Juliana Kuhlmann Abrantes

Holographic Particle Image Velocimetry forWall Turbulence Measurements

TESE DE DOUTORADO

Thesis presented to the Programa de Pos-Graduacao emEngenharia Mecanica of the Departamento de EngenhariaMecanica, PUC–Rio, and to Ecole Centrale de Lille, in thecontext of a joint agreement, as partial fulfillment of the re-quirements for the degree of Doutor em Engenharia / Docteuren Sciences

Adviser: Prof. Michel StanislasAdviser: Prof. Luis Fernando A. Azevedo

Rio de JaneiroMarch 2012

Juliana Kuhlmann Abrantes

Holographic Particle Image Velocimetry forWall Turbulence Measurements

Thesis presented to the Post–graduate Program of the Me-chanical Engineering Department of PUC–Rio, and to EcoleCentrale de Lille, in the context of a joint agreement, as par-tial fulfillment of the requirements for the degree of Doctor ofPhilosophy / Docteur en Sciences. Approved by the followingcommission:

Prof. Michel Stanislas

AdviserEcole Centrale de Lille

Prof. Luis Fernando A. Azevedo

AdviserPUC-Rio

Prof. Joseph Katz

Johns Hopkins University

Prof. Atila Pantaleao Silva Freire

COPPE/UFRJ

Prof. Francisco Ricardo da Cunha

UnB

Prof. Paulo Roberto de Souza Mendes

PUC-Rio

Prof. Jose Eugenio Leal

Head of the Science and Engineering Center — PUC–Rio

Rio de Janeiro — March 30, 2012

All rights reserved.

Juliana Kuhlmann Abrantes

Juliana Abrantes graduated as mechanical engineer and in-dustrial engineer in 2003 from PUC-Rio (Rio de Janeiro, RJ),and got her Master’s degree in 2005 from the same institu-tion. This DSc. Thesis was a joint work between PUC-Rioand Ecole Centrale de Lille in a double-diploma program.

Bibliographic data

Abrantes, Juliana K.

Holographic Particle Image Velocimetry for Wall Tur-bulence Measurements / Juliana Kuhlmann Abrantes; ad-viser: Michel Stanislas; adviser: Luis Fernando A. Azevedo– 2012.

142 f: il. ; 30 cm

Tese (Doutorado em Engenharia Mecanica) – Pon-tifıcia Universidade Catolica do Rio de Janeiro, Rio deJaneiro, 2012.

Inclui bibliografia.

1. Engenharia mecanica – Teses. 2. Tensao cisalhante. 3.Holografia. 4. Turbulencia de parede. 5. PIV holografico.I. Stanislas, Michel. II. Azevedo, Luis Fernando A.. III.Pontifıcia Universidade Catolica do Rio de Janeiro. De-partamento de Engenharia Mecanica. IV. Tıtulo

CDD: 621

Acknowledgments

To my advisors, Professors Michel Stanislas and Luis Fernando Azevedo,

for their continuous guidance and support throughout the periods spent in

both France and Brazil.

To PUC-Rio, for the financial support, without which this work would

not have been realized.

To all my family, who is constantly there for me.

To Thiago, who is always by my side.

To my colleagues at PUC-Rio, and to the friends I made at Ecole Centrale

de Lille, who are very dear to me.

To the people at the Mechanical Engineering Department for the constant

help, particularly to Grace, Marcia and Rosely.

To professors and researchers at the Laboratoire de Mecanique de Lille,

particularly Sebastien Coudert, Jean Marc Foucaut and Matthieu Marquillie,

who provided valuable contributions to the work of this thesis.

To the staff at Ecole Centrale de Lille, who was so helpful during the

whole process.

Resumo expandido

Abrantes, Juliana K.; Stanislas, Michel; Azevedo, Luis FernandoA.. Medicao de Escoamentos Turbulentos na Regiao daParede Utilizando a Tecnica de Velocimetria por Imagem

de Partıculas Holografica. Rio de Janeiro, 2012. 142p. Tese deDoutorado — Departamento de Engenharia Mecanica, PontifıciaUniversidade Catolica do Rio de Janeiro.

Escoamentos turbulentos sobre superfıcies estao entre os mais impor-

tantes em aplicacoes de engenharia. Em particular, a regiao imediatamente

proxima a parede e onde se da a maior parte da producao de turbulencia.

Em uma camada limite turbulenta, energia do escoamento de corrente livre e

convertida em flutuacoes e entao dissipada por acao viscosa na parede atraves

de um processo contınuo. A tensao cisalhante na parede, e portanto o atrito,

e entao relacionada a dinamica da estruturas turbulentas da regiao, e este e o

principal aspecto pratico que torna o conhecimento sobre este tema tao crucial.

O trabalho descrito aqui consiste no desenvolvimento de uma con-

figuracao especıfica da tecnica denominada PIV holografico (do ingles “holo-

graphic particle image velocimetry”). A tecnica PIV, traduzida como ve-

locimetria por imagem de partıculas, constitui uma importante ferramenta de

medicao de campos de velocidade na area de mecanica dos fluidos, e sua uti-

lizacao na forma bi-dimensional “classica”e algo consolidado nesta area. En-

tretanto, sua versao tri-dimensional holografica vem sendo explorada na forma

digital apenas mais recentemente. A configuracao implementada neste trabalho

de tese visa expandir a utilizacao da tecnica de PIV holografico para medicoes

em pequenos volumes proximos a paredes de grandes instalacoes de escoamento

de ar, como tuneis de vento. O objetivo inicial e produzir vetores velocidade

suficientes para que se possa obter perfis de velocidade axial media na regiao

proxima a parede, o que por sua vez pode proporcionar uma medida direta

e precisa da tensao cisalhante. Adicionalmente, dependendo das condicoes ex-

perimentais, esta tecnica possui o potencial de ir alem e fornecer campos de

velocidade instantaneos com boa resolucao espacial, o que ajuda a aprofundar

o conhecimento da dinamica das estruturas turbulentas na regiao de parede.

O capıtulo I apresenta algumas definicoes teoricas sobre camadas limite

turbulentas, com uma descricao dos tipos de estrutura normalmente encon-

tradas na regiao de parede e a definicao de algumas equacoes e parametros

fundamentais, entre eles a tensao cisalhante e o coeficiente de atrito. Neste

mesmo capıtulo sao discutidas algumas tecnicas existentes para medicao de

velocidade em escoamentos, com maior atencao dedicada a tecnica PIV, enfa-

tizando sua evolucao a partir da forma bi-dimensional. Tambem sao discutidas

tecnicas diretas e indiretas de medicao de tensao cisalhante em superfıcies. E

importante notar que, em geral, e difıcil se obter incertezas inferiores a 1−2%.

O metodo proposto no presente trabalho envolve a determinacao da tensao

cisalhante a partir da medicao do perfil de velocidade axial medio obtido com

a tecnica holografica na sub-camada viscosa (y+ < 5) da regiao de parede.

Os fundamentos teoricos da holografia sao apresentados no capıtulo II,

com a descricao de ondas eletromagneticas e dos fenomenos de difracao e

interferencia. O processo holografico, descrito em seguida, e composto de duas

etapas: o registro e a reconstrucao dos hologramas. A tarefa fundamental e

registrar, e posteriormente reconstruir, a amplitude e a fase de uma onda de

luz proveniente de um objeto iluminado. Na etapa de registro, e necessario

que informacao sobre a fase da onda seja de alguma forma convertida em

variacoes de intensidade que possam sensibilizar o meio de registro, e a maneira

de se fazer isto e atraves de interferencia. Assim, uma segunda onda —

a onda de referencia, com amplitude e fase conhecidas — e superposta a

onda desconhecida espalhada pelo objeto, e elas interferem. E este padrao

de interferencia objeto/referencia que e registrado na placa holografica e

denominado holograma. Posteriormente, na etapa de reconstrucao, o holograma

e iluminado por uma onda de reconstrucao com a mesma forma da onda de

referencia, e a frente de onda transmitida e composta de quatro termos, um

deles sendo diretamente proporcional a onda do objeto original, e outro a

sua conjugada (as chamadas imagens real e virtual). Desta forma, olhando

atraves do holograma, pode-se ver uma imagem tri-dimensional do objeto.

Ainda neste capıtulo, e feita a distincao entre holografia fora do eixo (“off-

axis”) e holografia em linha (“in-line”), na qual o mesmo feixe serve como

iluminacao para o objeto e para referencia. Em seguida, o conceito de holografia

digital — versao utilizada no trabalho desta tese — e introduzido. Neste

caso, a placa holografica e substituıda por uma camera digital sem lente, e a

frente de onda de interferencia e registrada no sensor e armazenada como uma

imagem em nıveis de cinza — o holograma digital — no computador. A etapa

de reconstrucao consiste entao em uma simulacao numerica de propagacao

da frente de onda a partir do holograma digital. A integral de difracao

de Rayleigh-Sommerfeld, que representa a propagacao da onda difratada, e

apresentada na secao em questao, assim como a denominada aproximacao

de Fresnel e a representacao matematica da onda de reconstrucao. Detalhes

da implementacao numerica sao descritos, e tambem algumas restricoes e

limitacoes da holografia digital, tais como aquelas relacionadas ao criterio

de amostragem para que as franjas de interferencia possam ser resolvidas

espacialmente no sensor, e o problema de profundidade de foco. Na secao

seguinte, a introducao de uma lente objetiva de microscopio no sistema

holografico — que constitui o que se denomina microscopia holografica — e

discutida. Neste caso, o campo complexo magnificado do objeto e registrado

e reconstruıdo, o que melhora as resolucoes obtidas tanto na direcao axial

quanto nas transversais. Finalmente, ao fim deste capıtulo, a holografia digital

no contexto da velocimetria por imagem de partıculas (PIV ) e descrita.

No capıtulo III, uma montagem preliminar em linha, implementada para

testes iniciais, e descrita. Esta montagem foi utilizada com o intuito de fornecer

hologramas de boa qualidade para que o desenvolvimento de um software

proprio de reconstrucao e processamento pudesse ser iniciado, e tambem

para proporcionar uma familiarizacao com o processo holografico na pratica.

Hologramas de uma pequena regua e de uma nuvem de partıculas geradas por

spray foram registrados e reconstruıdos com o software desenvolvido. Estes

hologramas e suas reconstrucoes tambem servem muito bem o proposito de

exemplificar diversos dos conceitos e limitacoes introduzidos no capıtulo II.

A configuracao holografica final, mais complexa e desenvolvida no con-

texto da tese especificamente para medicoes em um grande tunel de vento, e

apresentada no capıtulo IV. Apos uma breve descricao do tunel propriamente

dito, que fica no Laboratorio de Mecanica de Lille, na Franca, toda a mon-

tagem otica e detalhada. Nesta configuracao, o feixe proveniente do laser e

dividido por um separador, de forma a gerar os feixes destinados a iluminacao

do objeto (agora um pequeno volume de partıculas na regiao proxima a parede

dentro do tunel de vento) e a iluminacao de referencia. As partıculas dentro

do volume de medicao no tunel sao iluminadas lateralmente e espalham luz a

90o (“side scattering”). Esta luz espalhada — a onda do objeto — passa em

seguida por uma lente objetiva e e magnificada. O campo magnificado e entao

recombinado com o feixe de referencia para intereferir, e a frente de onda de

interferencia e registrada no sensor CCD. Detalhes da configuracao sao expli-

cados e apresentados em diversas figuras ao longo deste capıtulo. Em seguida, o

importante procedimento de calibracao e apresentado. Devido a magnificacao

variavel introduzida pela lente objetiva, uma calibracao correta e fundamen-

tal, produzindo equacoes que mapeiam corretamente as posicoes das partıculas

detectadas no volume reconstruıdo de volta as coordenadas fısicas do volume

de medicao dentro do tunel de vento. Estas equacoes sao apresentadas ao fim

deste capıtulo, assim como a geometria final de um tıpico volume reconstruıdo

e mapeado.

No capıtulo V, hologramas das partıculas registrados com o tunel de

vento em operacao sao apresentados, com exemplos de planos reconstruıdos

e sua evolucao na profundidade, que corresponde a direcao normal a parede

do tunel. Apos reconstrucao dos volumes, dados relativos a distribuicao de

intensidade, gradiente espacial, alem das partes reais e imaginarias, sao manti-

dos e armazenados. Algoritmos de pos-processamento sao implementados para

deteccao e validacao de partıculas, e tambem para a determinacao de suas

posicoes com a melhor precisao possıvel. Estruturas “tubulares”sao criadas em

torno de cada partıcula detectada para uma analise mais detalhada, de forma

a otimizar a estimacao de suas posicoes no volume. As equacoes de mapea-

mento sao entao aplicadas, gerando matrizes com as posicoes das partıculas

no volume de medicao original. Finalmente, o algoritmo de acompanhamento

de partıculas para calculo de velocidade e discutido, e resultados de testes

de dupla exposicao para deteccao de pares de partıculas em dois instantes de

tempo muito proximos sao apresentados, revelando que apenas alguns pares

sao detectados. Por este motivo, o objetivo inicial de se medir campos de ve-

locidade completos ainda nao pode ser atingido, o que e natural em se tratando

do desenvolvimento de uma nova tecnica de medicao.

No capıtulo de discussoes dos resultados, algumas possıveis explicacoes

para o fato de nem todos os pares estarem sendo detectados sao discutidas, e

otimizacoes na configuracao otica sao propostas. Considerando que os hologra-

mas registrados neste experimento foram o resultado de uma primeira tenta-

tiva de empregar uma configuracao nunca utilizada antes e que requer ajustes

complexos, pode-se concluir que resultados muito positivos foram atingidos,

do registro a reconstrucao dos hologramas e algoritmos de determinacao das

coordenadas das partıculas. Comprovou-se que uma excelente resolucao na

deteccao da posicao de foco e atingida, em boa parte devido a utilizacao de

uma objetiva para magnificacao. Um software que envolve todas as etapas

do processo foi desenvolvido, e podera ser utilizado em futuras aplicacoes da

tecnica em diversos experimentos. Em breve um experimento no mesmo tunel

de vento sera realizado novamente, com as otimizacoes discutidas devidamente

implementadas.

Palavras-chave

tensao cisalhante. holografia. turbulencia de parede. PIV holografico.

Abstract

Abrantes, Juliana K.; Stanislas, Michel; Azevedo, Luis FernandoA.. Holographic Particle Image Velocimetry for Wall Tur-bulence Measurements. Rio de Janeiro, 2012. 142p. DSc Thesis— Departamento de Engenharia Mecanica, Pontifıcia UniversidadeCatolica do Rio de Janeiro.

Constinuously improving the understanding of wall turbulence dynamics

has been the goal of many experimental and numerical studies for decades.

The main practical aspect that makes this knowledge so crucial is the

fact that the wall shear stress is closely related to the dynamics of the

near-wall structures. Experimental techniques in fluid mechanics have also

experienced a great amount of advances in recent years. The present work

details the development of an experimental configuration aimed at providing

3D-3C flow measurements in the very near-wall region of a large wind

tunnel facility, which can lead to the assessment of the wall shear stress

with improved accuracy. With that goal, a technique known as Holographic

Particle Image Velocimetry is used, and measurements are made in small

volumes close to the wall in the wind tunnel at the Laboratoire de Mecanique

de Lille. Full measurements in volumes as small as 1.5 mm3 are made

possible with the use of a microscope objective for magnification of the

object field. Particles are illuminated from the side and the 90o scattered

field recombines with reference wave for holographic in-line recording. A

calibration procedure is performed in order to relate reconstruction space

coordinates to real measurement volume coordinates. Analysis of resulting

particle fields shows that particle images reconstruct with very good axial

accuracy, leading to believe that the configuration is indeed suited for

this type of measurement. However, in this first attempt to use this

configuration, despite careful alignments and adjustments, the inherent

sensitivity of the coherent holographic process with respect to different

factors prevented particles from being detected with enough equivalence in

PIV frames 1 and 2, and not all particle pairs could be retrieved successfully.

Thus, some optimizations and adjustments which might be needed in order

to improve the particle tracking results are discussed. Nevertheless, results

are promising and discussions about them provide interesting insight to

some important issues.

Keywords

shear stress. holography. wall turbulence. HPIV.

Contents

I Introduction 17

I.1 Wall Flows 17

I.2 Fluid Flow Measurements 21Velocity Measurements 22

Wall Shear Stress Measurements 24

I.3 Description of the Current Work 33

II Holography 36

II.1 Basic Physical Concepts 36

II.2 The Two Steps in the Holographic Process 44

II.3 In-line Holography 48

II.4 Digital Holography 49

II.5 Digital Holographic Microscopy 56

II.6 Holographic PIV 58

III In-line Holographic Setup for Initial Tests 63

III.1 Description of the Setup 63

III.2 Results: calibration ruler and particles 66

IV Specific Setup for Wind Tunnel Measurements 74

IV.1 The Wind Tunnel Facility 74

IV.2 The Side Scattering Holographic Setup 77

IV.3 Calibration procedure 85

V Wind Tunnel Results: Particle Holograms, Reconstructed ParticleFields and Tracking Algorithm 102

V.1 Acquisition of the Holograms 102

V.2 Particle Volume Reconstruction 104

V.3 Particle Detection, Validation and Focusing Criteria 108

V.4 Results: Double Exposure Analysis and Tracking Algorithm 121

VI Final Considerations 127

Bibliography 130

A Holographic Imaging: Image Locations, Magnification, and WaveRepresentation 135

B Discretization in the Numerical Reconstruction Process 139

C Uncertainty Analysis 141

List of Figures

I.1 Mean velocity gradient at the viscous sublayer: accurate ve-locity measurements in the linear region lead to the directassessment of the wall shear stress. 29

I.2 Results from digital holographic microscopy measurementsextracted from [Sheng et al, 2008]: (a) Typical instantaneousvolumetric velocity field; (b) linear regression of the scatterplot of axial velocity within the viscous sublayer. 33

II.1 Illustration of the Huygens Principle 40II.2 Double slit interference 40II.3 Diffraction at infinity. 41II.4 Near-field or Fresnel diffraction at plane ��: phenomena are

practically only observed towards the borders M and M � ofthe beam. In the plane Π Fraunhofer diffraction is observed. 42

II.5 Fresnel diffraction by a screen. 42II.6 Diffraction by a circular sinusoidal grating. 43II.7 Recording of a hologram. 45II.8 Optical reconstruction of the original wavefront. 47II.9 Recording of an in-line or Gabor hologram. 48II.10 Reconstruction of an in-line hologram: twin images are formed

at a distance z0 in each side of the hologram. 49II.11 Three possible recording configurations for digital HPIV, ex-

tracted from [Meng et al, 2004]: (a) single-beam in-line holog-raphy with forward scattering, (b) dual-beam in-line hologra-phy with 90o scattering and (c) dual-beam in-line holographywith forward scattering. 50

II.12 Geometry and coordinates for representing numerical recon-struction. 51

II.13 Limitation in the angular extent for the in-line configuration. 55II.14 Reconstruction of a small particle with axial resolution δz. 56II.15 [Sheng et al, 2006]: Ensemble-averaged intensity distribution

along the depth direction. The insert is an isointensity surfaceplot of a typical reconstructed particle at 75% of its peakintensity. 58

II.16 Example extracted from [Pu and Meng, 2000]: An instanta-neous 3D velocity field obtained from the tab wake obtained byHPIV. The measurement volume is 44×56×32 mm. Approx-imately 400.000 3D vectors have been gaussian-interpolatedfrom about 80.000 paired vectors originally extracted. Meanvelocity of the vectors has been subtracted and part of themeasurement volume is cut out to show flow structures. Forclarity, only surface vectors are shown. 61

III.1 In-line Gabor configuration mounted for preliminary tests. 63

III.2 Spatial filtering: (a) spatial filter components used in thepresent in-line experiment; (b) profile of a typical incomingbeam; (c) image in the focal plane of a lens for the profileon the left; (d)Airy pattern: projection of the output “clean”beam when pinhole is inserted; the central spot is the Airy

disk, with gaussian intensity profile. 65III.3 Calibration ruler: hologram (left) and reconstruction in best

refocusing plane (right). 66III.4 Hologram (left) and reconstruction of a cloud of particles at

z = 11.5 cm (right). 68III.5 Hologram (left) and numerical refocusing of two spray parti-

cles, one at z = 11.5 cm (middle) and the other at z = 11.8cm (right). 69

III.6 Iso-contour of a single particle at 75% of the maximum inten-sity: the elongation in depth is noticeable. 69

III.7 Reconstructed intensity image (left) and corresponding spatialgradient distribution (right) at z = 11.5 cm. 70

III.8 Depth evolution for a single particle: normalized intensity colorcontours. 70

III.9 Depth evolution for a single particle: normalized gradient colorcontours. 71

III.10 Depth evolution for a single particle. Top: intensity field;Bottom: gradient field. z spacing between planes is 50 µm. 71

III.11 Using an objective lens for magnification. Hologram (left) andreconstructed image (right). 73

IV.1 Turbulent boundary layer wind tunnel at LML. 75IV.2 Schematic view of the tunnel configuration during the period

of the holographic experiments of this thesis. A bump modelwas mounted for a different project ([Cuvier et al, 2011]). 76

IV.3 Photo of the measurement section. The bump model mountedfor turbulent boundary layer control can be observed. 76

IV.4 Optical configuration: in-line side scattering setup for the windtunnel. A microscope objective lens is introduced to magnifythe object beam. 77

IV.5 Optical setup structure with glass plate simulating tunnel wallfor tests on the side. After alignment procedures and differenttests, the plate was removed and the structure brought to itsposition below the wind tunnel for realignment, holographiccalibration procedure and flow-on hologram recording. 80

IV.6 Detail of two of the vertical structural profiles in the opticalsetup. 80

IV.7 Setup for coherence length measurements. 82IV.8 Photograph of the optical setup placed below the measure-

ment station of the LML wind tunnel. Beam combiner andmicroscope objective cannot be seen properly because theyare “hidden” behind a part of the tunnel structure. 83

IV.9 Details of the optical setup. Right side arm comprises mirrors,density filters, and spatial filter. 83

IV.10 Detail of objective, beam combiner and camera positioning.All these components were mounted in stages that providedfreedom for precise alignment. 84

IV.11 Optical components employed in the laser output re-directionfor the experiments. 85

IV.12 Photo of the laser and re-directing optical components. 85IV.13 Scheme of imaging planes for a volume with two particles. 86IV.14 Scheme of the setup for final calibration procedure. 87IV.15 Reconstruction of a pinhole calibration hologram in four dif-

ferent planes. From (a) to (d), pinhole source image is refocusing. 89IV.16 Enlarged image of a refocused calibration pinhole image. 89IV.17 Model for the microscope objective, composed of two inner

lenses but modeled as a single thin lens. Po = HoAo < 0,Pi = HiAi > 0, f > 0, HoHi = d. Here, index “o” denotes“object” and “i”, “image”. 90

IV.18 Model for whole-system imaging equationing, given a particleor point source p in plane Aop inside the tunnel. z is the maincoordinate for the lens equation. Z and z are local coordinateswith origin on the CCD (hologram) plane, and in referenceplane Ao, respectively. In the lens equation reference frame z,HiH = di > 0 and HoAo = do < 0. In the hologram frame Z,the distance from the magnified image of particle p (plane Aip)to the hologram is Zip < 0, and the distance from the hologramto the refocused reconstructed plane of that magnified particleimage is Z �

ip > 0. 91IV.19 Plot of di values for the different calibration pinhole shifts

∆z = 0.1 mm within the wind tunnel. Red line correspondsto the average value (223.01 mm). 96

IV.20 Geometry transformation between: (a) volume in holographicreconstruction coordinates (x�i, y

�

i, Z�

i) and (b) final calibratedvolume in real coordinates, already switched to boundary layerusual axes (see table IV.1). The reconstruction depth rangeZ �

span ≈ [18.7 ↔ 94.0] mm was used later in numericalreconstruction of particle fields so that the final volume spanin real coordinates was [0 ↔ 1.5] mm in the wall-normaldirection, according to eq. (IV.3.18). Because volume (a) isquite elongated, the Z �

i axis is not in scale. 97IV.21 Out-of-proportion sketch illustrating the effect of the small

wall angle. 98IV.22 Real-volume spans resulting from calculating di and do using

the calibration process with different values of ZR� . The non-linear mapping relation from III to real space can be observed.100

IV.23 Verification of reference source distance value through a com-parison with the ruler image magnification. 101

V.1 Example of a typical particle hologram taken from wind tunnelexperiments. 103

V.2 (a) Reconstructed plane in a given depth position withinZ �

span. Particle enclosed by the red circle is around its focusposition. (b) Depth series of cropped images around that singleparticle, with 50 µm spacings between them. 105

V.3 Data storage structure for the reconstructed volume. 106V.4 Visualization interface for NetCDF files generated from the

holograms. Different options are available, such as choice oftha data variable or grid variable to be presented, linear andnon-linear color scales, zoom, movie-type visualization alongdepth, etc. 107

V.5 Tube data structure. Plane-by-plane data and grids are createdby cropping planes and grids from a volume reconstructed witha finer step Z �

finestep. The structure is basically the same asfor volumes, but the unlimited dimension here is the numberof tubes (or the number of particle candidates). 109

V.6 Top: series of tube-plane images (intensity above and gradientbelow) of particle candidate A. Bottom: corresponding whole-tube intensity histogram. 111

V.7 Top: series of tube-plane images (intensity and gradient) ofparticle candidate B. Bottom: corresponding whole-tube in-tensity histogram. 112

V.8 Top: series of tube-plane images (intensity only) of particlecandidate C. Bottom: corresponding whole-tube intensity his-togram. 113

V.9 Tubular structure created around pre-estimated position Z �

cA

of validated particle A. This particle has a good signal-to-noiseratio. For visualization purposes, some planes are not depictedhere. Intensity values are normalized. 114

V.10 Tubular structure for particle B. This one has a noisier back-ground and presents more of a challenge for final position esti-mation. Higher intensity red regions seem to appear in a longerdepth extension than in the case of particle A. 114

V.11 Particle A: Intensity iso-contour at 75% of the peak intensity. 116V.12 Particle B: Intensity iso-contour at 75% of the peak intensity. 116V.13 Plane-by-plane criteria evaluation for particle A. Top:

intensity-based criteria; middle: gradient-based criteria; Bot-tom: combined final criterion for particle focus positionevaluation. Steps between planes in reconstruction space is 50µm. 117

V.14 Plane-by-plane criteria evaluation for particle B. Top:intensity-based criteria; middle: gradient-based criteria; Bot-tom: combined final criterion for particle focus positionevaluation. Steps between planes in reconstruction space is 50µm. 118

V.15 A typical reconstructed volume in calibrated optical coordi-nates. For a conversion to usual BL coordinate directions, referto table IV.1. 121

V.16 Two examples of double exposure tests, each comprising par-ticles compiled from three volumes, and also collapsed in thespanwise direction. y is the wall-normal direction, and flow isfrom left to right. Red particles are from exposure 1 and greenparticles, from exposure 2. Time between exposures is ∆t = 5µs. 122

V.17 Mean velocity profiles extracted from [Cuvier et al, 2011], α =−2o, β = −22o, U∞ = 10 m/s. Boundary layer characteristicsevaluated in this experimental work are δ = 19 cm, δ∗ = 16.4mm, θ = 13.5 mm, Reθ = 10100, H = 1.21 and uτ = 0.465 m/s.124

V.18 Search region for particle tracking algorithm. Radius R of thesearch sphere is (2u�guess) · ∆t, u�guess being the fluctuationvelocity guess for that wall-normal position y1i. 125

V.19 Example of a velocity evaluation trial with the particle track-ing code. Different guesses were tested and an apparent biasseems to occur. 126

A.1 Holographic (A) recording and (B) reconstruction geometrieswith respect to hologram frame from figure IV.18. Referencewave is generated by a point source located at coordinates(XR, YR, ZR). The object point source p is located at coor-dinates (xp, yp, Zp). During reconstruction step, the hologramis assumed to be illuminated by a spherical wave originatingfrom a point source at coordinates (XR� , YR� , ZR�). In the the-sis experiment, both object and reference sources are locatedin the right side of the figure and are diverging waves, whereasthe location of reconstruction wave source in the figure is inthe right side, but can actually be chosen to be either in theleft or the right side in the numerical implementation. 136

A.2 Two different possibilities for reconstruction situation (B) infigure A.1: in (B.1), the reconstruction wave is diverging, thushaving its source located at a negative position ZR� < 0.In (B.2), the reconstruction wave is converging, with sourcelocated at a positive position ZR� > 0. Here, in both cases,simply to facilitate visualization, XR� and YR� have been setto zero (whereas in figure A.1 generic values are attributed),corresponding to waves centerd in the optical axis, that is,

R�(ξ, η) = exp�−

jπ

λZR�

[ξ2 + η2]�. 137

B.1 Discretization in numerical reconstruction implementation.Reconstruction wave is centered in the optical axis. 140

List of Tables

IV.1 Conversion of optical equationing coordinates to boundary layerusual coordinates. 98

V.1 Tube steps and overall lengths of four different particle tubes:the ones corresponding to particles A and B, and two otherscorresponding to hypothetical particles positioned close to thewall and close to the top of the volume. 115