Ultra-high-speed tomographic digital holographic

velocimetry in supersonic particle-laden jet flows ‡

N A Buchmann1, C Atkinson1 and J Soria1

Laboratory for Turbulence Research in Aerospace & Combustion (LTRAC),

Department of Mechanical and Aerospace Engineering, Monash University (Clayton

Campus), Melbourne, VIC 3800, Australia.

E-mail: nicolas.buchmann@monash.edu

‡ The final publication is available at IOPScience via http://iopscience.iop.org/0957-0233/24/2/024005/

Ultra-high-speed tomographic holography in supersonic particle-laden jets 2

Abstract. Ultra-high-speed tomographic digital holographic velocimetry is used to

measure the three-component, three-dimensional (3C3D) velocities and trajectories

of micron-sized particles in a supersonic underexpanded jet flow. In high-speed

digital in-line holography the depth resolution or depth-of-field is severely restricted

by the limited resolution of the digital recording array, which leads to significant

elongation of the reconstructed particles in the depth direction. It is shown that

by applying tomographic digital holography this limitation imposed by the high-

speed recording array is relaxed and that the accurate reconstruction of 3D particle

intensities is possible without the depth-of-field problem. This method is demonstrated

by measuring 110 µm solid particles suspended in a “mildly underexpanded” jet with

a nozzle pressure ratio (NPR) of 2.0. The interference pattern produced by both the

suspended particles and the density gradient field are simultaneously recorded by two

digital high-speed cameras at a frame rate of 500,000 fps with an exposure time of

250 ns. Individual object fields are reconstructed by tomographic holography and the

velocity of the micron-sized particles is analysed by cross-correlation Particle Tracking

Velocimetry (PTV). The accuracy of the particle velocity measurements is estimated

to be within 5 m/s or approximately 4.5% of the particle velocity. In addition, the

method is used to study the particle-flow interactions by means of coherent imaging,

which reveals a complex interaction between the micron-sized particle and the flow

structure of this high-speed 3D unsteady turbulent particle-laden flow.

Keywords: Tomographic digital holographic PIV, PTV, volumetric 3D particle recon-

struction, supersonic impinging jet, cold gas-dynamic spray.

1. Introduction

Supersonic particle-laden jet flows are found in a number of applications ranging from

rocket engines, particle impactors [8] and needle-free-dug delivery [33] to cold-gas-

dynamic spray processes [31]. In the cold gas-dynamic spray process, small solid

particles (1 − 50µm) are accelerated to high velocities to form a solid deposit or

coating on a substrate upon impaction. By accelerating a gas flow through a supersonic

nozzle and entraining the particles in the flow field, particle velocities in the order of

300−1200m/s can be achieved [31]. The cold gas-dynamic spray process is characterised

by a supersonic jet impinging onto a flat surface, which produces complex fluid dynamic

phenomena that are dominated by the intrecate shockwave structure of the jet [10].

The optimal performance and quality of the coating process largely depends on the

particle impact velocity and impact angle [31]. The trajectories of the spray particle are

a complicated function of the fluid dynamics of the impinging supersonic jet flow and for

example are affected by the highly unsteady and turbulent nature of the supersonic gas

flow and its complex shock and expansion wave structure. To date the understanding

of this complex particle-laden flow and its relation to cold gas-dynamic spray is severely

limited due to the lack of quantitative experimental data such as the measurement of

particle impact velocity and particle impact angle.

Ultra-high-speed tomographic holography in supersonic particle-laden jets 3

Current predictions of the impact velocity, location and angle of the coating

particles are based on either one-dimensional isentropic flow or Reynolds Averaged

Navier-Stokes equations [14, 18], providing only mean quantities that are fundamentally

inappropriate for the prediction of the particle dynamics. Understanding and prediction

of the true particle dynamics requires knowledge of the three-dimensional (3D) time-

dependent unsteady turbulent flow field, which has historically been difficult to measure

due to the very small time-scales involved in these supersonic particle-laden impinging

jets.

Previous studies [17, 37] used shadography and Schlieren photography to investigate

the effect of particle loading and particle size in underexpanded free jets and found

that the Mach disk moves upstream towards the the nozzle exit as the particle

loading increases. Additionally, [37] performed joint particle velocity measurements by

means of a modified laser doppler system and numerical simulations. Their results

showed a large mismatch between the numerical and experimental results, which

were explained by the presence of particle bow shocks (see Section 4) that alter

the particle drag and are not included in any of the previous numerical simulations.

More recently, [5] performed high-speed particle shadowgraphy and coherent imaging

measurements in an underexpanded free jet to visualize the particle-flow interaction

(see ”http://www.youtube.com/watch?v=dYZ8rNXgsSQ” for more details), and clearly

showed the presence of these bow shocks and their interaction with the jet shock

structure.

In order to gain a better understanding of the complex fluid-particle interaction in

these high energy, 3D turbulent flows, well-resolved experimental data in both time and

space are required. Such data is difficult to obtain due to the large dimensional gap

between the size of these very small particles (O(10−5)m) and their very large velocities

(O(103)m/s). The need to resolve the three-dimensional displacement associated with

these particles over a length scale comparable with their size, the field-of-view and the

resolution of the imaging sensor requires the use of high-speed imaging and particle

tracking [20] or reconstruction systems that are at the limit of today’s imaging and

measurement technology.

One popular mean of recording 3D particle location and velocity is via holography.

Initial experiments using holographic recording for three-component, three-dimensional

(3C-3D) velocimetry were performed using film-based recording [12, 4, 19]. However

the complexity associated with recording and optical reconstruction of the holograms

has lead to a growing preference for the use of digital holographic recording [16, 21, 23],

particularly for the study of micro-scale flows [38], micro-droplets [28, 25] and small-scale

flow oscillations [36]. The advantages of digital holography over holographic film-based

recording are the short exposure times and high frequencies that are necessary for high-

speed (∼ kHz) time-resolved [29] or in the present case ultra-high-speed (∼ MHz, [34])

measurements.

The present paper demonstrates an ultra-high-speed (up to 1,000,000 fps) Coherent

Laser Imaging (CLI) and digital in-line holography technique capable of simultaneously

Ultra-high-speed tomographic holography in supersonic particle-laden jets 4

measuring the turbulent density gradient field and the 3D particle locations and

velocities. Similar to shadowgraphy or Schlieren, in CLI the density gradient field

produces a refraction pattern of the collimated light source while the micron-sized

particles form a Fresnel diffraction pattern that can be numerically reconstructed

to obtain particle sizes, locations and velocities. To overcome the large depth-of-

field problem commonly associated with digital in-line holography, a combination of

magnified digital in-line holography [25] and tomographic holographic particle image

velocimetry (TDHPIV) [40] is used. The principle of TDHPIV has previously been

demonstrated by the authors [40] on the basis of synthetic particle fields and particle

impregnated glass plates. In the present case only low particle seeding densities are

considered, such that the trajectories of individual particles can be unambiguously

determined. Such low seeding density PIV measurements are commonly referred

to as particle tracking velocimetry (PTV) [1], however the term TDHPIV will be

used throughout this paper in order to remain consistent with [40]. In tomographic

holography, digital in-line holograms are recorded from different viewing directions

analogous to tomographic PIV (TPIV) [7, 2] to remove the depth-of-field constrain

and to obtain the reconstructed 3D intensity distributions of the particle field. The

resulting particle fields can then be analysed by means of 3D cross-correlation based

PIV or in present case PTV to obtain the 3D velocity of individual particles. The

present investigation represents the first practical application of this TDHPIV method

to experimental fluid flow measurements.

The paper is organised as follows. The first part reviews the principle of multi-

camera tomographic digital in-line holography and discusses the depth-of-field problem

as it pertains to ultra-high-speed magnified digital in-line holography. Following a de-

scription of the supersonic jet facility and the optical setup a calibration procedure

suitable for magnified multi-camera in-line holography is introduced. Next, the CLI

measurements of the turbulent supersonic underexpanded jet flow and its particle-fluid

interaction are presented. This is followed by the TDHPIV measurements of 3D particle

velocities and trajectories and a discussion of the measurement uncertainty.

2. Multi-Camera (Tomographic) digital in-line Holography

2.1. Depth-of-Field Problem

At present the greatest impediment to the use of digital holography is the limited

effective resolution or depth encoding normal to the hologram plane. As a consequence

in digital particle holography it is generally difficult to accurately estimate the

depth location associated with an individual particle. In terms of three-dimensional

holographic intensity reconstruction this limited depth encoding manifests as an ellipsoid

or cigar like reconstruction of what should instead be a spherical particle. The hologram

normal elongation depends on the effective aperture angle and in practical cases can be

Ultra-high-speed tomographic holography in supersonic particle-laden jets 5

several orders of magnitude larger than the true particle diameter [42].

The effective resolution or elongation of a reconstructed particle τ in the hologram

normal direction can be derived from the intensity spread around a reconstructed particle

due to the diffraction through the hologram and the defocusing about the particles true

location [26] and can be expressed as

τ =λ

Θ2, (1)

where λ is the wavelength and Θ the aperture half angle. In in-line holography the

scattered light (assuming Mie scattering) is predominantly contained in the forward

scattering lobe [11], and as such can limit the effective half angular aperture of the

hologram to

Θp =λ

d, (2)

where d is the particle diameter. For example, a particle of 45 µm diameter and a

wavelength of 532 nm results in a particle elongation of τp ≈ 3.8 mm or approximately

84d.

In digital holography Θp is often further limited by the extent to which the CCD

or CMOS chip under-samples the true interference fringe spacing. The spacing of these

fringes is not band-limited and as such the depth information is limited by the resolution

of the recording media △x (i.e. pixel size) [23]. In this case the hologram can be referred

to as “resolution-limited”, where the effective aperture angle is given by

Θr = tan−1

(

λ

2△x

)

. (3)

In digital high-speed holography the resolution limit is of particular concern due to

the very large pixel size of the digital high-speed recording array. For example, for

△x = 66.3 µm (Shimazu HPV-1) the estimated depth-of-field is τr = 33.1 mm.

The influence of this resolution limit and associated depth-of-field problem in

digital in-line holography can often be mitigated through the use of magnified or

microscopic holography [35, 25]. By placing a lens or microscope objective in front

of the camera, the interference fringes are magnified such that the effective resolution

of the hologram is increased. Of course, this magnification also reduces the field-of-view

of the measurement and limits the upper bandwidth of the recorded hologram. In such

cases the hologram may become “size-limited” with an angular aperture half angle of

Θs = tan−1

(

N△x

2MZ

)

, (4)

where N is the number of pixels of size ∆x across the digital recording array, Z is the

distance from the object plane to the hologram and M the magnification factor. For

a digital high-speed imaging array with N = 312, △x = 66.3 µm, Z = 40 mm and

M = 10, the “size-limited” depth-of-field is τs ≈ 0.8 mm.

In in-line holography the ability to accurately resolve the depth location of a

given particle may be limited by any one of these effects depending on the particle

Ultra-high-speed tomographic holography in supersonic particle-laden jets 6

size, the pixel resolution and size of the digital recording array as shown in Figure

1. For ultra-high-speed applications the limited sensor resolution and large sensor size

severely restrict the depth resolution of such measurements. In the above example the

limiting factor is the sensor resolution △x if no magnification is used. By increasing the

magnification to M ≈ 3 the “resolution-limited” depth-of-field reduces rapidly below

that of the “diffraction-limited” depth-of-field such that the depth resolution is now

limited by the particle size. For large magnification factors M > 20 the field-of-view

reduces significantly and the hologram becomes “size-limited”

1 5 10 15 20 25 30

1

3

5

7

9

M

depth-of-�eld

[mm]

resolutionlimited

di ractionlimited

sizelimited

τr

τs

τp

Figure 1. Variation in depth-of-field as function of the magnification factor M in

the limit of particle diffraction (Eq. 2), sensor resolution and sensor size (Eq. 3 & 4);

N = 312, △x = 66.3 µm, Z = 40, λ = 532 nm.

2.2. Principle of Tomographic Holography

The theory and detailed procedures for TDHPIV are described in [39, 40]. A brief

summary of the procedure as it applies to the present experiment is provided here

for completeness. The process can be applied to either in-line or off-axis holography,

however only in-line holographic recording will be considered in this paper. The optical

set-up for in-line holography has been detailed in [6, 42, 28], the set-up of the current

experiment is discussed in section 3.2.

TDHPIV overcomes the holographic depth-of-field problem by combining

information from two or more instantaneous holographic recordings of a particle seeded

flow at different viewing angles and by using the fact that the particle elongation in each

hologram extends in a different direction. Since the reconstructed particle ellipsoids have

a unique major axis of rotation that remains centered about the true centroid of each

particle, an approximation of the actual particle can be determined from the volume

intersection of each ellipsoid as shown in Figure 2.

Ultra-high-speed tomographic holography in supersonic particle-laden jets 7

Hologram 1

x1

z1

x

z

x2

Hologram 2

Measurement volume

z2

Figure 2. Schematic of intersection of elongated particle reconstructions from multiple

holograms. Gray ellipsoids represent the particles reconstructed from hologram 1;

white ellipsoids are particles reconstructed from hologram 2.

In tomographic holography generally an in-line laser beam for each holographic

recording is aligned normal to the hologram plane of each camera and arranged such

that each beam intersects the measurement volume. Holograms of a calibration object

are then recorded for each system and used to determine a mapping between the global

coordinates of the measurement volume and the local coordinates of each camera k of

the following form

~xk = fik( ~X), (5)

where fik( ~X) represents the mapping from global coordinates to the local coordinates

of the hologram k. The mapping function fik for a magnified holography system is

obtained in section 3.3.

Digital intensity distributions IH(x, y, 0) associated with the interference between

the object wave (scattered from the particle field) and the reference wave (laser beam)

are simultaneously recorded on the electronic sensors in each camera, such that intensity

and phase information associated with each particle is simultaneously recorded in

a digital hologram from each viewing angle. The complex object amplitude field

U(x1k, x2k, x3k) associated with the 3D particle distribution as seen by each hologram

k is then reconstructed relative to the local hologram coordinates using the Rayleigh-

Sommerfeld diffraction formula [9],

U(x1k, x2k, x3k) =1

iλ

∫

Σ

IH(x1k, x2k, 0)exp(ikr01)

r01× cos(~n, ~r01)dxdy, (6)

where λ is the wavelength, k the wavenumber, r01 is the distance from a point of

Ultra-high-speed tomographic holography in supersonic particle-laden jets 8

the sensor (x, y, 0) to a point in the reconstruction plane (x1k, x2k, x3k) and ~n is the

outward unit normal vector of the diffraction surface. For the dimensions used in digital

holography cos(~n, ~r01) ≈ 1, [23] and Eq. 6 is evaluated as the convolution between

IH(x, y, 0) and the diffraction kernel

h(x1k, x2k, x3k; x, y) =exp(ikr01)

iλr01, (7)

such that the complex object amplitude at any point in the reconstruction is given by

U(x1k, x2k, x3k) =

∫

Σ

IH(x, y, 0)h(x1k, x2k, x3k; x, y)dxdy. (8)

This convolution can be efficiently performed in Fourier space such that the complex

amplitude field is evaluated as

U(x1k, x2k, x3k) = F−1 [F [IH(x, y, 0)]F [h(x1k, x2k, x3k; x, y)]] . (9)

In order to minimize the influence of the virtual image associated with the in-line

holographic reconstruction, the reconstruction is performed using an iterative filter as

introduced by [27]. The reconstructed intensity field associated with each hologram is

then given by Ik(~xj), where the intensity is given by the product of the complex object

amplitude field and its complex conjugate,

Ik(~xk) = U(~xk)U∗(~xk). (10)

Within the numerical algorithm, the z-coordinate position of the reconstructed image

is determined from the non-dimensional parameter

α = (N△x2/λZ)1/2, (11)

defined as the square-root of the ratio between the“size-limited” and “resolution-limited”

aperture half angle. For α > 1 the recorded hologram is “resolution-limited”, while for

α < 1 it is “size-limited”. The current reconstruction algorithm performs best for α ≈ 1,

[42].

Once reconstructed, the intensity field associated with each hologram can be

represented in terms of their location in the global coordinates by

Ik(~xk) = Ik(fik( ~X)). (12)

In practice this mapping is used to re-interpolate the intensity field reconstruction

of each hologram onto a common discretised grid in the global domain. In order

to remove the background intensity associated with each reconstruction the mapped

volumes are thresholded such that the remaining non-zero intensities closely correspond

to the true particle locations. The tomographic reconstruction of the M holograms is

then performed by taking the product of the M mapped fields as given by

I( ~X) =

M∏

k=1

Ik(fik( ~X)), (13)

such that only the overlapping regions of non-zero reconstructed intensities remain,

analogous to the multiple line of sight estimation used in accelerated TPIV [2]. The

Ultra-high-speed tomographic holography in supersonic particle-laden jets 9

resulting volumes can then be analysed using either PTV or PIV, without the errors

associated with the significant depth-of-field uncertainty.

Naturally the number of holograms used and the angular separation between

them influences the shape of the reconstructed particles. The influence of these

parameters on the particle shape, intensity and the generation of reconstruction artefacts

due to overlapping ellipsoids (ghost particles) has been investigated using synthetic

reconstructions [3]. For moderate particle densities of 1012 particles per m3 the results

show a diminishing improvement when more than three holograms are used with optimal

angles of 45 to 90 between each. For the present investigation only two ultra-high-speed

cameras are used and the measurements are therefore limited to relatively sparsely

seeded volumes (i.e. 6 0.4 · 1012 particle per m3). The maximum particle density for a

three-camera system is approximately 4 · 1012 particles per m3 [3].

2.3. Coherent Laser Imaging (CLI)

Coherent laser imaging is a method to visualise the density variations within a

compressible flow similar to Shadowgraphy or Schlieren imaging. However, unlike these

two techniques, CLI is based on monochromatic coherent laser light illumination and

uses an experimental setup identical to digital in-line holography. The collimated laser

beam is passed through the compressible flow field and the density changes within the

flow refract the light and cause a variation of the light intensity in the image plane where

a coherent shadowgraph image is formed. From geometric optics it can be shown that

the recorded light intensity variations are directly proportional to the second derivative

of the density field, [15], which is integrated along the line-of-sight. The sensitivity of

the CLI system, i.e., the magnitude of the recorded intensity variations, is adjusted

by varying the distance Z between the object and image plane, which is analogous to

changing the value α of the holographic system.

In an underexpanded jet, strong density gradients can occur across shocks, which

cause diffraction rather than refraction of the laser light due the large difference in re-

fractive index. In these cases an additional contribution to the coherent shadowgram is

light diffraction [30] that appears as dark bands in the recorded images (see Fig. 9 for

example).

3. Experimental Setup

3.1. Supersonic Underexpanding Jet Facility

The particle-laden supersonic jet facility is shown in Figure 3. The setup

allows the controlled injection of micron-sized particles into the gas flow before

entering a converging nozzle of diameter D = 2 mm and a nozzle area

ratio, defined as the nozzle inlet to nozzle exit area of 400. The gas flow

through the nozzle is characterised by the nozzle pressure ratio defined as

Ultra-high-speed tomographic holography in supersonic particle-laden jets 10

Lnozzle

Nozzle

Pressure Regulator

Particle Entrainment

nozzle inlet

Figure 3. Schematic of the particle-laden supersonic jet facility. Note that the

depicted nozzle shape corresponds to actual shape of the nozzle.

NPR = P0/P∞, where P0 is the static pressure upstream of the nozzle and P∞ is

the ambient pressure. For NPR > 1.9 the flow in the nozzle becomes choked and

underexpanded at the nozzle exit. Gas flow in the nozzle up to a nozzle pressure ratio

of 7.5 is provided through a compressed air line. The particles are introduced via a

cyclone particle seeder and suspended co-axially into the gas flow via a second air line.

The solid particles used for the current investigation are in the form of a nylon powder

(Vestosint 1301) with a volume weighted mean diameter of dp = 110 µm and a specific

density of ρp = 1.06 g/cm2 (Table 1).

The response of the particles to a sudden change in flow velocity, for example across

a shock or compression wave can be expressed by the particle response time τp, which

can be derived from the generalised Stokes number, [22]. For compressible flow and

non-Stokesian particles, the generalised Stokes number, defined as the ratio of τp to the

characteristic time scale of the flow τf = D/U is given as

Stk = Stkvisc. ·Ψ(Kn) · Φ(Rep), (14)

where U is the velocity at the nozzle exit, Stkvisc. = ρpd2pU/18µD the Stokes number

under the assumption of linear Stokes drag (i.e. Rep < 1), Φ(Rep) the non-Stokes

drag correction factor for large particle Reynolds numbers [13] and Ψ(Kn) ≈ 1 the

Cunningham slip correction factor [8]. The particle Reynolds number is based on the

particle diameter and the gas velocity at the nozzle exit. Assuming choked flow at the

nozzle exit (U = 313 m/s) and a particle diameter of 110 µm the particle response time

is τp = 3.67 (Tab. 1). This response time is approximately three orders of magnitude

larger than the characteristic time scale of the flow, which indicates a considerable lag

time in the particle response across a shock wave.

Ultra-high-speed tomographic holography in supersonic particle-laden jets 11

Table 1. Particle Properties: volume weighted mean diameter, 10%- and 90%-

percentiles of the size distribution, density, Reynolds number, generalised Stokes

number and particle response time.

dp[µm] p10%[µm] p90%[µm] ρp[kg/cm3] Rep Stk τp[ms]

110 64 188 1.06 2090 574 3.67

Nd:YAGlaser

ND

L1

L2

L3

AP

M1 M250:50 BS

M2

Camera 1

Camera 2

Jet nozzle

lens

focal plane

X1 X3

X2

x3,1

x1,1

x2,1

x3,1

x1,1 x

2,2

working

distance

Figure 4. Schematic of the optical setup in top-view used for the high-speed

tomographic holographic measurements. The jet nozzle is located at the intersection

of the two laser beams and is pointing downwards in the X2 direction.

3.2. Optical Setup

The optical setup of the magnified tomographic in-line holography system is shown in

Figure 4. The illumination consists of a 200 mW continuous single-mode wave diode

pumped laser (CrystaLaser CL532-300-S) with a wavelength of 532 nm and a coherence

length of more than 300 m. After passing through a set of neutral density filters (ND,

0.02), the laser beam is expanded and collimated through a series of spherical lenses

(L1, L2, L3) before passing through an aperture (AP ) to remove the low intensity regions

of the Gaussian beam profile. The diameter of the final expanded collimated beam is

approximately 22.5 mm. Subsequently, the beam is divided into two beams of equal

intensity through a 50:50 beam splitter (BS) and directed via mirrors (M1,M2) through

the center line of the jet nozzle onto the recording plane.

The digital imaging and recording system consists of two digital ultra-high-speed

cameras (Shimadzu HPV-1) capable of recording 102 consecutive images at a frame rate

Ultra-high-speed tomographic holography in supersonic particle-laden jets 12

of up to 1,000,000 fps with 10-bit intensity dynamic range. The cameras have a sensor

size (N × M) of 312 px × 260 px and a pixel pitch of △x = 66.3µm. In order to

magnify the hologram plane a lens of 105 mm focal length (Micro Nikkor) is mounted

to each camera separated by an extension ring and an extendable bellow. The main

features of this arrangement are its adjustable magnification (M = 1−4) and extended

working distance (i.e. location of hologram plane in front of lens) of approximately 100

mm. A large working distance is required to insure that the flow field and particularly

its acoustic field remain undisturbed by the instrument and is desirable to minimises

the risk of particles depositing on the lens during recording. Note that a traditional

microscope objective of similar magnification only has a working distance of several

millimetres. The imaging system is located on a three-axis micro-meter stage allowing

it to be traversed along and normal to its optical axis. This means that the distance of

the hologram plane relative to the nozzle axis Z can be varied, allowing various values

of α and adjustments of the sensitivity and depth-of-field of the CLI and holographic

system.

The exact magnification factor of the magnified holography system is determined

by recording a calibration grid (1 mm × 1 mm spacing) located at the focal plane (see

Fig. 5a). The magnification factor is defined as the ratio of the line segment between

two intersecting grid lines in image space and its true spacing of 1mm. The line spacing

is obtained by determining the intersection of each grid line in the image through cross-

correlation with a template image (i.e. cross). Done this way, the magnification averaged

over all grid points is M = 2.97 for the first and M = 2.95 for the second camera. This

corresponds to an effective resolution of 22.32 µm/pixel and 22.48 µm/pixel for the first

and second camera, respectively. As a consequence, the smallest resolvable scale (i.e.

smallest resolvable particle size) is approximately 45 µm. The common field-of-view for

both cameras is 2.9D × 3.4D where the longer side of the camera chip is orientated in

the streamwise direction. At this magnification the “resolution-limited” depth-of-field

(Eq. 3) is τr = 3.77 mm.

The image distortions introduced by the lens system are assessed by the variation of

the magnification factor across the image plane as shown in Figure 5b. The magnification

factor in both cameras varies by approximately ±0.5% from the center of the image

towards the edges. This corresponds to a variation in the recorded grid line spacing

of approximately ±0.25 pixel or a change in magnification of 0.11µm/pixel across the

image. In comparison, the grid lines have a width of about 1 pixel and the accuracy by

which they can be detected is approximately 0.1 pixel. The variation in magnification

can be accounted for by appropriate interpolation of the recorded hologram images, but

is ignored here for simplicity.

3.3. Calibration Procedure

As outlined in Section 2 the reconstruction of the 3D particle intensity volume requires

a mapping from the global Cartesian coordinates of the measurement volume, with

Ultra-high-speed tomographic holography in supersonic particle-laden jets 13

-0.5%

-0.4

%

-0.4% -0.3%

-0.3%

-0.3

%

-0.2

%

-0.2%

-0.2

%-0.2%

.1%

-0.1%

.1%

-0.1%

-0.1%

0%

0%

0%

0%

0%

0.1%

0.1%

.1%

0.1%

0.2%

0.2

%

0.2%

0.2

%

0.2%

3%

0.3%

0.4% 0.4

%

0.5

%

X (px)

Y(p

x)

100 150 200 250

50

100

150

200

250

(a) (b)

Figure 5. (a) Image of the calibration grid used to determine the magnification

factor of the magnified holography system; (b) Variation in magnification factor due

to optical distortions introduced by the lens system.

coordinate directions ~X = Xj = (X1, X2, X3) to the local coordinates of each camera

k with coordinate directions ~xk = xik = (x1k, x2k, x3k) as illustrated in Figure 6. A

general tomographic holography calibration method for a lens-less optical system has

been described previously in [40]. Here, this procedure is adapted for the current

experimental conditions.

Assuming a constant magnification and no lens distortions (see Sec. 3.2) the

mapping from the global coordinate system to any arbitrary coordinate in the local

camera coordinate system can be represented as a linear transformation of the following

form

xik = (aik,jXj −Oik) · M, (15)

where aik,j is the second-order transformation tensor for camera k, Oik the distance of

the local coordinates to the origin of the global coordinate system and i, j = 1, 2, 3.

The mapping function in Eq. 15 is determined using the following procedure: A

single pinhole (50 µm) positioned on a three-axis micrometer stage is traversed along the

global X1 and X2 direction by a know distance L. At each location the portion of the

laser beam penetrating through the pinhole is recorded and the images are subsequently

combined to form the vertices of the global coordinate system as shown in Figure 7a.

The reconstruction of this calibration image at the recording plane (x3,k = 0) can be

seen in Figure 7b from which a rotation of the camera by the angle α around the vertical

axis is clearly visible due to the reduced spacing in horizontal direction. Subsequently,

the individual vertices of the coordinate system are identified by cross-correlation with

a template marker to determine their location to sub-pixel accuracy within the local

coordinates (x1,k, x2,k) and for each camera. As described in [40] the distance between

Ultra-high-speed tomographic holography in supersonic particle-laden jets 14

the vertices in the local coordinate system provides the components of the unit vector

xik in the direction of the global coordinates Xj as illustrated in Figure 8. Since the true

spacing L between the vertices in the global coordinate system is known, its mapping in

the global coordinate system can be obtained by a simple magnitude relationship. As

an example for the X1 direction, this relation ship reads

|L · X1 + 0 · X2 + 0 · X3| = |a1k,1x1k + a2k,1x2k + a3k,1x3k| ·M−1, (16)

where the components a1k,1 and a2k,1 of the global X1 axis in the x1k and x2k direction

are determined from the calibration image. The component a3k,1 in the camera normal

direction x3k is obtained as

a3k,1 = ±√

L2M2 − a21k,1 − a2

2k,1. (17)

The sign of the normal component a3k,1 can either be determined from the recording

geometry or by translating the pinhole in the global X3 direction [40]. The normal

component a3k,2 along the X2 direction, which is often more difficult to determine can

CMOS array

x3k

x1k

x2k

X3

X1

X2

Projection Lines

Reconstruction Plane

traversingPinhole

α

Figure 6. Schematic of the global and local coordinate system and the calibration

procedure.

X1

X2

(a)

X1

X2

(b)

L

L sinα

Figure 7. Detail of the calibration image: (a) recorded pinhole pattern along the

global X1 and X2 direction; (b) reconstruction of the pinhole patter at the recording

plane x3k = 0.

Ultra-high-speed tomographic holography in supersonic particle-laden jets 15

then be obtained from the vector dot product x1k · x2k = 0 as

a3k,2 = −a1k,1a1k,2 + a2k,1a2k,2a3k,1

. (18)

Finally, the mapping along the global X3 direction is determined from the vector cross

product as

x3k = x1k × x2k. (19)

The accuracy of this calibration procedure was perviously assessed by [40] and was

found to be accurate within 0.1% of the marker spacing. In the present case this corre-

sponds to approximately 1 µm. When the inaccuracies of the pinhole translation (±2.5

µm) are included the uncertainty of the overall calibration procedure is ±3.5 µm or 0.16

pixel. A further improvement in calibration accuracy can be achieved by replacing the

pinhole translation step with a single three-hole aperture to avoid the errors due to the

translation of the single pinhole.

cameraplane

x3k

x1k

x2k

X1

X2

a1k,1

x1k

+ a2k,1

x2k

+ a3k,1

x3k

L X1

+ 0X2

+ 0X3

Figure 8. Schematic projection of global coordinates Xj to camera coordinates xik.

4. Results: Coherent Laser Imaging and digital in-line Holography

4.1. Visualisation of the Gas Phase

To interpret the experimental results in the next sections it is necessary to first consider

the structure of the underexpaded jet. Only a brief explanation, adequate for the present

work, is provided here with a more detailed description available in [32, 24]. For this

purpose, the top row in Figure 9 shows a sample of the the recorded CLI images of the

underexpanded particle-laden jet for different nozzle pressure ratios (NPR). For NPR

> 1.9 the flow at the exit of the converging nozzle reaches sonic speed (Mach number,

Ultra-high-speed tomographic holography in supersonic particle-laden jets 16

NPR = 2.0

α = 2.71

NPR = 3.0

α = 2.71

NPR = 4.0

α = 3.13

NPR = 5.0

α = 3.84

NPR = 6.0

α = 3.84

Figure 9. Coherent Laser Imaging sequence of 110 µm particles suspended in an

underexpanded jet at varying NPR recorded at a frame rate of 500,000 fps and 250

ns exposure time. (top) recorded hologram; (middle) hologram after background

subtraction; (bottom) reconstruction of the hologram at the jet centre axis. Flow is

from top to bottom and particle locations are identified by circles.

Ma = 1) and the pressure at the nozzle exit increases above ambient pressure. Outside

the nozzle the gas pressure is restored to ambient pressure through a series of expansion

and compression waves that lead to an acceleration and deceleration of the flow within

the first “shock cell”. This process repeats itself several times (see Fig. 9, NPR =

2 & 3) before the jet core reaches subsonic speed. For higher NPRs the compression

waves merge and form a conical or oblique shock at the end of the first shock cell (i.e.

NPR = 3 & 4), while for NPR & 4 a circular normal shock or Mach disk forms at

the center line (e.g. NPR 5-6). Behind the Mach disk the flow is subsonic, while the

surrounding annular flow remains supersonic. For NPRs < 3.8 the flow is said to be

Ultra-high-speed tomographic holography in supersonic particle-laden jets 17

Shock ‘cells’slip line

Oblique shock

Normal shock

(mach disk)

, mixing region

re!ected

oblique shock

intercepting

oblique shock

p0

poo

Figure 10. Schematic of the “highly underexpanded” jet.

“mildly underexpanded” and above that the flow is considered “highly underexpanded”

[32]. A schematic description of the flow structure of the “highly underexpanded” jet is

shown in Figure 10.

The middle row of Figure 9 shows the pre-processed holograms/CLI images after

background subtraction. From these images both the density variation of the flow field

and the diffraction patterns of the particles are observed. As the NPR increases the

fluctuations in the density field increase as can clearly be seen in the first two rows of

Fig. 9 as a variation in the background intensity. This causes significant strength

of the density gradient signal to be recorded on the camera sensor and leads to a

deterioration of the recorded particle interference pattern. This problem is amplified by

the limited intensity dynamic range of the digital high-speed imaging sensor (i.e. 10 bit).

Moreover, the presence of the density field deteriorates the reference signal imbedded

in the illumination beam, which is no longer a plane reference wave and introduces

errors in the reconstruction of the particle holograms. In order to compensate for these

effects, the hologram plane is located closer to the jet center axis as the NPR is increased

(i.e. increasing α). Moving the hologram plane closer to the object plane weakens the

effects of the density field but also reduce the size of the interference patter leading to

“resolution-limited” recording of the particle holograms.

Reconstructions from the above holograms at the jet centre axis (X3 = 0) are shown

in the bottom row of Figure 9. At low NPRs (i.e. NPR = 2 & 3) the surrounding density

field has little influence on the reconstruction quality and the reconstructed particles can

be distinguished clearly from the background. The diameter of the particles, determined

from the reconstructed images by inspection ranges between 67 to 157 µm with an

accuracy of ±11 µm. This agrees well with the original particle size distribution (see

Table 1). At higher NPRs the signal to noise ratio (i.e. particle signal to density signal)

decreases making it increasingly difficult to identify the reconstructed particles from

the background. In these case the assumption of a planar reference wave during the

reconstruction is violated and a separate planar reference wave (i.e. reference beam)

should be used for these recordings.

Continuous particle motion during the exposure time causes a movement of the

recorded diffraction pattern, [41]. Typically, if the particle movement during the

exposure time is less than the fringe spacing the resolution of the diffraction pattern

Ultra-high-speed tomographic holography in supersonic particle-laden jets 18

will remain unaffected. However, if the particle movement is large (i.e., on the order of

the fringe spacing) the diffraction pattern will be “smeared” with the consequence of

a reduced effective aperture angle and decreased resolution capability of the hologram.

According to [41] this “smearing” of the diffraction pattern becomes notable once the

particle movement S during the exposure time exceeds one tenth of the particle diameter

(i.e.. S ≥ d/10), but remains acceptable as long as S ≤ d/2. For the current work

the minimum possible exposure time is limited to 250 ns, which results in a particle

movement of S ≈ d/4 during the exposure time.

4.2. Visualisation of the Particle-Fluid Interaction

A visualisation of the particle-flow interaction is shown in Figure 11. The images are

recordings at α = 5.42, an exposure time of 250 ns and a frame rate of 1,000,000

fps. A sequence of six consecutive images of 110 µm particles suspended in a “highly

underexpanded” jet at NPR = 5.0 separated by 1 µs is shown. To enhance the image

quality, the recorded holograms are corrected by subtracting a background image and

histogram adjustment.

The sequence shows a particle traveling near the centerline and penetrating through

the Mach disk to cause clear distortions of the normal and surrounding oblique shocks.

As the particle approaches the Mach disk, a bow shock is formed at its tail indicating

a significant velocity lag between the particle and the local flow. This bow shock then

merges with the Mach disk creating a momentarily conical shock structure. After the

particle has passed the original shock structure is re-established. Upstream of this, a

second particle trailing an even stronger bow shock approaches the Mach disk. This

particle however, is located further away from the center line and does not pass through

the Mach disk (not shown here), causing significantly less disturbance in the flow field.

The strength of this shock interaction depends on both the particle size, the particle

slip velocity and the location of the particle within the gas flow. Therefore, in order to

study the particle dynamics in these high-speed unsteady turbulent flows it is pertinent

Figure 11. Visualization of particle-shockwave interaction recorded at 1,000,000 fps

of 110 µm particles suspend in a “highly underexpanded” jet at NPR = 5.0 (flow is

top to bottom).

Ultra-high-speed tomographic holography in supersonic particle-laden jets 19

to determine the 3D particle location with respect to the annular flow geometry of the

underexpanded jet.

5. Results: Ultra-High-Speed Tomographic Holographic Velocimetry

To demonstrate the ultra-high-speed magnified TDHPIV technique, measurements in a

“mildly underexpanded” jet (NPR = 2.0) are conducted using 110 µm nylon particles

injected into the gas flow at a rate of approximately 36.9×10−6 kg/s (≈50,000 particles

per second). Holograms are recorded at a frame rate of 500,000 fps with an exposure

time of 250 ns and α = 2.71.

5.1. 3D Particle Reconstruction

The recorded hologram and reconstruction at the central plane (Z = 40 mm) are shown

in the first column of Figure 9. The estimated depth-of-field is dominated by the

angular aperture of the forward scattering lobe of the particles and is approximately

τp = 22.7 mm. In comparison the “resolution-limited” and “size-limited” depth-of-field

are τr = 3.77 mm and τs = 0.07 mm for this experiment.

To account for the slight differences in magnification between the two cameras

the recorded hologram images are interpolated onto a common image resolution of 20

µm/pixel via bicubic interpolation prior to the holographic reconstruction. Additionally

a recorded background hologram is subtracted to remove the background artifacts as

seen in the middle row of Fig. 9. The object fields are reconstructed in the depth

direction with a resolution of 20 µm/pixel over a domain of 4D, symmetrically around

the central plane. Subsequently, the reconstructed intensity volumes Ik(~xk) are mapped

to the global coordinate system (Eq. 14) using the mapping function (Eq. 15) and

volume intersection weighted interpolation similar to that of TPIV [2]. The intensity

volumes are thresholded to remove the background intensity and multiplied (Eq. 13) to

obtain the final 3D particle intensity field.

An example of the reconstructed, mapped and multiplied 3D intensity field at

varying background intensity thresholded levels [1500; 2000; 2500] is shown in Figure 12

for a 2 × 1 × 2 mm3 sub-volume. Figure 12 clearly shows the significant elongation of

the reconstructed particles in the depth direction, the intersection of the two camera

views and the faithful reconstruction of the 3D particle intensities without the depth-

of-field problem after multiplication. For relatively low threshold levels most of the

noise is removed after the multiplication and the 3D particle locations are revealed as

shown in Figure 12a-b. Increasing the threshold level reduces the background noise

further resulting in a clear reconstruction of the true 3D particle locations. In this

case four particles, located roughly in the center of the sub-volume, are reconstructed.

The reconstructed particles are slightly elongated in the x−z−plane due to the use of

only two ultra-high-speed cameras in a 90-deg in-plane orientation. The volume of the

Ultra-high-speed tomographic holography in supersonic particle-laden jets 20

Figure 12. Illustration of the tomographic holography reconstruction at varying

threshold levels: (a), (c), & (e) reconstructed ellipsoids from camera 1 and 2; (b),

(d) & (f) resulting particle intensities after multiplication. Intensity threshold levels

are (top) 1500; (middle) 2000; (bottom) 2500.

reconstructed particles is estimated numerically in [40] for a spherical particle. For the

current configuration with only two viewing directions the reconstructed particle volume

is approximately Vrecon = 1.27Vparticle, where Vparticle is the true particle volume.

5.2. 3D Particle Trajectories

The complete reconstruction of the particle trajectories is shown in Figure 13. A total

of four individual trajectories are detected within one recording sequence (i.e. 200 µs or

102 images). The reconstructed 3D particle intensities are represented by a constant iso-

contour level at an intensity threshold of 2500 and colour-coded by time after the start of

Ultra-high-speed tomographic holography in supersonic particle-laden jets 21

the recording. A top-view of the reconstructed particle trajectories is shown in Figure 14.

The intensity “smear” in the top half of the measurement is a reconstruction artefact

and arise due to the limited number of viewing directions used in the tomographic

reconstruction. With an increasing number of viewing directions (i.e. cameras) these

artefacts will begin to disappear.

The velocity along the trajectories is obtained by 3D cross-correlation PIV analysis

of the reconstructed particle intensities (see [2] for more details) and is plotted in Figure

15 for particle 2 & 4. The particles exit the nozzle with a velocity of approximately

100 − 110 m/s, which is lower than the gas velocity at the nozzle exit ue = 313 m/s.

Due to their relatively long response time (τp = 3.67 ms) and short nozzle length

(Lnozzle = 120 mm), the particles are not able to attain the gas velocity at the nozzle

exit and travel at subsonic speeds. The local particle Mach number, evaluated at the

nozzle exit is Map = 1− up/ue ≈ 0.65. After leaving the nozzle the particles decelerate

by 10 − 20% until they reach a distance of approximately 1.5D from the nozzle exit

Figure 13. Reconstruction of micron-sized particles in a supersonic underexpanded

jet (NPR = 2) recorded at 500,000 fps. Particle trajectories are color-coded by time

after the start of the recording.

Ultra-high-speed tomographic holography in supersonic particle-laden jets 22

Figure 14. Top view of the particle trajectories shown in Fig. 13

where they accelerate again to regain most of their exit velocity. The nature of this

decrease and increase in velocity is not yet clear and requires further assessment in

conjunction with full field velocity measurements of the gas phase. In comparison,

the length of the first “shock-cell” is approximately 0.4D at a NPR = 2.0, [32]. The

transverse particle velocities are one order of magnitude lower than the streamwise

velocities and the particles experience some oscillations in the x−z−plane potentially

caused by a tumbling motion of the non-spherical particles and/or velocity field induced

fluctuations.

5.3. Uncertainty of the measured particle velocity

If the uncertainties due to the variation in magnification are neglected it can be shown

from geometric considerations that the error in the centroid location of the particle

ǫc is proportional to the calibration error δik in the locale x1 and x2 direction. The

calibration error in the camera normal direction x3 can be neglected as it is typically

much smaller than the depth-of-field. Hence, the error in the particle centroid location

error is expressed as

ǫc =√2δik, (20)

where it is assumed that δik is the same in all directions and for both cameras. Recalling

an estimated calibration error of δik = 0.16 pixel the position error of the particle

centroid is approximately 0.23 pixel (5.2 µm) or 0.05 particle diameter. In comparison,

alternative methods of determining the centroid of an elongated particle including

ellipses or complex amplitude fitting are discussed in [23] and generally have an accuracy

on the order of 1-2 particle diameters (see [23] for more details).

Ultra-high-speed tomographic holography in supersonic particle-laden jets 23

0 0.5 1 1.5 2 2.5 380

90

100

110

120

130

|x |/D

v

particle 2

particle 4

2D trajectory

(m/s)

1 shock cellst

(a)

0 0.5 1 1.5 2 2.5 3−15

−10

−5

0

5

10

15

|x |/D

u(m/s),

w(m/s)

particle 2, u−vel.

particle 4, u−vel.

particle 2, w−vel.

particle 4, w−vel.

(b)

Figure 15. Measures particle velocities along the length of the trajectory |x|/D,

� particle 2, � particle 4, −− 2D approximation: (a) streamwise velocity (v); (b)

traversal velocities (u, w). Errors bars are ±5 m/s.

The error in the estimated particle velocity is proportional to twice the centroid

location error (neglecting the cross-correlation error of ≈ 0.1 pixel)

ǫu =2ǫc∆t

=4√2

δik∆t

. (21)

For the results shown in Figure 15 and an acquisition rate of 500 kHz, the expect

uncertainty in the estimated velocity is ǫu ≈ 5 m/s or approximately 4.5% of the particle

centerline velocity, as indicated by the error bars in the figure.

Since the depth location of the particles is known, the individual holograms can

be reconstructed in a single plane at the exact depth location of each particle and the

streamwise velocities can be estimate by means of 2D cross-correlation of the succes-

sive time-steps. Done in this way, errors due the tomographic reconstruction of the

3D particle fields are avoided proving an alternative measure of the streamwise particle

velocity. Note, the velocities in the x−z−plane cannot be measured by this approach.

The results for the projected 2D trajectories are also plotted in Figure 15(a). A good

agreement between the two measurements is achieved with the 2D approximation show-

Ultra-high-speed tomographic holography in supersonic particle-laden jets 24

ing the same velocity changes along the particle trajectory. The differences between the

two approaches is within the estimated error range. Furthermore it should be noted that

the measured transverse velocities are of the order of the estimated velocity error. An

improvement in the measurement accuracy can be achieved by increasing the number

of cameras and by improving the calibration accuracy as mentioned in section 3.3.

6. Concluding Remarks

This paper has presented ultra-high-speed magnified tomographic digital holographic

velocimetry measurements of solid particles in a supersonic underexpanded jet flow to

study their 3D flow kinematics and interaction with the surrounding high-speed gas

flow. It was shown that in ultra-high-speed digital holography the depth resolution of

the holograms is severely restricted by the relatively large pixel size of modern digital

high-speed imaging sensors and can be overcome by recording multiple magnified in-line

holograms from different orientations using THDPIV. By this approach the limitations

imposed by the camera in high-speed digital in-line holography are relaxed allowing the

faithful reconstruction of the 3D particle intensity distribution without the depth-of-field

limitation. Experimental demonstration of this approach was presented by reconstruct-

ing 110 µm particles in a “mildly underexpanded” jet of NPR = 2.0 at a framerate of

500,000 fps and measuring their 3D location and velocity along the particle trajectory

via cross-correlation analysis. For the presented case, the depth-of-field in the hologram

reconstruction was limited by the relative large particle size of 110 µm and no longer

by the recording system, which provides further margins for improvements in the fu-

ture. The accuracy of the measured particle velocity was assessed to be within 4.5% of

the particle centerline velocity or ±5 m/s. Measurements at higher NPRs are impeded

by the jet’s density gradient field, which causes a deterioration of the plane reference

illumination during the recording process. At high NPRs the holographic particle re-

construction is at best limited to regions near the center line and outside the shock

region where the distortions of the reference wave are less. The particle-fluid interaction

has been visualised by coherent laser imaging (CLI), which has revealed a significant

influence of the micron-sized particle on the underlying shock structure within the un-

derexpanded jet. This influence however, depends on the the exact 3D particle location

with respect to the cylindrical flow geometry and underpins the necessity for full 3C-3D

measurements of the particle dynamics in these high-speed unsteady 3D turbulent flows.

Acknowledgment

K. M. Ingvorsen is greatly acknowledged for conducting the experiments in Sec. 4.2

and for producing Fig. 11. The authors also acknowledge the financial support of the

Australian Research Council through the Discovery Project DP1096474.

Ultra-high-speed tomographic holography in supersonic particle-laden jets 25

References

[1] R. J. Adrian and C.-S. Yao. Development of pulsed laser velocimetry (PLV) for measurement of

turbulent flow. In X. B. Reed Jr. and J. L. Patterson, G. K. abd Zakin, editors, Proceedings of

the Symposium on Turbulence, pages 170–186, Rolla, MO: University of Missouri 1984.

[2] C. Atkinson and J. Soria. An efficient simultaneous reconstruction technique for tomographic

particle image velocimetry. Experiments in Fluids, 47:553–568, 2009.

[3] C. H. Atkinson and J. Soria. Multi-camera digital holographic PIV: Tomographic DHPIV. In

Proc. 16th Australasian Fluid Mech. Conf., pages 184–190, Gold Coast, Australia, December

2007.

[4] D. H. Barnhart, R. J. Adrian, and G. C. Papen. Phase-conjugate holographic system for high

resolution particle image velocimetry. Appl. Optics, 33:7159–70, 1994.

[5] N. A. Buchmann, D. Mitchell, K. M. Ingvorsen, D. Honnery, and J. Soria. High spatial resolution

imaging of a supersonic underexpanded jet impinging on a flat plate. In Sixth Australian

Conference on Laser Diagnostics in Fluid Mechanics and Combustion, Canberra, Australia,

pages 43–46, 2011.

[6] S. Coetmellec, C. Buraga-Lefebvre, D. Lebrun, and C. Ozkul. Application of in-line digital

holography to multiple plane velocimetry. Measurement Science & Technology, 12(7):1392–7,

2001.

[7] G. E. Elsinga, F. Scarano, B. Wieneke, and B. W. van Oudheusden. Tomographic particle image

velocimetry. Experiments in Fluids, 41:933–947, 2006.

[8] L. J. Forney. Particle impaction in axially symmetric supersonic flow. Aerosol Science and

Technology, 15:49–59, 1991.

[9] J. W. Goodman. Introduction to Fourier Optics. McGraw-Hill, New York, 1st, edition, 1968.

[10] L. F. Henderson. Experiments on the impingement of a supersonic jet on a flat plate. Zeitschrift

fur angewandte Mathematik und Physik, 17(5):553 –569, 1966.

[11] J. R. Hodkinson. Particle sizing by means of the forward scattering lobe. Appl. Optics, 5(5):839–

844, 1966.

[12] F. Hussain, D. D. Liu, S. Simmonds, and H. Meng. Holographic particle velocimetry: prospects and

limitations. In Proc. Fluids Engineering Division, American Society of Mechanical Engineers,

volume 148, pages 1–11, 1993.

[13] R. Israel and D. E. Rosner. Use of generalized stokes number to determine the aerodynamik

capture efficiency of non-stokesian particles from a compressible gas flow. Aerosol Science and

Technology, 2(1):45–51, 1982.

[14] B. Jodoin, F. Raletz, and M Vardelle. Cold spray modeling and validation using an optical

diagnostic method. Surface Coating Technology, 200:4424–4432, 2006.

[15] Harald Kleine, Hans Groenig, and Kazuyoshi Takayamac. Simultaneous Shadow, Schlieren and

Interferometric Visualization of Compressible Flow. Optics and Lasers in Engineering, 44:170–

189, 2006.

[16] T. M. Kreis and W. P. O. Jupter. Principle of digital holography. In Proceedings of the 3rd

International Workshop on automatic processing of fringe pattern, pages 185–95, Bremen,

Germany 15–17 September 1997.

[17] C. H. Lewis and D. J. Carlson. Normal shock location in underexpanded gas and gas-particle jets.

AIAA Journal, 2(4):776–777, 1964.

[18] S. Li, B. Muddle, M. Jahedi, and J. Soria. A numerical investigation of the cold spray process

using underexpanded and overexpanded jets. J. of Thermal Spray Technology, 21(1):108–120,

2011.

[19] A. Lozano, J. Kostas, and J. Soria. Use of holography in particle image velocimetry measurements

of a swirling flow. Experiments in Fluids, 27(3):251–261, 1999.

[20] H. G. Mass, A. Gruen, and D. Papantoniou. Particle tracking velocimetry in three-dimensional

flows. part i. photogrammetric determination of particle coordinates. Experiments in Fluids,

Ultra-high-speed tomographic holography in supersonic particle-laden jets 26

15:133–146, 1993.

[21] S. Maurata and N. Yasuda. Potential of digital holography in particle measurement. Appl. Optics,

32:567–574, 2000.

[22] A. Melling. Tracer particles and seeding for particle image velocimetry. Measurement Science &

Technology, 8(12):1406 – 1416, 1997.

[23] H. Meng, G. Pan, Y. Pu, and S. H. Woodward. Holographic particle image velocimetry: from film

to digital recording. Measurement Science & Technology, 15:673–685, 2004.

[24] D. M. Mitchell, D. R. Honnery, and J. Soria. The visualization of the acoustic feedback loop in

impinging underexpanded supersonic jet flows using ultra-high frame rate schlieren. Journal of

Visualization, DOI: 10.1007/s12650-012-0139-9, 2012.

[25] D. Nguyen, D. Honnery, and J. Soria. Measuring evaporation of micro-fuel droplets using magnified

DIH and DPIV. Experiments in Fluids, 50:949–959, 2011.

[26] T. Okoshi. Three-dimensional imaging techniques. Academic Press Inc., New York, 1976.

[27] L. Onural and P. D. Scott. Digital decoding of in-line holograms. Optical Engineering,

26(11):1124–32, 1987.

[28] V. Palero, M. P. Arroyo, and J. Soria. Digital holography for micro-droplet diagnostics.

Experiments in Fluids, 43:185–195, 2007.

[29] V. R. Palero, J. Lobera, and M. P. Arroyo. Three-component velocity field measurement in

confined liquid flows with high-speed digital image plane holography. Experiments in Fluids,

49:471–483, 2010.

[30] J. Panda and G. Adamovsky. laser light scattering by shock waves. Physics of Fluids, 7(9):2271–

2279, 1995.

[31] A. Papyrin, V. Kosarev, S. Klinkov, A.Alkimov, and V. Fomin. Cold Spray Technology. Elsevier,

2007.

[32] A. Powell. The soundproducing oscillations of round underexpanded jets impinging on normal

plates. J. Acoust. Soc. Am., 83(2):515–533, 1988.

[33] N.J. Quinlan, M.A.F. Kendall, B.J. Bellhouse, and R.W. Ainsworth. Investigations of gas and

particle dynamics in first generation needle-free drug delivery devices. Shock Waves, 10:395–404,

2001.

[34] M. Raffel, J. Kompenhans, B. Stasicki, B. Bretthauer, and G. E. A. Meier. Velocity measurement

of compressible air flows utilizing a high-speed video camera. Experiments in Fluids, 18:204–215,

1995.

[35] J. Sheng, E. Malkiel, and J. Katz. Digital holographic microscope for measuring three-dimensional

particle distributions and motions. Appl. Optics, 45(16):3893–3901, 2006.

[36] J. Sheng, E. Malkiel, and J. Katz. Using digital holographic microscopy for simultaneous

measurements of 3D near wall velocity and wall shear stress in a turbulent boundary layer.

Experiments in Fluids, 45:1023–35, 2008.

[37] M. Sommerfeld. The structure of particleladen, underexpanded free jets. Shock Waves, 3:299–311,

1994.

[38] J. Soria, O. Amili, and C. Atkinson. Measuring dynamic phenomena at the sub-micron scale.

In International Conference on Nanoscience and Nanotechnology, Melbourne, Australia, pages

129–132, 2008.

[39] J. Soria and C. Atkinson. Multi-camera digital holographic imaging PIV versus tomographic

imaging PIV - comparison and contrast of these two 3C-3D PIV techniques. In Proc.

International Workshop on Digital Holographic Reconstruction and Optical Tomography for

Engineering Applications, Loughborough, UK, pages 33–43, 2007.

[40] J. Soria and C. Atkinson. Towards 3C-3D digital holographic fluid velocity vector field

measurement—tomographic digital holographic piv (Tomo-HPIV). Measurement Science &

Technology, 19(7):074002, 2008.

[41] C. S. Vikram. Particle Field Holography. Cambridge University Press, 1992.

[42] K. von Ellenrieder and J. Soria. Experimental measurement of particle depth of field in

Ultra-high-speed tomographic holography in supersonic particle-laden jets 27

digital holography. In International Workshop on Holographic Metrology in Fluid Mechanics,

Loughborough, UK, 2003.