February 2006 Chuck DiMarzio, Northeastern University 10842-2-1

ECEG398 Quantum Optics Course Notes

Part 2: Thermal Imagers

Prof. Charles A. DiMarzio

and Prof. Anthony J. Devaney

Northeastern University

Spring 2006

February 2006 Chuck DiMarzio, Northeastern University 10842-2-2

Thermal Fields

• Mean Number (Text Eq.2.141):

• Std. Deviation (Text Eq. 2.149):

• Energy Density (Text Eq. 2.151):

1

1/

Tkh Ben

2nn

1

14/3

3

Tkh Bec

hnhU

February 2006 Chuck DiMarzio, Northeastern University 10842-2-3

Single-Mode Mean

100 200 500 1000 2000 5000 10000lambda , Wavelength , nm1. 1032

1. 1026

1. 1020

1. 1014

1. 108

0.01

nbar :Red Solid : T300 K,Grn Dash : 5000 K

February 2006 Chuck DiMarzio, Northeastern University 10842-2-4

100 500 1000 5000 10000 50000100000.lambda , Wavelength , nm

0.00001

0.001

0.1

SNR :Red Solid : T300 K,Grn Dash : 5000 K

Single Mode SNR

Upper Trace is Poisson

0.1mm

February 2006 Chuck DiMarzio, Northeastern University 10842-2-5

Spectral Radiant Exitance

Watch the Units:

Md

dM

d

dMM 22

M

c

d

dMc

d

dM

d

d

d

dMM

22

U

cnhM

February 2006 Chuck DiMarzio, Northeastern University 10842-2-6

Signal & Noise Radiant Exitance

100 200 500 1000 2000 5000 10000lambda , Wavelength , nm0.01

10

10000

1. 107

1. 1010

1. 1013

Spect . Rad . Ex., Wm^3:Red Solid : T300 K,Grn Dash : 5000 K

cnhM

cnnhM noise2

)(

February 2006 Chuck DiMarzio, Northeastern University 10842-2-7

Lambert’s Law

A

A’

February 2006 Chuck DiMarzio, Northeastern University 10842-2-8

Spectral Radiance

x

y

z

d

d

February 2006 Chuck DiMarzio, Northeastern University 10842-2-9

Black-Body Equation (1)

10-1

100

101

102

10-10

10-5

100

105

1010

, Wavelength, m

M,

Sp

ectr

al

Ra

dia

nt

Exi

tan

ce,

W/m

2/

m

February 2006 Chuck DiMarzio, Northeastern University 10842-2-10

Black Body Equations (2)

10-1

100

101

10210

-10

10-5

100

105

1010

, Wavelength, m

M,

Spe

ctra

l Rad

ian

t Exi

tan

ce, W

/m2 /

m

T=300k

500

1000

2000

5000

10000

February 2006 Chuck DiMarzio, Northeastern University 10842-2-11

Solar Irradiance on Earth

0 200 400 600 800 1000 1200 1400 1600 1800 20000

500

1000

1500

2000

2500

3000Data from The Science of Color, Crowell, 1953

, Wavelength, nm

E

, S

pe

ctra

l Irr

ad

ian

ce,

W/m

2/

m

Exoatmospheric filename=m1695.mSea Level

5000 K Black Body Normalized to 1000 W/m2

6000 K Black Body Normalized to 1560 W/m2

February 2006 Chuck DiMarzio, Northeastern University 10842-2-12

Typical Outdoor Radiance Levels

VisibleNear IR

Mid IRFar IR

Atmospheric Passbands

Ultraviolet6000K Sun6.9 G Lux

SunlitCloud6.9 k Lux

BlueSky 300K

night sky

February 2006 Chuck DiMarzio, Northeastern University 10842-2-13

Thermal Imaging

M

/Del

ta T

10-1

100

101

1020

.5

1

T = 300 K

10-1

100

101

1020

2

4

6

, Wavelength, m

M

/D

elta

TT = 500 K

February 2006 Chuck DiMarzio, Northeastern University 10842-2-14

Etendue

Viewedby Pixel

PixelArea

NA of Detector Lens

NA ofObjective

Area of PRC

NA ofPRC

A isConstant

2112 NA

2NA

Single Mode

dNA /2A

A

dAdLP

February 2006 Chuck DiMarzio, Northeastern University 10842-2-15

Spectral Flux (Power) Per Mode

100 200 500 1000 2000 5000 10000lambda , Wavelength , nm1. 1015

1. 1012

1. 109

1. 106

0.001

1

Pl, Wmmode :Red Solid : T300 K,Grn Dash : 5000 K

February 2006 Chuck DiMarzio, Northeastern University 10842-2-16

Probability DistributionsLaserMode

ThermalMode

ManyThermalModes

Re(E) Im(E) |E| |E|2 n

(Delta) (Delta) (Poisson)

(Gaussian) (Rayleigh) (Exponential)

(Bose-Einstein)

(Poisson)SummedonDetector

February 2006 Chuck DiMarzio, Northeastern University 10842-2-17

Detected Photons (Signal & Bkg)

B

Acnn qDet

1

Ps

PBKG

BPF

Preamp AmpFilter

PNoise

q

February 2006 Chuck DiMarzio, Northeastern University 10842-2-18

Detector Examples: Spectral Photon Radiance

10464-3-32

February 2006 Chuck DiMarzio, Northeastern University 10842-2-19

Detector Examples: Total Background Power

10464-3-31

February 2006 Chuck DiMarzio, Northeastern University 10842-2-20

Noise Photons (Bkg. Limited)

B

Acnq

1

B

Acnn qDet

1

February 2006 Chuck DiMarzio, Northeastern University 10842-2-21

Noise-Equivalent Power

Bh

LA

Bh

Pn qqDet

Bh

LAq

Bh

NEPq

qq

q

LABh

Bh

LABhNEP

1

February 2006 Chuck DiMarzio, Northeastern University 10842-2-22

Detector Examples: NEP

10464-3-3

February 2006 Chuck DiMarzio, Northeastern University 10842-2-23

D-Star

qq

ABLhLABhNEP

LhD q

*

max *D

ABNEP

February 2006 Chuck DiMarzio, Northeastern University 10842-2-24

Detector Examples: Detectivity, D*

10464-3-34

February 2006 Chuck DiMarzio, Northeastern University 10842-2-25

Estimating the Temperature

B

Acnn qDet

1

1

1/

Tkh Ben

Ce

Tkh

e

dT

ndTkh

B

Tkh

B

B

2/

2/

1

TB

ACcn qDet

1

February 2006 Chuck DiMarzio, Northeastern University 10842-2-26

Noise-Equivalent Delta T

B

Acnq

1

TB

ACcn qDet

1

TNEB

ACcq

1

February 2006 Chuck DiMarzio, Northeastern University 10842-2-27

Calculating NET

TNEB

ACc

B

Acn qq

11

C

n

cA

BTNE

q

T=300Kelvin, q=0.8, B=30 Hz, =1m, A=(10mm)2, =0.1 sr

7 X 106 Photons/Kelvin NET=5 mKelvin