Four-dimensional dynamic flow measurement by holographic...

Four-dimensional dynamic flow measurement byholographic particle image velocimetry

Ye Pu and Hui Meng

The ultimate goal of holographic particle image velocimetry (HPIV) is to provide space- and time-resolvedmeasurement of complex flows. Recent new understanding of holographic imaging of small particles,pertaining to intrinsic aberration and noise in particular, has enabled us to elucidate fundamental issuesin HPIV and implement a new HPIV system. This system is based on our previously reported off-axisHPIV setup, but the design is optimized by incorporating our new insights of holographic particle imagingcharacteristics. Furthermore, the new system benefits from advanced data processing algorithms anddistributed parallel computing technology. Because of its robustness and efficiency, for the first time toour knowledge, the goal of both temporally and spatially resolved flow measurements becomes tangible.We demonstrate its temporal measurement capability by a series of phase-locked dynamic measurementsof instantaneous three-dimensional, three-component velocity fields in a highly three-dimensional vor-tical flow—the flow past a tab. © 2005 Optical Society of America

OCIS codes: 290.5850, 090.0090, 120.7250, 110.6880.

1. Introduction

Turbulent flow is a highly complex and yet ubiquitousphysical phenomenon that we know little about. Theunderstanding, modeling, and control of turbulence re-quires proper experimental tools to reveal the fluctu-ating three-dimensional (3D) vorticity at a wide rangeof time and length scales, which has posed an over-whelming challenge to modern technology in manyaspects. The recently matured particle image velocim-etry (PIV) technique only partially fulfills this need byproviding two-component1,2 or three-component3,4 ve-locity measurement on a two-dimensional (2D) plane.Further explorations5,6 attempted to expand PIVcapabilities to cover a volumetric domain by rapidlyscanning the volume plane by plane. However, in-stantaneous, full-field 3D measurement with sufficientspatial resolution and dynamic range is beyond thereach of conventional PIV.

Holographic particle image velocimetry (HPIV) is afull-field, instantaneous, 3D flow diagnostics tool thatholds the promise to provide unprecedented experi-mental capability for fluid dynamics research. Usingholography, HPIV records and reconstructs two 3Dimages, at distinct moments in time, for the smallparticles dispersed in the fluid flow under investiga-tion. The recording is considered instantaneous be-cause the process completes as fast as a laser pulse(usually in a 10 ns range). From the displacements ofparticles ��x� during the time interval ��t� betweenthe two recording moments, the fluid velocities arededuced as u � �x��t. Extension of the measure-ment in the temporal domain (by recording multipleholograms) leads to cinematic HPIV, which providesboth space- and time-resolved velocity field measure-ments.

HPIV can be implemented in either in-line or off-axis configurations. Because of its simplicity, in-lineholography attracted earlier application of particleholography.7–11 However, because of its excessive in-trinsic speckle noise in the reconstructed image,12 in-line holography was restricted to measurements ofsparsely dispersed particles.10,11 Thus later develop-ments in HPIV have concentrated on off-axis hologra-phy, which shows significantly improved imagingsignal-to-noise ratio (SNR) over the in-line versions,allowing for much higher seeding densities and thusgreater spatial resolutions.13,14 Indeed, most of therecent film-based HPIV studies use off-axis hologra-phy.13–18 On the other hand, the newly emerged digital

When this research was performed the authors were with theLaser Flow Diagnostics Laboratory, Department of Mechanical andAerospace Engineering, State University of New York at Buffalo,Buffalo, New York 14260. Y. Pu ([email protected]) is nowwith the Department of Electrical Engineering, California Instituteof Technology, Pasadena, California 91125. The e-mail address forH. Meng is [email protected].

Received 21 April 2005; revised 7 September 2005; accepted 8September 2005.

0003-6935/05/367697-12$15.00/0© 2005 Optical Society of America

20 December 2005 � Vol. 44, No. 36 � APPLIED OPTICS 7697

HPIV is mostly implemented in an in-line version dueto poor resolutions of current electronic imagers. Re-cent reviews in the area of HPIV can be found in Refs.19 and 20.

Despite the large variety of designs in practice, fun-damental knowledge about the physics in HPIV isnevertheless rather limited. In particular, our under-standing about the imaging characteristics of particleholography and the associated speckle noise is still ata rudimentary level. The lack of such knowledge hin-ders the objective justification of a particular designand the reliable estimation of its accuracies and capa-bilities. The rationales for common HPIV designs aremostly based on engineering convenience rather thanquantitative analysis. Such systems inevitably sufferfrom great operational difficulties and unrepeatableresults. Consequently, four-dimensional HPIV mea-surement, a natural and highly anticipated extensionto the HPIV technique, remains an elusive goal.

In view of this lack of knowledge, we have devel-oped theories of the signal and noise properties forparticle holography.21,22 We show that imperfect 3Dparticle images formed by the wavefront reconstruc-tion of the light scattering and the associated specklenoises hold the primary responsibility for the limit inthe accuracy and capacity of HPIV. These two issuesare intrinsic to the physical process in HPIV. Theirnegative effects can be alleviated only by betterchoices of system parameters but never be elimi-nated.

In this paper we first provide a synopsis of theimaging and noise properties of particle holography,based on the determining factors in the capability ofHPIV. These lead to guidelines for direct evaluationof HPIV designs. We then report our latest develop-ment in off-axis HPIV technology. We demonstratethe temporal potential of HPIV with a phase-lockedmeasurement of a flow passing a wall-mounted tab,which reveals a sequence of a vortex shedding processin a complete cycle. This experiment shows thatHPIV holds great promise for four-dimensional (3Dspace plus time) measurements of fluid flow.

2. Basic Configurations and Fundamental Issues inHolographic Particle Image Velocimetry

Light scattering by small particles plays a paramountrole in HPIV, since it is the signal that the hologramrecords and reconstructs. As will be shown in laterdiscussions, the scattering wavefront from each par-ticle and the spatial dispersion of the scatteringsources (particles) lead to two fundamental issues inHPIV: intrinsic aberration and intrinsic noise. Be-cause of this importance of scattering phenomena, wecategorize HPIV configurations by the recording an-gle ��H�, i.e., the angle between the normal vector ofthe recording plane and the propagation vector of theobject-illuminating light. Figure 1 illustrates theseHPIV configurations, while also stressing the criticalrole of polarization. There are three major categoriesof HPIV configurations: forward (or near-forward) re-cording ��H � 0°�, backward (or near-backward)recording ��H � 180°�, and 90 deg recording ��H

� 90°�. On the basis of the polarizations of the refer-ence and object waves, 90 deg recording is furtherclassified as a vertical polarization configuration,where the polarizations of the object wave and thereference waves are parallel everywhere, and a hor-izontal polarization configuration, where the polar-izations of the object wave and the reference wavesare not parallel to each other but share a parallelcomponent.

In the 90 deg recording configurations [Figs. 1(c)and 1(d)], an optional backreflection mirror can beemployed to boost the scattering intensity. The holo-gram records the sum of two wavefronts scatteredfrom both illuminations, whereby the intensity of theobject wave is approximately doubled. The recon-structed image is a coherent sum of two overlappingimages containing an intrinsic aberration from each.This mirror, however, should be excluded when verysmall tracer particles (comparable or smaller thanthe recording wavelength) are used due to the spatialintensity fluctuation of the standing wave created bythe mirror.

Optical access at nonorthogonal angles is certainlypossible and was successfully employed for the mea-surement in gas flow.13 However, without special op-tical treatment, liquid media and the walls of the flowfacility can cause severe aberrations and distortions,

Fig. 1. Optical configurations for off-axis HPIV. (a) Forward scat-tering; (b) backward scattering; (c) 90 deg scattering, verticalpolarization configuration; (d) 90 deg, horizontal polarization con-figuration. Ei, illuminating wave; Er, reference wave; H, hologramplane; nH, normal vector of holographic plane; �H, recording angle;�r, reference angle; M, mirror; BS, beam splitter.

7698 APPLIED OPTICS � Vol. 44, No. 36 � 20 December 2005

which seriously damage the signal integrity. For thisreason, we favor the chosen three orthogonal angles.

In Subsections 2.A and 2.B we discuss the intrinsicaberration and intrinsic speckle noise in off-axis par-ticle holography and the effects of particular HPIVconfigurations on these issues.

A. Intrinsic Aberration

In an ideal particle holography system, for each par-ticle the hologram records spherical waves converg-ing at the center of the particle without aberration.This paradigm is often the assumption of many HPIVdevelopments. We have shown in recent work,21 how-ever, that even a perfect hologram (aperture limited)is unable to faithfully reconstruct the 3D image of aparticle (i.e., a sphere). The reconstructed 3D imagepresents dramatic changes in image morphologies de-pending on the recording angle �H and particle size dp.This imperfection is a result of highly uneven inten-sity and phase distribution of the scattering wave-front23 across the hologram aperture, and we treatsuch imperfection as a special type of aberration.

The consequence of the intrinsic aberration ishighly complex 3D particle image intensity distribu-tions, as well as bodily deviations of the particleimages from their true locations, causing great diffi-culties to identify and locate the particles precisely.The intrinsic aberration also degrades the SNR of thereconstruction images and thus reduces the informa-tion capacity in HPIV (to be discussed in Section 3).Such degradation can be quantified with the imageintegrity � �0 � � � 1�, defined by the ratio of theactual image intensity to the image intensity of anundistorted spherical wave with the same energy. Aperfect particle image has � � 1, while aberrationsresult in lower image integrity values.

Numerical simulations21 show that the intrinsicaberration varies significantly with �H, and the neg-ative effect of intrinsic aberration on the measure-ment accuracy is minimal in a 90 deg configuration.The relationship between the intrinsic aberrationand the particle size clearly calls for use of smallerparticles since the scattered wave more closely re-sembles a spherical wave. However, because of theconstraints of optical configuration and available la-ser power, the size of the particles used in most re-ported HPIV systems often ranges from 10 to 50 �m,with exceptions in Refs. 13 ��0.5 �m� and 18��1–3 �m�. Significant intrinsic aberration is ex-pected at this size range.

Although most practical cases are dominated byextrinsic aberrations from imperfect optics and holo-grams, these aberrations can be eliminated throughphase-conjugate reconstruction13 or complex correla-tion.24 Conversely, the intrinsic aberration cannot beremoved. Therefore the measured particle position isalways subject to a deviation due to the intrinsicaberration, although in special cases the particle dis-placement may not be subject to deviation.24 The roleof the intrinsic aberration in the measurement ofparticle displacements becomes more subtle in in-novations where phase aberrations are canceled

through complex correlation of the local scatteredfield.24 Although the accuracy of displacement mea-surements has been greatly improved through theremoval of the intrinsic phase aberration, the re-maining amplitude modulation could still be severeenough to prevent the reach of submicrometer accu-racy.

B. Intrinsic Speckle Noise

Speckle noise is intrinsic in coherent imaging. Be-cause of the self-interference of a large amount ofreconstructed waves from particle images dispersedin the 3D space, the speckle noise problem in particleholography is especially severe and has long been themajor obstacle for HPIV to reach a high spatial sam-pling rate. The SNR in a reconstructed holographicimage can be expressed as25

I0�N

�I0��IN�

�1 2I0��IN�, (1)

where I0 is the focal intensity of the aberration-free(diffraction-limited) particle image, and we haveshown in Ref. 22 that in particle holography,

I0�IN�

�

tan2 �

�2nsL. (2)

Given a proper holographic recording and the min-imum SNR required by a particular algorithm forcorrect extraction of particle positions, the intrinsicspeckle noise is the essential limiting factor for themaximum achievable number density of particles(seeding density). Equation (2) suggests that theseeding density ns and the axial depth L must satisfythe following relationship:

nsL �

tan2 �

�2 I0�IN�min, (3)

assuming spherical-wave reconstructions and infini-tesimal sampling pixels (i.e., the best case). Analysesin Ref. 22 also show that, statistically, the specklenoise has very similar spectral characteristics to par-ticle images regardless of the optical configuration.Consequently, 2D or 3D filtering is ineffective in theremoval of speckle noise. Therefore inequality (3) rep-resents a fundamental limit in the information a ho-logram can deliver. In later discussion, we refer tothis limit as the information capacity of a hologram.

In practice, where particle images contain intrinsicaberrations and the sampling pixel has a finite size,this limit is reduced by a factor of ��, where � is theratio of the pixel size to the mean speckle size.26

Inequality (3) stresses the importance of the angularaperture �. In a forward-scattering configuration, �is usually determined by the size of the seeding par-ticle. In configurations utilizing other scattering


angles, � is limited by the recording and reconstruc-tion optics, which can be much larger. Hence, evenwithout the superposition of the reference wave, in-line configurations often possess an inferior SNRthan other designs due to its typically smaller angu-lar aperture (which, however, can be improved byusing smaller particles). Inequality (3) also revealsthe importance of our controlling the depth dimen-sion L: Given a HPIV configuration and the SNRrequirement, higher spatial resolution can beachieved at the expense of reduced L. This suggeststhat 90 deg recording is again in favor because L canbe easily controlled by adjusting the illuminatingbeam to illuminate only the region of interest.

3. Capacity and Accuracy of Holographic ParticleImage Velocimetry

The capability of HPIV system in flow measurementsis bound by two factors: seeding density, which de-termines the spatial data sampling rate, and particleposition uncertainty, which sets the primary limit inthe accuracy and dynamic range of the measurement.

The number density of tracer particles determinesthe spatial resolution of the flow velocity field andhence the size of the smallest resolvable flow struc-tures. The depth of the test volume L determines thelargest eddy size that the measurement can capture.For a uniform particle dispersion, we take the meanfree distance between particles as the smallest eddysize: � �3�4ns�1�3. Let us assume the integrallength to be L and the Kolmogorov length scale (thesmallest intrinsic scale of turbulent motions) to be ;the maximum flow Reynolds number resolvable inHPIV measurement is27

Remax � �L�4�3 � �4nsL3

3 �4�9

. (4)

Equation (4) shows that, given the information ca-pacity �nsL� of a HPIV system, Remax scales almostlinearly with L. As an example, let us consider anoptimal case where �� 1 and tan � � 1 isachieved, and we require a minimum SNR of5�I0��IN��min � 50�. The information capacity is there-fore 2.2 � 105 mm�2 (at � � 532 nm). At L� 50 mm, we are able to achieve ns � 4.4� 103 mm�3 and resolve Remax � 1.45 � 10

4. At L� 10 mm, on the other hand, we are able to use ahigher seeding density of ns � 2.2 � 10

4 mm�3 butcan only resolve Remax � 3.48 � 10

3.The uncertainty in the reconstructed particle posi-

tion ��p� is specific to the optical setup, particle size,particle relative refractive index, and the specific al-gorithm to extract the particle position. The flow ve-locity extracted from displacement ��x� betweenparticles in the double exposures inherits its uncer-tainty �� from the uncertainty in the particle posi-tions ��p�. Uncertainties in �t are usually negligibleowing to the picosecond accuracy in typical moderntiming devices. Thus, for velocities obtained fromindividually paired particles,

�� p2 �p2��t � �2�p��t. (5)

In most practical cases, one can assume small dis-placement gradients within the local domain wherethe correlation is performed. Thus, at a cost of low-ered spatial resolution, the displacement uncertaintycan be roughly reduced to 1��m by calculating themean velocity from a group of m particles.28

For monodispersed particles, the system errors dueto Mie scattering and the holography process do notsignificantly effect the accuracy of particle displace-ments, since most of the deviations in particle posi-tions cancel out. If the particle size is nonuniform, theuncertainty in particle size is translated into the un-certainty of the particle positions and displacements.

In optical reconstruction, other sources of errorsinclude mechanical misalignments29 and vibrationsduring the scanning of the reconstructed image field.Furthermore, the shrinkage of the holographic emul-sion due to chemical processing also drasticallydegrades the reconstructed images and introducessignificant measurement error. The above analysis,nonetheless, lays out the theoretical limit in the ca-pacity and accuracy of HPIV. In particular, theselimits also apply in digitally recorded hologramswhere emulsion shrinkage, mechanical misalign-ments, and vibrations are eliminated.

4. Gemini Holographic Particle ImageVelocimetry System

One of the established HPIV systems is the Geminisystem14 developed in our laboratory. It employs 90deg scattering and off-axis holography. The engineer-ing intuition behind this design turned out to be ef-fective; the Gemini system has proven to be a robustHPIV instrument and conforms to the guidelines laidout by the theory. The system consists of two majorcomponents: (1) a holographic recording and recon-struction subsystem and (2) a data processing sub-system. Over the past few years, this system hasevolved significantly, incorporating the latest under-standing of particle holography and advanced paral-lel computing technology into its implementations. Inthe following, we present this integrated system in itsoptical configuration, data processing algorithms,and distributed parallel computing cluster.

A. Optical Configuration

We have previously reported the optical configura-tion of the holographic recording and reconstructionsubsystem in the Gemini HPIV in Ref. 14. Here webriefly describe the optical configuration of theGemini system. Figure 2(a) illustrates the opticalconfiguration for the HPIV recording stage. We usean injection-seeded, dual-cavity Nd:YAG laser(Spectra-Physics PIV-400) in this system, whichgives a pair of temporally and spatially separatedlaser pulses, each of 8 ns duration. The pulse sepa-ration time �t is adjusted according to the estimatedflow speed. The two laser pulses are split into twoparts by the beam splitters. Eighty percent of the


light energy from each beam is reflected and used forillumination. The remaining part of each laser beamis further manipulated by a variable beam splitterand serves as the reference beams at two distinctangles. With this angular-multiplexing scheme, twoholograms can be recorded and reconstructed inde-pendently.

As shown in Fig. 2(b), the holographic reconstruc-tion system shares the same optics as the recordingsystem to minimize aberrations. The developed holo-gram is now placed back at the original position withthe emulsion side facing opposite to that of the re-cording, such that each reference beam becomes the

complex conjugate of that used in the recording. Inthis way, an unscrambled real image of the 3D par-ticle field is reconstructed.

We use the 3D scanning approach to interrogatethe reconstructed particle images. A Pentium PC con-trols the data acquisition. This computer serves asthe acquisition node (or the master node in terms ofa master–slave programming model) in a distributedcomputing environment, as well as a stand-alone pro-cessing power if no parallel computing facility isavailable. Image acquisition and camera movementare synchronized with the laser pulses to ensure dataintegrity.

Fig. 2. Scheme of off-axis holography in the Gemini HPIV system. (a) Recording, (b) reconstruction and data processing. HEM,high-energy mirror; WP, half-wave plate; BS, beam splitter; PBS, polarizing beam splitter; PCI, peripheral component interconnect.


B. Extraction of Particle Information

Given the constraint of information capacity and thedesired spatial resolution to measure complex andpotentially turbulent flows, it is always preferable toextract as much information (position, size, and dis-placement) as possible from each individual particleimage so that optimal spatial resolution is attained.On the other hand, the extremely complex 3D mor-phology of the particle images, exacerbated by thespeckle noise, poses a great challenge to the retrievalof the particle information. This problem is especiallysevere when detailed information is needed for cate-gorization of particles.

We have implemented the particle reconstructionby edge detection (PRED) algorithm, a 3D image seg-mentation and labeling algorithm that extracts the3D exterior surface of a particle image based on 2Dsegmentation and recursive 3D labeling.30 The taskof PRED is to travel through the 3D spatial structureof each particle image, pick up as many pixels belong-ing to the image as possible, and calculate the centercoordinate of the image. Essentially, the algorithmconsists of two steps: (1) extract all particle 2D bound-aries in every image slice (plane) with a hybrid edge-and region-based 2D segmentation algorithm and (2)collect the 2D boundaries with a recursive graphtraveling algorithm to form 3D surfaces of the parti-cle images. Interested readers should see Ref. 30 forfurther details.

Because of the intrinsic aberration, the positionwhere maximum intensity is located (i.e., the focalpoint) does not represent the image center reliably,especially when faced with speckle noise. Since theintensity concentrates at the vicinity of the particlecenter, we define the region with intensity exceedinga threshold as the image region, or the image. We usethe first moment (center of mass) of intensity en-closed in the image region, i.e., the centroid, to rep-resent the center of the image:

xc ��i �j �k Iijkx�i �j �k Iijk

, �i, j, k� � VT, (6)

where xc � xc yc zc�T is the coordinate of the cen-troid, VT is the volume of the image region, i, j, k arethe discrete coordinates of the pixels, x � i j k�T isthe coordinate of any pixel enclosed in VT, and Iijkis the intensity value at that pixel.

The extraction accuracy of PRED is benchmarkedwith a numerically generated planar distribution of 3Dparticle images sampled at a 50 �m distance. Theimage intensities are calculated based on Mie-scattering theory and appropriate pixel sizes. AfterPRED extracts the particle image centroids, we fitthe centroid coordinates to a plane, as shown inFig. 3(a). The distance between the centroid to theplane represents the extraction error of PRED, whosehistogram is plotted in Fig. 3(b). The standard devi-ation of this error, i.e., the uncertainty in the extrac-tion, is �5 �m, in which the axial componentdominates. Here we specify the overall uncertainty

(worst case) instead of three separated components.This also applies to the calibration in Section 5.

C. Extraction of Particle Displacements

We have implemented a concise cross correlation(CCC) algorithm that correlates and tracks 3D par-ticle movement with discrete particle centroid coor-dinates.14 The name came from the fact that particlecentroid coordinates are much more concise informa-tion than the particle image itself.

The first step of CCC is to calculate the mean dis-placement (translation) between two groups of parti-cle coordinates through correlation. We assign eachparticle an imaginary sphere with virtual radius rcentered at its centroid location, and define a corre-lation kernel function between the ith particle in thefirst group and jth particle in the second group as

�ij�x, y, z; r�

� exp��x � xi xj�2 �y � yi yj�2 �z � zi zj�22r2 .(7)

The correlation function is indeed a summation of all

Fig. 3. Calibration of PRED algorithm through planar distrib-uted particle images generated by simulations of Mie scattering.(a) Spatial distribution of particle centroid extracted by PRED. (b)Statistics of the coordinate errors at various SNRs. Results areaverages calculated from ten tests: A total of 500 particle images isgenerated in each test, and on average 480 particles are extractedby PRED.


the individual correlation kernel functions:

C�x, y, z� � �i�1

N

�j�1

N

�ij�x, y, z; r�, (8)

whose highest peak in 3D space represents the meandisplacement between the two groups of particles.The virtual radius r serves as the size of particleimages in a fast-Fourier-transform-based correla-tion.28 This artificially assigned, adjustable particlesize is the key to the great robustness of CCC againstgradients of displacement or velocity. The value of r isdetermined empirically, and the correlation resultsare robust as long as r is larger than the averageamplitude of the displacement gradient within thevolume under investigation. The correlation is morerobust against displacement gradients with larger rvalues. On the other hand, a larger r value wouldslightly increase the correlation error by a few per-cent. This 3D correlation is properly decomposed intothree one-dimensional correlations performed in thespace domain for a significant speed-up. After thecorrelation, CCC next individually pairs each particlebased on the information obtained from the first stepand a shortest distance classification criterion. The

correlation error is largely eliminated by the pairingstep, although such an error results in an increasedprobability of incorrect pairing.

We benchmark the performance of CCC with spiralmotions (translation T plus solid-body rotation �)of numerically dispersed particles in a volume-sizedD � D � D. Figure 4 demonstrates the benchmarkresults showing the robustness of CCC against vari-ous combinations of translations and deformations.Through optimization of the virtual radius, CCC han-dles velocity gradients much better than traditional3D fast-Fourier-transform based correlation.31

D. Distributed Parallel Processing

Processing of HPIV data (extraction of informationfrom 3D particle images) represents a major chal-lenge in the development of practical HPIV instru-ments. The vast amount of image data (often morethan 100 Gbytes of raw image data per hologram)takes more than 50 h for a single 600 MHz Pentium-grade computer to process just one snapshot. Exper-iments involving multiple snapshots can producetens or even hundreds of holograms. This memory-and computation-intensive task calls for a parallelcomputing architecture to bring the total processingtime down to a few hours.

Fig. 4. Benchmark tests of CCC algorithm based on simulated spiral fluid motion consisting of a linear translation T plus a solid-bodyrotation �1 in a volume of D�D�D. (a) Probability of successful correlations as a function of rotation angle � for different levels oftranslation T. (b) Relative error in correlation results. (c) Probability of paired particles among all particles in one interrogation cell. (d)Percentage of erroneously matched centroids among all paired centroids � is expressed in radians. T is expressed in percentage of D.


On the basis of our initial experimentation with aparallel version of the processing algorithm,32 wehave recently implemented a parallel computing in-frastructure with commodity Pentium PCs connectedwith a high-speed, low-latency network (Myrinet) tosatisfy the computing needs. Because of the on-boardcommunication processor on board the Myrinet inter-face card, an intensive communication task is off-loaded from the main processor in each computingnode, making the computing and acquisition opera-tions largely overlapped with the communication.

Figure 5(a) depicts the hardware infrastructure ofthe distributed parallel processing system. The ac-quisition node controls the 3D traverse system toscan the 3D image volume and acquires image datafrom the digital camera. After image data for oneinterrogation cell (IC) is collected, the acquisitioncomputer dispatches the data to one of the processingnodes through the Myrinet switch. The 1.28 Gbyte�sdata rate of Myrinet ensures prompt and efficientdistribution of image data among the processingnodes. The processing nodes send the results back tothe acquisition node after they finish their tasks.Figure 5(b) shows the timing of the parallel comput-ing.

The software is based on a master–slave model,with the program running on the acquisition nodeserving as the master and the programs running on

the processing nodes serving as slaves. We use thestandard message-passing interface (MPI) for inter-process communication support. The master processcontinuously scans (through the traverse system) the3D image field one IC after another and dispatchesthe acquired image slices to the slave process, whichis a stand alone MPI program implementing thePRED and CCC algorithm.

5. Phase-Locked Holographic Particle ImageVelocimetry Measurement

The ultimate goal of HPIV is to provide both tempo-rally and spatially resolved 3D velocity measurements.With the Gemini HPIV system and the implementa-tion of the enhanced processing scheme, for the firsttime to our knowledge this goal has become tangible.However, the lack of a proper recording media trans-port system at the present stage prevents us fromcarrying out such a type of measurements. To demon-strate the capability of the Gemini HPIV system, weinstead perform a phase-locked measurement of a flowpassing a wall-mounted tab, where the measurementis synchronized with the flow phenomena, and the dy-namics of the coherent structure are revealed at asequence of phases.

To phase lock the coherence structure of the flowwith the laser pulses, we first build an active tab,which is driven through a linear solenoid. With aproper driving signal to the solenoid, the tab intro-duces a small amount of disturbances to the flow atthe tab tip. The disturbances are precisely synchro-nized with the laser pulses at a frequency very closeto the natural frequency of the vortex shedding, sothat the coherent structure of the flow will beattracted to the excitation frequency and synchro-nized to the laser pulses. With an accurate delaybetween the disturbances and the laser pulses, wecan record the flow structure at different phases. Be-cause the natural frequency of the tab wake is muchlower than the frequency of the laser pulses �10 Hz�,we use a dividing delay generator to produce thedriving signal so that the disturbances introduced tothe flow are a subharmonic of the laser frequency.Laser Doppler velocimetry (LDV) measurementshows that the flow has a natural frequency of 1.3 Hz.

Fig. 5. Distributed parallel computing cluster in the GeminiHPIV system. (a) Hardware infrastructure. The current systemimplemented the acquisition node and three processing nodes. (b)Timing of parallel operations. The design goal was to maximize theoverlap among the acquisition, communication, and computation.

Fig. 6. Flow visualization of vortex shedding based on phase-locked video imaging. Shown is the intensity average of 100 imagesphase locked with the excitation of the flow. These structureswould smear out after the averaging if the flow is not phase locked.


Thus the excitation is introduced at 1.25 Hz, the clos-est subharmonic of the laser frequency, to phase lockthe flow.

Flow visualizations indicate that the flow is prop-erly phase locked with the controlled excitation.Figure 6 shows the average intensity of 100 frames offlow visualization images. Because the flow is syn-chronized with the illumination pulse, the coherentstructures of the flow are clearly identifiable. Withoutthe phase-locked excitation, the natural flow wouldshow no identifiable structure since structures ineach snapshot are at different phase and hence cancelout.

Shown in Fig. 7 is the optical setup for the flowmeasurement. Because of the large size and the hor-izontal orientation of the test section, which is part of

Fig. 7. Optical setup for the HPIV measurement of flow passinga wall-mounted tab. Note that a horizontal polarization configu-ration is used for optical access.

Fig. 8. Calibration of particle centroid uncertainty. A total of2251 particles was extracted. The solid curve is a best-fit normalprobability distribution for reference. The overall uncertainty is46 �m.

Fig. 9. (Color online) Shown is the 3D vorticity isosurface of theHPIV measured flow at one instant. We cut out a portion of thedata volume to show the inner vorticity contour. Threshold for theisosurface is 0.5 �m.

Fig. 10. Statistics of residual flow divergence (an indicator oferrors in experimental data) compared with statistics of flow vor-ticity. (a) Probability density functions of divergence and vorticitymagnitude normalized by maximum vorticity value �m. Thedarker shaded area is P�� · v� � �T�, and the lighter shaded areais P�� v� � �T� . (b) The relative vorticity error ε�(�T) as afunction of �T.


a 6 in. (15 cm) recirculating water tunnel, we have tointroduce the illuminating beam from the top. There-fore, unlike our previous HPIV measurement14 where

the test section was vertical, here we are dealing withthe less preferred horizontal polarization configura-tion. To counter the decreased fringe visibility in this

Fig. 11. Vortex shedding cycle recorded and reconstructed by holographic PIV. The vortex structures are represented by the vorticityisosurface at �T � 0.5 �m.


type of configuration, we use fixation-free bleaching33(ferric ethylenediamine tetra-acetic acid III) in thechemical processing of the hologram for better dif-fraction efficiency and minimal emulsion shrinkage(which is one of the major causes for aberrations inpractical holography).

The centroid uncertainty is highly specific to theoptical and mechanical configuration. We calibratethis experimental setup by recording a hologram forstandard 10 �m particles distributed on a flat glasssurface and extracting the particle coordinates fromthe reconstructed images. The deviation of the mea-sured centroids from the regressed plane provides anindication of the measurement uncertainty in thecentroid positions. Figure 8 shows the probability dis-tribution of the uncertainty obtained in this manner.The standard deviation of this distribution is�46 �m, which is dominated by the axial component.A major part of the uncertainty is due to the aberra-tions in the hologram, as well as mechanical mis-alignments and vibrations during 3D scanning. Notethat in this calibration we omit the effect due to theaberrations induced by the fluid media because of thesmall angular aperture.

We record eight holograms in a batch with 100 msconsecutive phase delay in between. These eightphases cover one complete cycle of the vortex shed-ding process. On average approximately 50,000particles are extracted for each snapshot in this mea-surement, out of which �20,000 particles are indi-vidually paired to produce velocity vectors. Note thatthis result is actually worse than our previous exper-iment reported in Ref. 14 due to the drastically in-creased recording distance �400 versus 150 mm�,reduced angular aperture �8.5° versus 15°�, and useof horizontal polarization. The time interval betweenthe double exposure is 8 ms. LDV measurements sug-gest that the free-stream flow velocity is �60 mm�s.Therefore the mean displacement between particleimages reconstructed by the hologram is �480 �m.Given the 46 �m centroid uncertainty from our cali-bration and the discussion on the velocity uncertaintyin Section 4, there is approximately 9.5% relativevelocity error in the paired velocity vectors. WeGaussian interpolate the velocity onto regular gridswith a core size of 0.6 IC spacing before further cal-culations for derivatives. This Gaussian interpolationalso serves as a low-pass filter to minimize the effectof the velocity errors, in which on average five pairsparticipate in the calculation of each vector on a reg-ular grid, reducing the relative error to 4.2%. Fromthis interpolated data field, we calculate its vorticity.Figure 9 shows the vorticity isosurface at a threshold�T � 0.5 �m for one of the eight snapshots. Here �m isthe maximum magnitude of vorticity in the measure-ment field. Better means for calculating spatial de-rivatives from scattered 3D data exist34; however, thesimple interpolation suffices for demonstration pur-poses. The vorticity structures shown in Fig. 9 areconsistent with findings from previous flow visualiza-tion, PIV, and direct numerical simulations on thetab wake.35–37

The choice of vorticity isosurface threshold ��T�must ensure that the errors in the vorticity struc-tures be sufficiently small while major vortex struc-tures are properly revealed. Although it is difficult togive a direct measure on the vorticity error, a com-parison between the statistics of residual divergenceand vorticity data provides a good estimate. This isbecause, statistically, random errors contribute to thedivergence and vorticity equally, while real velocitygradients do not contribute to the divergence in anincompressible flow. Hence the probability P�� v� � �T� indirectly measures the amount of error inthe vorticity isosurface obtained at �T. The relativevorticity error, specific to the threshold �T, can bedefined as ��T� � P�� · v� � �T��P�� v� � �T�. Toillustrate the effect of �T on these statistics, inFig. 10(a) we plot the probability density functions ofthe magnitude of vorticity and divergence, both nor-malized by the maximum vorticity �m. These statis-tics are performed on data from all eight snapshots.The darker shaded area is P�� · v� � �T� (a measureof vorticity error), and the lighter shaded area isP�� v� � �T�. Clearly, the higher the vorticityisosurface threshold �T, the less significant the vor-ticity error is contained within the isosurface. Wefurther plot the relative vorticity error ��T� as afunction of �T in Fig. 10(b). At �T � 0.5�m, with whichFig. 9 is generated, �� 2%.

The whole dynamic cycle of vortex shedding by thetab recorded by holographic PIV is demonstrated inFigs. 11(a)–11(h), where the vortex structures arerepresented by the vorticity isosurface at �T� 0.5�m. We mark one particular coherent structureA and follow its spatial–temporal evolution. It can beseen that, structure A originates from the unstableshear layer enveloping the tab edge and evolves intoa distinct 3D structure at the instant in Fig. 11(d),while another structure B follows suit. Both A and Bare identified with the aid of a video animation toreveal the correspondence of structures across thepicture frames. The full dynamic process can best bedemonstrated with animated video clips (not in-cluded in this paper).

6. Conclusion

The accuracy and capacity of HPIV are limited byfundamental imaging issues related to particle scat-tering and holography, including intrinsic aberrationand intrinsic speckle noise. Although often ignored inprevious research, the distributions of intensity andphase in the wavefront associated with Mie scatter-ing contribute to system errors, thus resulting in un-certainties in the particle image positions. Suchsystem errors set the primary limit for the accuracyfor HPIV measurements. The intrinsic speckle noise,resulting from the self-interference of the 3D dis-persed particle images, sets a fundamental limit forthe information capacity, which determines the spa-tial resolution, the measurable spatial extent, andthe applicable range of flow Reynolds number inHPIV measurements. These new insights are derived


from our latest understanding of the imaging char-acteristics of particle holography.

The latest HPIV system in this report not onlyincorporates such new insights, but also integratesadvanced data processing algorithms and distributedparallel computing technology. For the first time toour knowledge, the goal of both temporally and spa-tially resolved flow measurements becomes tangible.Although the system does not yet include film trans-port and is thus not cinematic, we have demonstratedits temporal measurement capability by a series ofphase-locked dynamic measurements of instanta-neous 3D, three-component velocity fields in a highly3D vortical flow.

The authors thank the National Aeronautics andSpace Administration for their support through grantNAG3-2464 and the National Science Foundation fortheir support through grant CTS-9625307. Valuablecontributions from Lujie Cao, Andrew G. Bright,and Scott Woodward to the experiments are greatlyappreciated.

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