combustor using diode laser absorption,” Journal of Propulsion and Power In

Press (2013).

[122] I. A. Schultz, C. S. Goldenstein, M. Spearrin, J. B. Je↵ries, and R. K. Hanson,

“Multispecies mid-infrared absorption measurements in a hydrocarbon-fueled

scramjet combustor,” Journal of Propulsion and Power In Press, 1–24 (2013).

[123] J. Nicholls, H. Wilkinson, and R. Morrison, “Intermittent detonation as a

thrust-producing mechanism,” Jet Propulsion 27, 534–541 (1957).

[124] P. Wolanski, “Detonative propulsion,” Proceedings of the Combustion Institute

34, 125–158 (2013).

[125] S. Sanders, D. Mattison, L. Ma, J. Je↵ries, and R. Hanson, “Wavelength-agile

diode-laser sensing strategies for monitoring gas properties in optically harsh

flows: application in cesium-seeded pulse detonation.” Optics Express 10, 505–

14 (2002).

[126] R. M. Spearrin, C. S. Goldenstein, J. B. Je↵ries, and R. K. Hanson, “Quantum

cascade laser absorption sensor for carbon monoxide in high-pressure gases using

wavelength modulation spectroscopy.” Applied optics 53, 1938–46 (2014).

[127] A. Burcat and R. Branko, “Third millennium ideal gas and condensed phase

thermochemical database for combustion with updates from active thermo-

chemical tables,” Tech. rep., Argonne National Laboratory and Technion Israel

Institute of Technology (2005).

[128] M. Toepper, “Operability and performance of a two-dimensional supersonic tur-

bine cascade coupled with a pulse detonation combustor,” Ph.D. thesis, Naval

Postgraduate School (In Production).

190 BIBLIOGRAPHY

[129] K. Sun, R. Sur, J. B. Je↵ries, R. K. Hanson, T. Clark, J. Anthony, S. Machovec,

and J. Northington, “Calibration-free wavelength-scanned WMS H2O absorp-

tion measurements in an engineering-scale high-pressure coal gasifier,” Applied

Physics B (2014).

[130] C. L. Strand, “Scanned wavelength-modulation absorption spectroscopy with

application to hypersonic impulse flow facilities,” Ph.D. thesis, Stanford Uni-

versity (2014).

[131] E. L. Petersen, “A shock tube and diagnostics for chemistry measurements at

elevated pressures with application to methane ignition,” Ph.D. thesis, Stanford

University (1998).

wavelength-modulation spectroscopy for …

Documents