Digital holographic particle image velocimetry

2

Digital Holographic

About the cover:

Ripples created by water droplets falling in a Curac¸ao swimming pool.

Particle holograms have some interesting similarities with ripples on a water surface that are created by falling water droplets. The fringes of a particle hologram (shown for example in fig-ure 4.9b) look very similar to the waves on a water surface created by falling droplets. One of the steps of hologram analysis is to determine the positions of recorded particles. The three-dimensional position of recorded particles can be extracted from a two-three-dimensional hologram just like the three-dimensional position of falling droplets (before impact) can be extracted from the two-dimensional ripple pattern that is created on the water surface. The mathematical equa-tions needed to extract a three-dimensional particle-field from a hologram are slightly different, but the principle is the same.

Digital Holographic

Particle Image Velocimetry

PROEFSCHRIFT

ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus prof. dr. ir. J.T. Fokkema, voorzitter van het College voor Promoties,

in het openbaar te verdedigen op vrijdag 28 november 2008 om 12:30 uur

door

Thomas Adriaan OOMS natuurkundig ingenieur

Dit proefschrift is goedgekeurd door de promotor: Prof. dr. ir. J. Westerweel

Samenstelling promotiecommissie: Rector Magnificus, voorzitter

Prof. dr. ir. J. Westerweel, Technische Universiteit Delft, promotor Prof. dr. ir. J.J.M. Braat, Technische Universiteit Delft

Prof. dr. F. Scarano, Technische Universiteit Delft

Prof. dr. H.J.H. Clercx, Eindhoven University of Technology Prof. dr. J.M. Coupland, Loughborough University, United Kingdom Dr. C. Fournier, St. Etienne University, France

Dr. ir. W.S.J. Uijttewaal, Technische Universiteit Delft

Prof. dr. ir. B.J. Boersma, Technische Universiteit Delft, reserve lid

This work is part of the research programme of the “Stichting voor Fundamenteel Onderzoek der Materie (FOM),” which is financially supported by the “Nederlandse organisatie voor Wetenschappelijk Onderzoek (NWO).”

ISBN: 978-90-9023273-7

Copyright c 2003-2008 by T.A. Ooms All rights reserved.

Contents

1.4 Challenges of DHPIV development . . . 12

1.4.1 Accuracy of measured longitudinal displacement . . . 13

1.4.2 Dynamic spatial range of measurement . . . 15

1.4.3 Computational cost . . . 19

1.5 Comparison to other 3D flow-measurement methods . . . 20

1.5.1 Comparison to film-based HPIV . . . 20

1.5.2 Comparison to tomographic PIV . . . 25

1.6 About this thesis . . . 26

2 Optimizing Fourier filtering 31 2.1 Introduction . . . 31

2.2 Analysis . . . 33

2.3 Simple numerical model . . . 37

2.4 Experimental procedure . . . 39

2.4.1 Digital hologram recording . . . 39

2.4.2 Numerical reconstruction . . . 40

2.5 Optimizing Fourier filtering . . . 41

2.5.1 Measurement of the scattered light intensity profile . . . 41

2.5.2 Measuring the effect of different Fourier filters . . . 42

2.6 Conclusions . . . 45

3 Suppressing a sign-ambiguity error and a bias error in the measured particle dis-placement 47 3.1 Introduction . . . 47 3.2 Theoretical analysis . . . 49 3.3 Numerical simulation . . . 53 3.4 Experimental procedure . . . 59 1

2 Contents

3.5 Suppressing the sign-ambiguity and the bias error of z∆m . . . 61

3.6 Conclusions and discussion . . . 66

Appendix A: Cause of the bias error of z∆m . . . 68

4 Measuring millimeter-scale channel flows with digital holographic microscopy 73 4.1 Introduction . . . 73 4.2 Principle . . . 75 4.3 Parameters . . . 78 4.4 Method . . . 82 4.4.1 Experimental procedure . . . 82 4.4.2 Data analysis . . . 87 4.5 Experimental results . . . 95

4.5.1 Laminar channel flow . . . 95

4.5.2 T-mixer flow . . . 98

4.6 Conclusions . . . 105

5 Discussion 107 5.1 Introduction . . . 107

5.2 Dynamic Spatial Range . . . 110

5.3 Dynamic Velocity Range . . . 112

5.4 Valid Vector Fraction . . . 117

5.5 Conclusions . . . 121

Bibliography 122

List of Publications 129

Acknowledgments 131

Summary

Digital Holographic Particle Image Velocimetry Thomas Ooms

This thesis contributes to the development of an instrument that can measure fluid flow velo-city in a three-dimensional (3D) measurement domain by holographic imaging.

During the last 20 years particle image velocimetry (PIV) has developed into a powerful method for measuring flow velocity in a planar cross-section of a flow. The method operates by illumi-nating and imaging small suspended particles in a thin light sheet. By assuming that the particles follow the flow well, and evaluating the images of particles that are recorded at different moments in time, a two-dimensional velocity profile can be obtained. The tools for PIV are commercially available and this technique is widely applied in fundamental and applied research.

One of the main motivations for the development of a three-dimensional flow measurement in-strument is that many flows have a strongly 3D profile, often due to turbulence which is inherently a 3D phenomenon.

Holographic particle image velocimetry (HPIV) is the method of holographically recording a 3D particle field suspended in a flow with the aim to measure the flow velocity. A particle hologram can be recorded on a film and optically reconstructed or recorded on a digital camera and numerically reconstructed. The latter technique is known as ‘digital holographic particle image velocimetry’ (DHPIV).

DHPIV is implemented by illuminating a volumetric section of a flow with suspended particles with a monochromatic coherent light beam. The light that scatters from the particles interferes with a well-defined reference beam which creates a hologram that is recorded by a digital cam-era. At least two holograms are recorded, generally at close consecutive moments in time. Then follows a reconstruction step which is essentially a numerical simulation of the optical recon-struction of a hologram on film and yields a numerical 3D image of the particle field at a single moment in time. By estimating the 3D positions of recorded particles and by pairing particle-images that originate from the same particle at consecutive moments in time, a 3D displacement field is obtained, which can be divided by the recording time-delay to yield a 3D velocity field. DHPIV requires improvement of the relatively large inaccuracy of the measured longitudinal flow velocity, which is caused by the strongly elongated shape of particle-images along the opti-cal axis. This work shows that by adding an optiopti-cal band-pass Fourier filter to the object beam of the recording setup, the effective optical numerical aperture (NA) of the system can be increased which leads to a reduction of the particle-image depth-of-focus by a factor 5 for the described system, which is expected to lead to a proportional improvement of the accuracy of the measured

4 Contents

longitudinal velocity.

When analyzing the reconstructions of two time-consecutive recordings of a moving particle field with a 3D-PIV-correlation analysis, unexpectedly, two correlation peaks occur in a typical correlation volume. These peaks are located symetrically at opposite longitudinal positions in the correlation volume. Because the two observed correlation peaks have a comparable height, a sign-ambiguity occurs in the longitudinal component of the measured particle displacement. The second peak originates from the virtual-image speckle pattern in the reconstruction and can be suppressed by applying an intensity-threshold operation to the reconstructed image.

In the final part of this work, DHPIV is applied to the measurement of microscopic flows. When microscopic flows are imaged with a conventional microscope the measurement domain is lim-ited to a relatively flat transverse planar region because microscopes typically have a high optical NA. Holography does not suffer from this limitation because an image at any selected longitu-dinal position can be numerically reconstructed. Interestingly, the high NA enhances the perfor-mance of DHPIV because it strongly reduces the particle-image depth-of-focus and hence im-proves the accuracy of the measured longitudinal velocity. Although high-NA holograms could not be recorded with a conventional in-line DHPIV system due to the Nyquist sampling criterion, microscopic digital holography does allow high-NA hologram recording: Although a high-NA microscopic hologram contains fringes that are separated by as little as the wavelength of the illumination, such a hologram can be properly sampled by a typical digital camera because it is magnified by an optical element (i.e. a microscope objective). Furthermore, microscopic flows are often independent which allows combination of velocity fields that originate from time-consecutive holograms, which implies a dramatic increase of the number of measured velocity vectors. This can be interpreted as an improvement of the spatial resolution. In this work, this method is applied to the measurement of a flow in a microscopic T-mixer. A measured three-dimensional velocity profile and a three-three-dimensional vorticity profile clearly show four counter-rotating streamwise-oriented vortices. Time-dependent measurements of the T-mixer flow with a low particle concentration show the same velocity profile. This last approach allows particle-tracking in the measurement volume and could be used for a Lagrangian analysis of the flow, for example to indicate a mixing process.

Samenvatting

Digital Holographic Particle Image Velocimetry Thomas Ooms

Dit proefschrift draagt bij aan de ontwikkeling van een instrument dat vloeistofstromingssnelheden kan meten in een driedimensionaal (3D) gebied door middel van holografische beeldvorming. Gedurende de laatste 20 jaar heeft ‘particle image velocimetry’ (PIV) zich ontwikkeld tot een succesvolle methode om stromingssnelheden te meten in een vlakke doorsnede van een stroming. Bij deze methode worden kleine deeltjes aan een stroming toegevoegd, belicht en op een camera afgebeeld. Alleen de deeltjes die zich in een dun lichtvlak bevinden dragen bij aan de meting. Door aan te nemen dat de deeltjes de stroming goed volgen en door gedurende een bepaalde tijdspanne een aantal opnamen te maken, wordt een tweedimensionaal snelheidsveld verkregen. PIV-apparatuur en PIV-software is commercieel verkrijgbaar en deze techniek wordt uitgebreid toegepast in fundamenteel en toegepast onderzoek.

Een van de voornaamste redenen voor de ontwikkeling van een instrument om driedimensionale stromingspatronen te meten is dat stromingen in de praktijk vaak driedimensionaal zijn. Dit kan worden veroorzaakt door turbulentie dat een inherent driedimensionaal verschijnsel is.

De methode ‘holographic particle image velocimetry’ (HPIV) heeft als doel het verrichten van 3D snelheidsmetingen van een stroming door holografische opnamen te maken van een toegevoegd 3D deeltjesveld. Een deeltjeshologram kan op een holografische film worden opgenomen en op-tisch worden gereconstrueerd, of met een digitale camera worden opgenomen en numeriek wor-den gereconstrueerd. De tweede techniek wordt ‘digital holographic particle image velocimetry’ (DHPIV) genoemd.

Met DHPIV wordt een volumetrisch deel van een stroming (met deeltjes) belicht met een monochro-matische coherente lichtbundel. Het licht dat door de deeltjes wordt verstrooid interfereert met een bekende referentiebundel, hetgeen leidt tot een hologram. Dit hologram wordt opgenomen door een digitale camera zonder lens. Meerdere hologrammen worden op snel opeenvolgende tijdstippen opgenomen. Hierna volgt een numerieke reconstructie van de hologrammen wat een simulatie is van de optische reconstructie van een film-hologram. Hieruit volgen 3D beelden van het deeltjesveld op opeenvolgende tijdstippen. Door afbeeldingen van hetzelfde deeltje op verschillende tijdstippen te vergelijken en door de 3D posities van de deeltjesbeelden te schat-ten, kan een 3D verplaatsingsveld worden verkregen. Door de verplaatsingen te delen door de tijdspanne tussen de opnamen wordt een 3D snelheidsveld verkregen.

De longitudinale component van de - met DHPIV - gemeten stromingssnelheid heeft een relatief grote onnauwkeurigheid die veroorzaakt wordt door een sterk uitgerekte vorm van

6 Contents

beeldingen in de richting van de optische as. Dit proefschrift laat zien dat de scherptediepte van een deeltjesafbeelding met een factor 5 verkleind kan worden door een optisch Fourier filter te plaatsen in de objectbundel van een DHPIV-opstelling. Dit effect kan ge¨ınterpreteerd worden als een toename van de effectieve numerieke apertuur (NA) en leidt naar verwachting tot een pro-portionele verbetering van de nauwkeurigheid van de longitudinale component van de gemeten stromingssnelheid.

Wanneer de reconstructie van twee achtereenvolgend opgenomen hologrammen van een bewe-gend deeltjesveld wordt geanalyseerd met een 3D-PIV-correlatiemethode verschijnen onverwacht tweecorrelatiepieken in het correlatievolume. Deze twee pieken bevinden zich op tegenovergestelde longitudinale posities in het correlatievolume. Omdat de twee correlatiepieken een vergelijkbare hoogte hebben, treedt een onzekerheid op in het teken (+ −) van de gemeten deeltjesverplaats-ing. De tweede piek wordt veroorzaakt door een ‘speckle’ patroon in het gereconstrueerde beeld dat gerelateerd is aan het gereconstrueerde virtuele beeld van het deeltjesveld. Dit ongewenste effect kan onderdrukt worden door een intensiteitsdrempel-functie toe te passen op het gerecon-strueerde beeld.

In het laatste deel van dit proefschrift wordt DHPIV toegepast op microscopische stromingen. Als deeltjes in een microscopische stroming worden afgebeeld met conventionele microscopie is het meetdomein beperkt tot een vlak transversaal gebied omdat microscopie gepaard gaat met een hoge optische NA. Holografie ondervindt geen last van deze beperking omdat een beeldvlak op iedere longitudinale positie numeriek kan worden gereconstrueerd. De hoge NA draagt juist bij aan de prestatie van DHPIV omdat het leidt tot een relatief kleine scherpte-diepte van deeltjesbeelden wat vervolgens leidt to een relatief hoge nauwkeurigheid van de longitudinale gemeten stromingssnelheid. Hoewel hologrammen met een hoge NA niet met een conventionele ‘in-line’ DHPIV configuratie kunnen worden opgenomen vanwege het ‘Nyquist sampling’-criterium, staat microscopische digitale holografie opname van hologrammmen met een hoge NA wel toe. In een hologram met een hoge NA is de afstand tussen de interferentie patronen typisch in de orde van de golflengte van de lichtbron. Omdat deze kleinschalige patro-nen in microscopische digitale holografie worden vergroot door middel van een optische element (een microscoop objectief), kunnen deze patronen worden opgenomen met een digitale camera. Verder zijn microscopische stromingen vaak tijdsonafhankelijk wat de mogelijkheid biedt om snelheidsvelden van hologrammen van verschillende tijdstippen te combineren. Dit leidt tot een sterke toename van het aantal gemeten snelheidsvectoren wat kan worden ge¨ınterpreteerd als een verbetering van de ruimtelijke resolutie van de metingen. In dit proefschrift wordt DHPIV toegepast op stromingen in een microscopische T-mixer. Een gemeten 3D snelheidsveld en een 3D vorticiteitsveld laten duidelijk vier vortices zien die tegenovergesteld draaien en in de stro-mingsrichting geori¨enteerd zijn. Tijdsafhankelijke metingen van de T-mixer-stroming met een lage deeltjesconcentratie laten hetzelfde stromingspatroon zien. Deze laatste benadering illus-treert de mogelijkheid om individuele deeltjes te volgen in een 3D meetvolume en kan gebruikt worden voor een Lagrangiaanse analyse van de stroming.

Chapter 1

Introduction

1.1

Motivation

The method of ‘Particle Image Velocimetry’ (PIV) was first described in the mid 1980s by Adrian and Yao (1985) and by Pickering and Halliwell (1985). It aims to measure the velocity of a fluid in a planar cross-section. This is realized by repeatedly illuminating and imaging many sus-pended micrometer-scale particles in a thin light sheet. By assuming that the particles follow the flow, the flow velocity field in a plane can be obtained. While PIV has proven to be a successful method for planar flow velocity measurements, a great interest exists in an instrument that can perform true volumetric flow measurements. This interest partially originates from fundamen-tal fluid dynamics research: Increasing understanding of turbulent flows, which are inherently three-dimensional (Tennekes and Lumley 1972), requires an instrument that can capture the full three-dimensional velocity profile of a turbulent flow.

Most flow velocity measurement techniques rely on imaging and localizing suspended particles that follow the flow’s motion. The collection of suspended particles can be regarded as a 3D object and because holography is a photographic technique that allows recording and reconstruc-tion of a 3D object, holography is an obvious candidate for the physical principle behind a 3D flow velocity measurement instrument. The technique that aims to perform 3D flow velocity measurements by holographically imaging many suspended particles is named Holographic Par-ticle Image Velocimetry (HPIV). The principle of this technique is explained in detail by Hinsch (2002) and Meng et al. (2004) who also state that HPIV is one of the most promising techniques for true three-dimensional flow measurements. Another promising method for 3D flow velocity measurements is named tomographic PIV which makes use of multiple simultaneous views of the particle field and a subsequent numerical reconstruction of the three-dimensional particle image field. Tomographic PIV is compared to holographic PIV in section 1.5.2.

A hologram can be recorded on a film and optically reconstructed (general method for well-known artistic applications) or recorded on a digital camera and numerically reconstructed. The latter technique is known as ‘digital holography’ (DH). This explains the title of this thesis, Digital Holographic Particle Image Velocimetry (DHPIV), which is a technique that aims to perform 3D flow velocity measurements by holographically imaging suspended, volumetrically-distributed particles on a digital camera. Because digital cameras can record a set of time-consecutive images, time-resolved flow measurements are in principle possible with this tech-nique.

8 Chapter 1. Introduction 1980 1985 1990 1995 2000 2005 2010 50 100 150 200 250 300 350 400 450 500 Time (year) Number of publications Digital holography Optical holography

Figure 1.1: The number of publications found by the search engine www.scholar.google.com on the term ‘digital holography’ and ‘optical holography’ versus year of publication. During the last 25 years, the number of publications with the term ‘digital holography’ grows fast compared to the number of publications with the related term ‘optical holography’. The rapidly increasing interest in digital holography is stimulated by the development of computers and digital cameras.

1.2

History of DHPIV

Although numerical analyses of optical holograms were already performed in the 1970s and 1980s by Kronrod et al. (1972) and Onural and Scott (1987), the first experiments with a digital camera as a holographic recording device were described in the 1990s by Haddad et al. (1992) and by Schnars and J¨uptner (1994). Haddad et al presented digital recording and numerical reconstruction of microscopic biological specimen. Schnars and J¨uptner illustrated the capability of digital holography by recording a 1-centimeter cubic die. Subsequently followed a great interest in digital holography (figure 1.1) which was mainly stimulated by the rapid development of micro-electronics, digital computers and digital sensor technology (Moore 1965).

The first digital holographic recordings of tracer particles in a flow were described by Adams et al. (1997) and Murata and Yasuda (2000) which marks the beginning of the scientific explo-ration of DHPIV. Since then, much research has been conducted on DHPIV.

1.3

DHPIV principle

The method DHPIV comprises a number of steps, as shown in figure 1.2.

The first step is hologram recording. Most described DHPIV experiments record a hologram with a so-called in-line setup (Ikeda et al. 2003, Malkiel et al. 2003, Pan and Meng 2003, Satake et al. 2004, Sheng et al. 2007). This setup is schematically shown in figure 1.3a. A collimated beam of monochromatic coherent light passes through a flow that contains many small sus-pended particles. The unscattered light forms a so-called reference beam and the (near-)forward

1.3. DHPIV principle 9

Figure 1.2: Main steps of the DHPIV method.

Figure 1.3: Some possible configurations of a DHPIV recording setup are an in-line configuration (a); a sideward scattering on-axis configuration (b) and a forward-scattering on-axis configuration (c). (Source: H Meng et al 2004

10 Chapter 1. Introduction

Figure 1.4: A typical digital hologram (L) and corresponding reconstruction (R). (Source: Pan G and Meng H 2003

Appl. Opt. 42827-833)

scattered light forms a so-called object beam. The two beams interfere and form a hologram which is recorded by a lensless digital camera. Another possible recording configuration is a so-called sideward-scattering on-axis configuration (figure 1.3b). In this case the object beam consists of light that has scattered sideward (in this case 90◦_{) and the reference beam is a}

sep-arate, generally collimated beam. The two beams are combined by a beam splitter. The term on-axis indicates that the reference beam and the object beam travel towards the digital cam-era along the same axis. This configuration avoids distortion of the reference beam by the fluid and/or the fluid container and uses the relatively isotropic scattering intensity profile compared to a forward-scattering configuration. This is expected to have positive effect on the accuracy of the longitudinal component of the measured flow velocity (Ooms et al. 2006a). A disadvantage of this configuration is the extreme reduction of the sideward-scattered light intensity compared to the forward-scattered light intensity. A third configuration is shown in figure 1.3c and is called a forward-scattering on-axis configuration. A so-called Fourier filter is needed to eliminate the unscattered plane-wave component from the object beam. In this configuration, the scattering intensity is relatively strong, but the scattering profile is highly anisotropic when relatively large particles are used compared to the illumination wavelength. The forward-scattering on-axis con-figuration is used in experiments described in chapter 2 and 3 of this thesis.

Hologram recording is followed by a digital preprocessing step in which unwanted hologram artifacts (i.e. reflections or scattering from dirt particles) can be removed, for example by filtering in the spatial domain of the hologram, filtering in the Fourier domain or by subtracting the time-average of a hologram time-array. A typical particle hologram contains a collection of circular concentric interference fringes and an example is shown in figure 1.4L.

Then follows the reconstruction step which is essentially a numerical simulation of the optical reconstruction of a hologram on a film: The hologram intensity is used as an amplitude trans-mission function and is virtually exposed to a reconstruction beam. Any profile can be chosen for the reconstruction beam but it is generally a plane wave, a converging spherical wave or a diverging spherical wave. Using the complex light amplitude immediately after the hologram and simulating the propagation of light (Goodman 1996) to further parallel planes leads to a 3D reconstruction of the object. The undiffracted zeroth order is filtered out numerically (Cuche et al. 2000) which leaves only a real image and a virtual image of the object (Hecht 2002). A method has been described by Onural and Scott (1987) to also eliminate the generally unwanted

1.3. DHPIV principle 11

Figure 1.5: Particle-image intensity profile along the optical axis. In DHPIV, the particle-image size along the optical axis can be as large as 40 times the particle diameter. (Source: Pan G and Meng H 2003 Appl. Opt. 42 827-833)

virtual image from the reconstruction. The real image of a typical reconstruction consists of a collection of particle images (high-intensity points in figure 1.4R) whose three-dimensional shape is an ellipsoid which is generally stretched along the optical axis. This shape originates from the limited angular aperture of the holographic system as will be discussed in section 1.4.1. As an example, figure 1.5 shows that the particle-image size along the optical axis can be as large as 40 times the particle diameter (based on a 20% intensity reduction). The particle image size perpendicular to the optical axis is generally about equal to the particle diameter. Hence, the particle-image size along the optical axis is typically 1 to 2 orders of magnitude larger than the particle-image size perpendicular to the optical axis. The consequence of the stretched shape of reconstructed particle images is discussed in section 1.4.1. The virtual image of a typical recon-struction is a volumetrically distributed speckle pattern (Goodman 1996). This pattern is visible as a relatively low-intensity background in figure 1.4R. The three-dimensional shape of a single speckle is also an ellipsoid that is stretched along the optical axis. Because the typical shape of particle images and the virtual-image speckle is similar, it can be difficult to distinguish a particle image from the speckle background. For this reason, experimental settings are generally chosen such that the intensity of the speckle pattern is much lower than the particle image intensity. Unlike in conventional imaging (i.e. imaging with lens systems), in holography the depth of the measurement domain is not limited by the depth-of-field1 _{of the imaging system. In principle,}

holography allows the reconstruction of an image plane at any distance from the hologram plane. For example, in the work of Sheng et al. (2006), the depth of the reconstructed domain is up to 3 orders of magnitude larger than the depth-of-focus1_{of the holographic imaging system.}

After the reconstruction step, two approaches can be followed to obtain a flow velocity vec-tor field, particle tracking velocimetry (PTV) or particle image velocimetry (PIV) (figure 1.2). The PTV approach is most suitable when the particle concentration in the fluid is low, or more specifically when individual particles can be identified in the reconstruction and when the average distance between neighboring particles is significantly larger than the average particle displace-ment between consecutive hologram recordings. The first step of the PTV approach is to identify the images the recorded particles in the time-consecutive hologram reconstructions. Then, a 3D

12 Chapter 1. Introduction

Figure 1.6: Example of a measured velocity vector field. (Source: Satake S et al. 2004 Opt. Rev. 11 162-164) position estimate is made of the recorded particles based on their reconstructed images. The following step is to match the corresponding particle images of time-consecutive recorded holo-grams. The final step is to convert the measured particle displacement field into a velocity field. Because DH is preferably performed with a very low particle concentration (Royer 1974, Meng et al. 1993, Malek et al. 2004), the PTV approach is currently used in most described DHPIV studies. An example of a flow velocity vector field which is obtained with a PTV analysis is shown in figure 1.6. The vector field illustrates a water flow around a 4 ×4×4 mm3_{brass cube.}

The capacity of digital image sensors (i.e. number of pixels) is expected to continue its growth in the near future (Moore 1965) which allows for an increase of the particle concentration (sec-tion 1.4.2). When the particle concentra(sec-tion is so high that individual particles can no longer be tracked, the PIV approach is preferred to the PTV approach (Raffel et al. 1998). Like the PTV approach, the PIV approach also requires that individual particle images can be distinguished (Raffel et al. 1998). The most straightforward PIV approach consists of cutting the 3D recon-struction of two time-consecutive holograms in several ’boxes’, or interrogation volumes, that preferably contain about 10 particles (Keane and Adrian 1992). Corresponding interrogation volumes are processed with a 3D correlation analysis which leads to an estimate of the local particle field displacement. With a known time-interval between consecutive recordings, a three-dimensional velocity vector field is obtained.

1.4

Challenges of DHPIV development

Development of a successful holographic PIV system requires solving - or at least improving - some specific weaknesses, which are clearly identified by Meng et al. (2004). This section discusses issues that are specific for digital HPIV.

1.4. Challenges of DHPIV development 13

1.4.1

Accuracy of measured longitudinal displacement

In many flows, flow motion occurs in all three spatial directions. When measuring the three com-ponents of the flow field with a 3D technique such as DHPIV, it is desirable that the inaccuracy of the measured velocity is comparable along the three spatial axes. More precisely, the inaccuracy of the longitudinal2_{velocity component should be of the same order of magnitude as the}

inaccu-racy of the transverse3 _{component. In case of a PTV analysis, this requires that the inaccuracy}

of estimated longitudinal particle positions is comparable to the inaccuracy of estimated trans-verseparticle positions. In case of a PIV analysis, this requires that the inaccuracy of estimated longitudinal positions of correlation peaks (Raffel et al. 1998) is comparable to the inaccuracy of estimated transverse positions of correlation peaks. In the PTV case, as well as the PIV case, fulfillment of this requirement depends mainly on the shape of the reconstructed particle images (longitudinal size compared to transverse size). If particles are considered point-sources and imaging is diffraction limited, the transverse size of a particle image (dpi) is (Goodman 1996):

dpi=1.22 λ

NA (1.1)

whereλis the illumination wavelength and NA is the effective numerical aperture (Hecht 2002). The longitudinal size of a particle image (DOFpi) is (Born and Wolf 1959):

DOFpi = λ

NA2 (1.2)

Clearly, the ratio between dpi and DOFpi depends on the NA. If particles cannot be considered

point sources, for example if their size is larger than the system diffraction limit (Goodman 1996), the ratio between dpi and DOFpi is also expected be approximately equal to the NA (Ooms et al.

2006a).

The NA is determined by a number of factors among which are particle scattering, hologram size, hologram position and hologram pixel spacing. As described by Westerweel and Adrian (To be published), the phenomenon of particle scattering is a combination of diffraction, reflection and refraction. Forward scattering, which is most commonly used in DHPIV, is dominated by diffraction (Westerweel and Adrian To be published). As shown in figure 1.7, Mie scattering theory shows that in the forward scattering domain, most of the scattered light is contained in a central diffraction lobe with an angular aperture of about (λ/dp) where λis the illumination

wavelength and dpis the particle diameter (Meng et al. 2004). This can be interpreted as an equal

limitation of the NA. When particles have a (practical) diameter of a few tens of micrometers, the NA is thereby limited to a few hundredths. The obvious solution of reducing the particle diameter is not necessarily effective in a practical situation: Because the scattered light intensity decreases strongly with a decreasing particle diameter (i.e. proportional to d2

p when dp> λ

(Adrian and Yao 1985)), the signal-to-noise ration (SNR) of the object beam increasingly suffers from unwanted speckle noise (i.e. light that scatters from dirt and dust on optical elements and on the fluid container). Furthermore, in an in-line configuration, a reduction of dp reduces

the scattered light intensity but leaves the reference beam intensity unchanged, which reduces the dynamic range of the digitized interference signal (between the object beam and reference

2_{Direction along the optical axis.}

14 Chapter 1. Introduction

Figure 1.7: Light scattering coefficients for polystyrene spheres (particle refractive index = 1.62) in water, the two curves represent the scattered intensity parallel- and perpendicular to the orientation of the polarization of the incident light,λ=514.5 nm. (a) dp=0.5 µm, (b) dp=2.0 µm, (c) dp=5.7 µm. (Source: Westerweel J. and

1.4. Challenges of DHPIV development 15

beam). If sufficient object illumination is available, a sideward scattering configuration could alleviate the effect of anisotropic scattering. However, sideward Mie scattering leads to particle images with astigmatism (Pu and Meng 2003).

The hologram pixel spacing (dr) also influences the NA because sampling theory prescribes a

maximum interference angle between the object beam and reference beam of arcsin(λ/2dr)

(Goodman 1996). This effect limits the NA of a conventional in-line DHPIV system to a few hundredths (Pan and Meng 2003, Ooms et al. 2006a).

Concluding, particle images in DHPIV have generally a much larger longitudinal size than trans-verse size. This generally leads to a larger inaccuracy of the measured longitudinal velocity compared to the measured transverse velocity. Based on results of Prasad et al. (1992) and West-erweel (2000), an estimate of the inaccuracy of the measured transverse velocity is γ_{· d}pi/∆t,

where the parameterγ ranges between 0.05 and 0.1 and∆t is the time interval between the two recordings. It is expected that this also applies to the inaccuracy of the measured longitudinal velocity (i.e.γ_{· DOF}pi/∆t) (Ooms et al. 2006a).

Work has been described that aims to improve the inaccuracy of the measured longitudinal ve-locity: Malkiel et al. (2003) used stereoscopic viewing in a DHPIV system, which was imple-mented by placing a mirror under an angle of 45◦_{in a rectangular container. Another approach}

was developed by Pan and Meng (2003) who use the phase of the reconstructed complex ampli-tude to increase the accuracy of the reconstructed particle depth coordinate. Although this work reports an impressive spatial resolution along the optical axis of approximately 10 µm, it can-not be applied to transparent4_{particles (Pan and Meng 2003). Work of Yang et al. (2005) aims}

to minimize the particle-image depth-of-focus by suppressing the anisotropic particle scattering behavior. This approach is implemented by numerically decoupling the reconstructed particle-image size and particle-particle-image position. This method requires foreknowledge of the particle diameter (tolerance estimated by Yang et al. (2005) to be ±5%) and a sufficiently small particle scattering intensity anisotropy (chapter 2). Liu and Hussain (1998) have shown a reduction of the particle-image depth-of-focus by adding an optical filter to a film-based off-axis HPIV recording setup. This thesis also discusses methods to improve the accuracy of the measured longitudinal velocity component, which are introduced in section 1.6.

1.4.2

Dynamic spatial range of measurement

Adrian (1997) describes the dynamic spatial range (DSR) of PIV as ‘the field-of-view (FOV) di-vided by the the smallest resolvable spatial flow variation’. Adrian (1997) further states that the smallest resolvable spatial flow variation, or highest spatial resolution, is achieved by measure-ment of single particle displacemeasure-ments. The highest spatial resolution is estimated as the average distance between particles. Chandrasekhar (1943) shows that this distance equals 0.55 ·C−1/3

p ,

where Cpis the particle concentration). When assuming a cubic measurement domain, the

max-imum DSR is: [DSR]max = (FOVx· FOVy· Lz·Cp)1/3 0.55 = N1/3p 0.55 (1.3)

4_{The tolerable transparency is not quantified by Pan and Meng (2003). Their method requires that the} light-amplitude transmittance of particles is real, which implies that particle-scattering by diffraction should strongly dominate above particle-scattering by refraction.

16 Chapter 1. Introduction

where FOVx and FOVyare the transverse dimensions of the measurement domain, Lzis the

lon-gitudinal dimension of the measurement domain and Np is the total number of particles in the

measurement domain. Expression 1.3 assumes that the transverse field-of-view is smaller than the transverse dimensions of the investigated flow (Lx and Ly). In the case that Lx,y< FOVx,y,

the variable FOVx,y should be replaced by Lx,y. In the extreme case where the particle-image

depth-of-focus (DOFpi) is larger than 0.55 ·C−1/3p , the estimated maximum longitudinal DSR

is different: The longitudinal elongation of the particle images causes spatial low-pass filter-ing of the measurement result (Sheng et al. 2003). The ‘smallest resolvable spatial flow vari-ation’ then equals roughly DOFpi. In this case the longitudinal DSR equals Lz/DOFpi instead

of Lz· C1/3p /0.55. In most cases however, expression 1.3 correctly describes [DSR]max and the

highest [DSR]max is obtained by maximizing Np. With DHPIV, however, increasing the particle

concentration beyond certain limits will prevent appropriate imaging. Two effects can be identi-fied that lead to image deterioration. The first effect is the reduction of the SNR by the speckle noise that is generated by particle scattering (Meng et al. 1993). The number of particles that can be recorded is also limited by the number of pixels of the digital camera (Meng et al. 2004, Koek et al. 2005). These two effects are discussed in this section.

Influence of speckle

The reconstruction of a hologram generally contains a real particle image and a speckle pattern that originates from the virtual image (Meng et al. 1993). The unscattered zeroth order beam is usually filtered out by high-pass filtering. The speckle pattern of the virtual image (noise) can hinder proper detection of the real particle image (signal). While in film-based holography the virtual image is easily spatially separated from the real-image by using an off-axis recording configuration (Goodman 1996), the limited spatial resolution of current digital recording devices does not allow this approach with DHPIV. As discussed in section 1.4.1, the maximum angle between the interfering object beam and reference beam (φmax) is typically a few hundredths

of a radian (i.e. 0.04 rad or 2.3◦ _{for λ=532 nm and d}

r =6.45 µm). Distinguishing particle

images from speckle noise by their appearance (i.e. size and shape) is also not possible because their appearance is similar to speckle (Meng et al. 1993). Hence the DHPIV method requires that the reconstructed particle images have a higher intensity than the surrounding speckle noise, which implies a minimal value of the SNR of the reconstruction. Meng et al. (1993) suggest that a SNR of at least 5 is required to distinguish particles from the speckle background. The work of Meng et al. (1993) further shows that the SNR is directly related to the product of the particle concentration (Cp), the depth of the measurement volume (Lz) and the particle diameter

squared (d2

p). Their work shows that the SNR decreases when the d2pCpLz-product increases.

The product d2

pCpLz can be intuitively understood by observing that (besides a factor π/4 for

spherical particles) it is a measure for the relative ‘amount of light’ that ‘hits’ a particle while passing through the measurement domain. It can be concluded that proper particle detection is only possible with a sufficiently low particle concentration, or more exactly a sufficiently low d2_pCpLz-product. A limitation of the CpLz-product clearly implies a limitation of the dynamic

spatial range (DSR) for a given field-of-view. Values of dp, Cp, and Lzof recent studies are given

in table 1.1.

Because the virtual image (noise) and the real image (signal) are generated by the same object (i.e. the particles) it is difficult to avoid this problem. Onural and Scott (1987) describe a method

1.4. Challenges of DHPIV development 17

Table 1.1: Values of dp, Cp, and Lzof recent studies. The studies with a ‘*’ are microscopic DHPIV measurements

(with optical magnification of holograms as described in chapter 4).

Study dp (µm) Cp(mm−3) Lz(mm) d2p· Cp· Lz (%)

Malkiel et al. (2003) 20 4 15 2.4

Ooms et al. (2006a) 40 −63 1 20 5

Satake et al. (2006) * 1.0 92×103 _9.2×10−2 0.85

Sheng et al. (2006) * 0.75 & 3.2 2×103 _{10 1.1 & 20}

Soulez et al. (2007) 94 − − −

Yamamoto and Uemura (2008) 9.0 0.17 6.9 9.5×10−3

that allows reconstruction of the real image without the conventionally present virtual image. Although the absence of the virtual image will lead to a higher SNR of the reconstruction (Liu and Hussain 1998), the speckle noise of the real out-of-focus particle-images continues to cause an intrinsic upper limit of the CpLz-product (Pu and Meng 2004).

Influence of the CCD sensor

The spatial resolution of DHPIV measurements is also limited by the limited number of pixels on a digital (CCD) sensor: While a typical holographic film has a spatial resolution of a few thousand line pairs per millimeter (lp mm−1), current CCD sensors have a typical resolution of

about 50 lp mm−1_{. Section 1.4.1 shows that this implies a limitation of the effective numerical}

aperture. Pu and Meng (2004) show that a limitation of the effective angular aperture (Ω) implies a limitation of the number of particles that can be recorded per transverse unit area ([CpLz]max).

They derive the relation:

[CpLz]max = πtan2Ω λ2h I0 <IN> i min (1.4) whereh I0 <IN> i

minis the minimal ratio between the particle image intensity and the mean speckle

noise intensity needed to distinguish particle images from the speckle noise background. The angular aperture (Ω) and the numerical aperture (NA) are related as NA = n · sinΩ, where n is the refractive index of the medium near the digital sensor. Because in DH, Ω_{1 and n = 1,} NA= sin(Ω_{) ≈ tan(}Ω). Relation 1.4 can therefore be written as:

[CpLz]max = πNA2 λ2h I0 <IN> i min (1.5)

If NA in expression 1.5 is replaced byλ/2dr (section 1.4.1) and if both sides of the equation are

multiplied by FOVxFOVy(= NxNydr2, where NxNyare the number of sensor pixels), the maximum

number of recorded particles (Np) is (Meng et al. 2004):

[Np]_max = πNxNy 4h I0 <IN> i min . (1.6)

18 Chapter 1. Introduction

Because proper particle detection requiresh

I0

<IN>

i

min=50 (Meng et al. 2004)

5 _{(where I0 is the}

signal - or particle-image intensity - and < IN>is the mean speckle noise intensity), relation 1.6

can be rewritten as:

[Np]_max≈

NxNy

50 . (1.7)

This implies a maximum of 20 × 103 _{particles per sensor-megapixel. In this analysis, the only}

source of speckle noise is assumed to be out-of-focus real particle images while the effect of the virtual image is ignored. The resulting value should therefore be considered optimistic.

A comparable analysis is performed by Koek et al. (2005). This work investigates the effect of the virtual-image speckle noise on the signal-to-noise ratio and ignores the effect of the out-of-focus real particle images. This work estimates the maximum number of particles that can be recorded on a digital sensor as:

[Np]_max=

NxNy

R

(1 +

R

min

. (1.8)

where

R

_R

[Np]_max= NxNy h I₀ <IN> i min . (1.9)

The great similarity between expression 1.6 and 1.9 is not surprising. The first analysis assumes that the noise originates from the out-of-focus real particle images and the second analysis as-sumes that the noise originates from the the virtual image. Because the energy of the real image and the virtual image are equal (Koek et al. 2005), the expression of [Np]_max should also be

similar.

Table 1.2 shows that the actual number of recorded particles in recently described experiments is often significantly lower than the above estimate (i.e. ranging from a few to a few thousand particles per sensor-megapixel). Clearly, other factors besides optimization of the DSR influence the chosen Np.

Table 1.2: The number of recorded particles in various studies. The studies with a ‘*’ are microscopic DHPIV measurements (with optical magnification of holograms as described in chapter 4).

Study Np Nx× Ny Np/Mpix

Malkiel et al. (2003) 13,500 2048 ×2048 3,200

Ooms et al. (2006a) 1,200 1376 ×1040 840

Satake et al. (2006) * 320 1024 ×1024 300

Sheng et al. (2006) * 5,800 2048 ×2048 1,400

Soulez et al. (2007) 5 1280 ×1024 4

Yamamoto and Uemura (2008) 27 1024 ×1024 26

1.4. Challenges of DHPIV development 19

By using lenses in the recording setup, as shown in figures 4.2 and 4.6, a hologram can be (de)magnified before it is recorded on the digital sensor (chapter 4). With a transverse magnifi-cation M, which is defined in figure 4.6, the transverse area of the measurement domain reduces by a factor M2_{. The Nyquist limit of the NA, however, increases by a factor M (chapter 4). In}

expressions 1.5 and 1.6, the factor M cancels out which indicates that [Np]max or the [DSR]max

would be insensitive to adding magnifying optics to a DHPIV setup.

1.4.3

Computational cost

Currently, the computing power of a state-of-the-art desktop computer is sufficient to perform a real-time 2D PIV analysis during measurements. This possibility allows, for example, an effec-tive adjustments of parameters during an experiment, which contributes to the user-friendliness of the 2D PIV technique. The data-analysis time of a holographic PIV measurement is typi-cally a few days (on a desktop computer). The current relatively slow data-analysis procedure of DHPIV is discussed in this section.

Hard drive

When an array of P hologram pairs is recorded, each hologram consists of Q megapixels and each hologram is reconstructed in R planes, the required hard drive (HD) space is therefore 32PQR megabytes (2 holograms per hologram pair and 16 bytes per voxel). With practical values (P = 50, Q = 4, R = 100) this corresponds to 640 gigabytes (GB). A state-of-the-art consumer hard drive can contain the results of only a few experiments. This limitation can be alleviated if intermediate data-analysis results (i.e. hologram reconstructions) are deleted after the analysis of each hologram pair. The measurement result (i.e. the vector data) requires very little storagespace, typically a few kiloBytes.

Random Access Memory (RAM)

After a hologram pair has been reconstructed (as two 3D particle image fields), a PTV analysis or a PIV analysis aims to extract a 3D particle displacement field. For this step, particle-image data is needed from various locations within the two three dimensional reconstructions. A practical calculation speed of this step requires that the two entire 3D reconstructions are simultaneously stored in the computer RAM. This requires a RAM capacity of 32QR megabytes. Using the same values as in the previous paragraph leads to a desired RAM size of 12.8 gigabytes. This value exceeds the typical RAM capacity of a state-of-the-art consumer computer by approximately a factor 4. A work-around for this deficiency is to load only a relevant selection of the hologram reconstruction into the computer RAM. In case of a PTV analysis, such a selection could com-prise a chosen spatial region around the investigated particle image, as shown in figure 4.13. In case of a PIV analysis, such a selection could comprise only the part of the reconstruction that falls within the investigated interrogation region. This work-around is time-consuming because it requires a repetitive exchange of large data-amounts between the computer HD and RAM. It is our experience that this work-around reduces the processing speed of a typical data-analysis by

20 Chapter 1. Introduction

about a factor 10.

Central Processing Unit (CPU)

The PTV data-analysis procedure as described in chapter 4 (P = 50, Q = 4 and R = 100) re-quired several days of computing time on a desktop computer (CPU = 2.5 GHz, RAM = 3.1 GB, operating system: Linux, software: Matlab). Most of this time was spent on inefficient actions (i.e. writing to- and reading from the computer HD). The computing time can be significantly reduced by increasing the computer RAM size as recommended in the previous paragraph. From this subsection, it can be concluded that DHPIV relies heavily on development of com-puting power (Moore 1965) for its future success.

1.5

Comparison to other 3D flow-measurement methods

1.5.1

Comparison to film-based HPIV

An example of a successful experiment with a film-based HPIV system is the measurement of a turbulent pipe flow by Barnhart et al. (1994). Although this experiment was performed in the early days of HPIV development, the measurement result contains approximately 425,000 in-stantaneous flow velocity vectors. The holographic recording setup is shown in figure 1.8a: Two pulsed Nd:YAG lasers are used and successively fired at time t1 and t2. Light of the first laser is directed along the left reference beam and towards the object (turbulent air flow in a pipe with suspended oil droplets). Light of the second laser is directed along the right reference beam and towards the object (along the same path as the object beam of the first laser). The object beam passes through the flow and partially scatters from the suspended particles. Light that scatters at about 15◦ _{- leftward and rightward - is guided by lenses and prisms towards a silver-halide}

film. The unscattered light falls onto a beam stop. The reference beams are expanded and colli-mated and approach the film at an angle of ±50◦with respect to the film normal. To reconstruct

the hologram (figure 1.8b), the film and the L11-P1-L12-L21-P2-L22 optical components are kept at the same relative positions. To reconstruct the t1-particle field, the film is exposed to a reconstruction beam that is the phase conjugate of the t1-reference beam. Light is diffracted towards the L11-P1-L21 system and towards the L21-P2-L22 system. Reconstruction of the particle field recorded at t2 works similarly with a reconstruction beam that is phase-conjugate to the t2-reference beam. The two particle-image fields (corresponding to recording at t1 and t2) that are reconstructed through the L11-P1-L21 system are evaluated with a correlation ana-lysis. This leads to a three-dimensional, but two component (3D2C) velocity vector field. The velocity vector component along the viewing direction is ignored because of its relatively large inaccuracy. Similarly, the two particle-image fields that are reconstructed trough the L21-P2-L22 system are correlated which leads to a second 3D2C velocity vector field. The two vector fields are subsequently geometrically combined to from a three-dimensional three-component (3D3C) vector field. The impressive measurement result is shown in figure 1.9.

In the following years more studies investigated film-based HPIV flow measurements and pre-sented high numbers of measured velocity vectors (table 1.3).

1.5. Comparison to other 3D flow-measurement methods 21

Figure 1.8: Hologram recording (a) and reconstruction (b) setup of Barnhart et al. (1994). R1 and R2 are two reference beams. O1 and O2 are two object beams. l01and l02are two pulsed Nd:YAG lasers, M1-M9 are mirrors, L1-L8, L11, L12, L21, L22 are lenses and P1 and P2 are prisms. t1 and t2 represent the time that the two respective lasers are fired.

Figure 1.9: Measurement result from Barnhart et al. (1994): A HPIV measurement of a turbulent pipe flow led to about 425,000 3D velocity vectors.

22 Chapter 1. Introduction

Table 1.3: Examples of investigations of film-based HPIV with the number of measured velocity vectors.

Study Velocity vectors Recorded particles

Barnhart et al. (1994) 425,943 360 ×103

Herrmann and Hinsch (2004) 16,640 103 ×103

Meng and Hussain (1995) 10,824 74 ×103

Pu and Meng (2000) 92,000 24 ×106

Sheng et al. (2003) 644,160 >357 ×103

Zhang et al. (1997) 818,583 <742 ×103

Figure 1.10: Holographic recording configuration: Nd:YAG is a pulsed laser, SH a shutter, PM a power meter, HW a half-wave plate, PBS a polarizing beam splitter, M a mirror, QW a quarter-wave plate, PC a Pockels cell, L1 and L3 plano-concave lenses, L2 and L4 plano-convex lenses that collimate the beam, L5 and L6 plano-convex lenses as a part of an optical high-pass Fourier filter, BS a beam stop, f the focal length of L5 and L6 and RI the real-image of the particle field.

A film-based HPIV system was also investigated in our laboratory. A setup was built with a polarization-sensitive bacteriorhodopsin (BR) film as a hologram recording medium (Koek 2006). In the hologram recording setup (figure 1.10), an object beam illuminates a flow with par-ticles. The flow is a moving vortex ring which is generated by injecting a falling water droplet into a water-filled tank. Hydrogen bubbles were used as tracer particles because of their high light scattering efficiency. The scattered object light passes through a optical bandpass Fourier filter (Ooms et al. 2006a) and interferes with a reference beam to form a hologram at the BR film. The information of two successively recorded holograms can be multiplexed on the BR film and fully separated during hologram reconstruction by using polarization of the light and polarization-sensitivity of the BR film (Koek et al. 2004). In the reconstruction step (figure 1.11), the BR film is exposed to a reconstruction beam with an appropriately chosen circular polarization (Koek et al. 2004) which leads to two separable real images which are digitized by a CCD camera. Data-analysis was performed with a 3D-correlation PIV analysis. The velocity slip of the hydrogen bubbles was corrected during data-analysis. The typical velocity profile of a vortex ring is visible in figure 1.12. It should be noted that the this velocity field was only measured in a single transverse plane because the tracer particles (i.e. hydrogen) bubbles were located in a single vertical plane.

Some general advantages and disadvantages of film-based HPIV, compared to DHPIV can be identified: The main advantage of using a film to record a hologram, compared to using a digital

1.5. Comparison to other 3D flow-measurement methods 23

Figure 1.11: Reconstruction setup: CW Nd:YAG represents a continuous-wave laser, R3 a quarter-wave plate, MHW a mechanical half-wave plate, SF a spatial filter, L4 a collimating plano-convex lens, RI the real-image of the particle field and CCD a scanning CCD camera.

Figure 1.12: Velocity field around a downward-traveling vortex ring. The ’donut’ represents the vortex ring and is added for visualization.

24 Chapter 1. Introduction

camera is the relatively huge information capacity of a film. The information capacity per unit length of a typical holographic film is typically a few thousand line-pairs per millimeter, whereas the information capacity per unit length of a digital sensor is typically 50 line-pairs per millime-ter. The information capacity per unit area of film is therefore about 4 orders of magnitude larger. Furthermore, the typical size of a holographic film is about 100 ×100 mm2_{, whereas the typical}

size of a digital sensor is 10 × 10 mm2_{. This indicates a surface area ratio of 2 orders of}

magni-tude. Combining these two factors suggests that the information capacity of a holographic film is about 6 orders of magnitude larger than the information capacity of a current state-of-the-art digi-tal sensor.6 _{Although the information capacity of digital sensors benefits from continuous rapid}

developments in the field of micro-electronics (Moore 1965), the moment that its information capacity is comparable to a holographic film is not within sight.

In HPIV experiments, the larger information capacity of a holographic film can result in a better accuracy of the measured longitudinal velocity component when the effective NA is increased (section 1.4.1). With a typical information capacity per unit length of the order ofλ, the Nyquist criterion no longer limits the NA of the system. In principle this allows that a particle field can be recorded with a NA that approaches unity7_{. Equations 1.1 and 1.2 suggest that this should}

lead to a comparable accuracy of the measured longitudinal- and transverse velocity component. Furthermore, equation 1.6 and 1.9 indicates that the number of recorded particles is proportional to the information capacity of the hologram-recording medium. Because the dynamic spatial range (DSR) is proportional to N1/3p (equation 1.3), it is expected that the DSR of a film-based

HPIV system is about 106/3_{(=100) times larger than the DSR of a digital-camera based HPIV}

system.

Most main disadvantages of film-based HPIV are of a practical nature. Figure 1.3 and 1.8 show a large difference in the complexity of the recording setup of a digital- and a film-based HPIV system. A high cost, difficulty to set up and operate a complex film-based HPIV system could prevent it from becoming a widely accepted measurement system. A second disadvan-tage is specific for HPIV with silver-halide films: These films require chemical processing after hologram recording, which is a time consuming task that requires a significant amount of ex-perience. Several holographic recording media such as photo-thermoplastics, photo-refractive crystals and photo-polymers have been investigated to solve this issue. However, these mate-rials perform relatively weakly in terms of resolution and sensitivity compared to silver-halide films (Hinsch 2002). Work on our HPIV system with a BR-film, exposed its own difficulties: First, the sensitivity of BR-films is notably lower than the sensitivity of silver-halide film (i.e. 3−5 mJ/cm2_{(Koek 2006) and 50−100 µJ/cm}2_{(www.slavich.com) respectively). Additionally,}

during hologram reconstruction, a BR film is sensitive to hologram-erasure which is caused by exposure by the reconstruction beam and by thermal effects. Even after optimizing experimental parameters such as the reconstruction beam intensity and introducing a shutter in the reconstruc-tion beam (Ooms et al. 2006b), extracting a real image of a particle field with a sufficient SNR was extremely challenging. Due to deterioration of the image SNR, the available read-out time of the reconstructed image was typically 60 seconds in our experiments.

Compared to film-based HPIV, an advantage of DHPIV is flexibility during numerical

data-6_{This estimate ignores the possible difference of dynamic range of a film-‘pixel’ and a digital ‘pixel’.}

7_{Although high-resolution films theoretically allow NA ≈ 1, practical consideration often lead to a NA of a few} tenths.

1.5. Comparison to other 3D flow-measurement methods 25

Figure 1.13: Schematic illustration of tomographic PIV recording configuration (from Elsinga et al. (2006)). processing. Spatial filtering in the hologram spatial domain or in the hologram Fourier domain, or numerical comparison of a hologram time-array can be performed relatively easily. Furthermore, in DHPIV, the complex amplitude of the reconstructed image is available, whereas only the intensity of the reconstruction is available in film-based HPIV. Coupland (1997) and Pan and Meng (2003) suggest that this additional knowledge can be used to determine particle-image displacement more accurately and reliably. A final advantage of DH is that digital sensors allow cinematic (time-resolved) recording.

The computational cost of the data-analysis of a film-based HPIV measurement and a digital HPIV measurement (section 1.4.3) are comparable: The procedure to extract velocity vectors from the hologram reconstruction (i.e. 3D PIV or PTV) is computationally equally expensive for film-based HPIV and digital HPIV. Digital reconstruction of the hologram is not needed with film-based HPIV, however, this step is found to be less time-consuming than the vector-extraction-procedure.

1.5.2

Comparison to tomographic PIV

Recently, successful 3D flow measurements have been reported with a tomographic PIV system (Elsinga et al. 2006). The method aims to perform three-dimensional three-component (3D3C) flow velocity measurements by viewing suspended tracer particles with multiple digital cam-eras with different viewing directions (figure 1.13). A three dimensional particle-image recon-struction is generated by combining the four recorded (2D) images with numerical tomography algorithms. The 3D reconstruction is split into several interrogation volumes which are then pro-cessed with a 3D cross-correlation analysis to extract the local particle displacement and hence the local flow velocity. Elsinga et al. (2006) describe an experiment were a turbulent air flow (Re = 2,700) behind a cylinder is recorded. About 65,000 particles (1 µm droplets) are recorded by four (1280 × 1024 pix) cameras and reconstructed. With a 75%-overlap of the neighboring interrogation volumes, this leads to 64×64×30 (= 122,800) velocity vectors with 4% spurious vectors. A vorticity analysis of the measured velocity field clearly illustrates K´arm´an vortices, as shown in figure 1.14.

When comparing tomographic PIV to DHPIV, some strong points can be identified: The number of recorded particles per camera-megapixel is clearly higher than the values presented in table 1.2. Although equation 1.7 indicates that it is theoretically possible to record a

few-tens-of-26 Chapter 1. Introduction

Figure 1.14: Measurement result of tomographic PIV (from Elsinga et al. (2006)).

thousands of particles on a single-megapixel camera, such experimental results have not been reported in literature.

Relative weaknesses of tomographic PIV compared to DHPIV can also be identified: The sys-tem requires a high-power laser (400 mJ per pulse in this case). There are two reasons for this requirement: First, the experimental configuration is based on the relatively weak sideward scat-tering of light (≈ 70◦ _{and 110}◦ _{w.r.t. direction of incidence). Second, the tomographic system}

requires that all particles in the measurement domain are imaged ‘in focus’. This requirement is fulfilled when the depth-of-field (DOField) is larger than the depth of the measurement domain. The depth-of-field is defined by Adrian (1997) as:

DOField=4(1 + 1 M)

2_f#2_{λ (1.10)}

where M is the lateral magnification and f # is the f-number of the objectives which can be typically chosen between 2 and 22 (www.nikon.com). A high f-number is selected to allow a reasonable depth of the measurement domain. While the depth-of-field is proportional to the square of the lens f-number, the intensity of the recorded images is inversely proportional to the square of the lens f-number, which explains the need for the high illumination-intensity. DHPIV does not require maximization of the optical f-number to obtain an acceptably large Lz because

a plane of focus can be numerically selected. The required amount of light for an in-line DHPIV setup is estimated to be 6 orders of magnitude lower (chapter 4). Another relative disadvantage of the tomographic system is the calibration procedure. Although calibration is occasionally also needed with DHPIV, the procedure is generally simpler (chapter 4).

1.6

About this thesis

Work presented in this thesis aims to develop a holographic system that can perform accurate and high-resolution three-dimensional flow velocity measurements. During the initial phase, this work focused on the development of a BR-film HPIV system and a digital HPIV system. After a few years of experience on both systems, the decision was made to continue only with the development of a digital HPIV system. The choice to discontinue work on the BR-film system

1.6. About this thesis 27

was mainly based on the relative difficulty to obtain high-SNR reconstructed particle images with an acceptable reliability and a sufficient read-out time.

Chapters 2, 3 and 4 of this thesis address specific issues and improvements in the field of DH-PIV. Chapter 2 has been published as (Ooms, T.A., Koek, W.D., Braat, J.J.M. and Westerweel, J.: 2006, Optimizing Fourier filtering for digital holographic particle image velocimetry, Measure-ment Science and Technology 17, 304-312) and chapter 3 has been published as (Ooms, T.A., Koek, W.D. and Westerweel, J.: 2007, Digital holographic particle image velocimetry: Elim-inating a sign-ambiguity error and a bias error from the measured particle field displacement, Measurement Science and Technology 19, 074003). Chapter 4 will be submitted as a journal paper in the near future. As a consequence, this thesis has turned into a collection of separate pieces of work. To present the reader with an overview, a short introduction of the three chap-ters is given in this section. Another consequence of the separation between the chapchap-ters is an occasional overlap of the content of chapters, for example in the description of the experimental setup and the data-analysis procedure.

As described in section 1.4, DHPIV requires improvement of specific performance parameters to become a truly successful instrument for three-dimensional flow measurements. Chapter 2 presents a method to improve the relatively large inaccuracy of the measured longitudinal flow velocity (section 1.4.1). By adding an optical band-pass Fourier filter to the object beam of the recording setup, the effective NA of the system is increased. This leads to a decreased particle-image depth-of-focus (by a factor 5 for the described system) which, in turn, leads to an improved accuracy of the measured longitudinal flow velocity.

In recently described investigations of DHPIV, hologram reconstructions are usually analyzed with a particle tracking approach (in contrast to a PIV correlation approach). The motivation for the particle tracking approach is the relatively low number of recorded particles which is limited by the number of pixels of the digital camera (equation 1.7). Because the number of pixels of digital cameras are expected to continue to increase in the near future due to continuous developments in the field of micro-electronics, it is expected that the number of recorded parti-cles in DHPIV measurements will grow proportionally. It is therefore expected that a DHPIV reconstruction will be increasingly often analyzed with a 3D-PIV-correlation approach in the future. Our work anticipates this trend by investigating the analysis of DHPIV reconstructions with a 3D-correlation method. During the investigation, interesting effects were observed: When analyzing a moving particle-field, two correlation peaks were observed in a typical correlation volume. Because the two observed correlation peaks have a comparable height, an ambiguity oc-curs in the measured particle displacement. This effect and a method to avoid the measurement ambiguity are described in chapter 3.

Chapter 4 discusses the suitability of DHPIV to measure micrometer- and millimeter-scale (mi-croscopic) flows. The motivation to investigate microscopic flows partially originates from the increasing interest in such flows in the academic- and industrial world (Nguyen and Wereley 2002), but also from the great suitability of DHPIV to measure small-scale flows: When a holo-gram is optically magnified before it is digitally recorded, the Nyquist sampling criterion relaxes in proportion to the magnification M. This suggests that the corresponding limitation of the NA increases to typical values of a few tenths (chapter 4). Such a value allows for a comparable inac-curacy of the measured longitudinal- and transverse velocity component, as explained in section 1.4.1. This is clearly a desirable property of a 3D flow-velocity-measurement instrument. The increase of the NA is inherent to a proportional reduction of the transverse field-of-view.