3D-3C Speckle Interferometry: Optical Device for Measuring

DISS. ETH No. 15961
3D-3C Speckle Interferometry:
Optical Device for Measuring
Complex Structures
A Dissertation submitted to the
SWlSS FEDERAL INSTITUTE OF TECHNOLOGY ZURICH
for the degree of
Doctor of Technical Seiences
prescnted by
GOUDEMAND Nicolas
Ingenieur diplorne de l'Ecole Nationale Superioure de Physiquo, Strasbourg, France
born on December 2, 1974
citizen of France
accepted on the recornmendation of
Prof. Dr. Paolo Errnanni, examiner
Prof. Dr. Pierre Jacquot, co-examiner
2005
Resurne
L'intitule de cette these "interferornetrie de speckle 3D-3C: instrurnent optique pour
la mesure de structures complexes" Iait reference
torferometrie de speckle
a l'application des techniques d'in-
a la mesure des trois composantes du champ dc dcplaccmcnts
tridimensionol (3C) sur des surfaces tridimcnsionelles (3D) quclconques.
Le but de ce projet etait en effet le d6veloppement d'un instrument optique
de mesure, base sur l'intcrfcrometrie de speckle, pour l'etude du comportement en
deforrnation de structures aux formes cornplexes. Nous presontons ici les differentes
etapcs de ce developpement: une analyse theoriquo synthetique de l'interferornetrie
dc speckle appliquco aux surfaces tridimensionolles fortement courbes, la conception
et la realisation d'un equipement specifique de mesure, ainsi que l'implementation de
routines originales de traitement d'image et de calibragc.
Une analyse d'erreurs cornplete de l'ensemble du processus de mesure a ete realisee,
EUle a pennis de souligner la. nccessite d'un calibrage precis de Ia geometrie du montage et d'un mapping precis de I'espaco de mesure, i. e. une modelisation du procesaus
d'imagerio ainsi qu'une mesurc de la forme tridimensionelle de la surfaco ctudieo.
La variation locale du vectcur sensibilite (qui relie la difference de phase mesuree au
veeteur deplaccment recherche) peut ainsi etre pris en compte de facon tres precise. Il
a
ete reconnu egalerneut
que les erreurs de mise au point peuvent affecter les resultats
des mesures, puisque le charnp de deplacement obtenu grace
a I'equation
standard
corrcspond aux deplaccmcnts des speckles dans le plan focal et non pas ncccssairement
aux deplacernents de la surface elle-mcme. En consequencc il est conseille de treuver
un comprornis conccrnant les dimensions des grains de spccklc, i.c. pour l'ouverture
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numeriqua de la camera,
Un montage compose d'elements
a fibres optiques a ete developpe, qui
permet de
mesurer et la forme tridimensioncllc de la surface etudiee et Ie champ de deplacements
tridimensioncl, Ce montage est base sur le principe du montage ESPI adeux faisceaux
d'illumination. Au minimum trois configurations ESPI
a deux faisceaux,
i. e. trois
vecteurs sensibilite independants, sont necessaires pour obtenir les trois composantes
du champ de deplaccment tridimensionel. Un commutatcur
a fibre
optique, contröle
par ordinateur, perrnet de passer altemativement d'une configuration
a une
autre.
La mesure de forme, ncccssairc au mapping, est realisoo cn utilisant deux des quatre
sources d'illumination, l'une d'elles etant translatcc perpendiculairement a 180 direetion
du faisceau, ee qui correspond
a une
projection de franges interferometrique.
Une analyse pixel par pixel facilite grandement l'etape de demodulation de phasc,
notamment dans le cas d'objets presentant des marches importantes, des regions
isolccs, des trous ou des zones ombragees. Elle est donc particuliörement interessante
dans le cas d'objets complcxes. Le principe de base des techniques de demodulation
de phasc temporelle est de considoror et d'utiliser chaque pixel tel un detecteur
independant. Une analyse temps/frequence des variations temporelles de son intensite permet alors d'extraire la phase recherchee, La methode du "decalagc de phase
dynamique" est un cas particulier interessant: basee sur l'analyse en ondelett.es, elle
pennet d'ctcndrc lc charup dapplication des tcchniqucs de specklo aux döforrnations
non quasi-stationnaires, Grace
a de nouvelles routines de post-traitement, nous avons
pü appliquer cette technique, devcloppee par le groupe du Professeur Jacquot
sanne,
a Lau-
a la mesure de forme et a l'analyse de deforrnations tridimensionelles,
Nous proposons egalemcnt de nouvelles routines de calibrage pour l'estimation
des pararnötres du montage: de facon similaire
a ce qui
se fait couramment en pho-
togrannnetrie, le processus de mesure est modelise et les parametres correspondants
du montage sont estimes en minimisant, par optimisation non-lincairc, la distance
entre les resultats de mesures spccifiques de calibrage et les resultats obtenus gräce
au modele.
N. Coudemand, July 5, 2005
IMES-ETH Zurich
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Enfin le systerne cornplet est valide experirnentalement gräce
a un
cas 3D-3C
facilement modelisable: la torsion d 'un cylindre creux.
N. Goudcmand, .July 5, 2005
IMES- ETH Zurich
Abstract
We use here the term of 3D-3C specklo interferornetry to refer to the application
of speckle interferometry for the measurement, on three-dimensional surfaces, of the
thrce components of the thrce-dimensional displacement field.
The goal of this work was to develop a specklc interferornetric rneasurement device for investigating the deformation behavior of complex shaped structures made
of innovative materials. This development implied a theorctieal analysis of speckle
interferometry applied to three-dimensional hardly eurved surfaces, the design of speeific measurernent equipmcnt and the implementation of original irnage proeessing
and ealibration routines.
A thorough error analysis of the whole measuring schemc was pcrformed, which
put into relief the necessity of a proeise calibration of the set-up geornetry and apreeise
mapping of the measuring space, including a modelization of the imaging process and
a measuremcnt of the three-dimcnsional shape of the analyzed surface, The loeal
variation of the sensitivity vector (which relates the measured phase differenee to the
wanted displacement) can thus be taken into consideration very accurately, It was
also recognized that dcfoeusing errors could affeet the measurement results, sinee the
displacement field given by the standard equation corrcsponds to the displacements
of the specklos in the focused plane and not necessarily to the surface displacements.
It is consequently adviscd to find a compromiso for the speckle dimension, i. c. for the
numerical apertute of the carnera.
An all-fiber set-up was developed, which allows both the rneasurement of the
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three-dimensional shape of tho analyzed strueture and the measurement of the threedimensional displacement field. It is based on the principle of the ESPI dual-bearn
Illumination set-up. A switch-box controlled by a personal computer enables to select
between at least thrcc dual-beam configurations, i.c. between three sensitivity vectors. It is thus possible to measure alternatively the three components in space of the
three-dimensional displacement field. The necded shape measurement is conductecl
before the deformation measuremcnt using two of the four bcams, one of them being
translated perpendicularly to the beam direction, which corresponds to an interferometric fringe projection,
A pixelwise analysis is particularly interesting in the case of complex objects,
since it enables easy unwrapping even in the casc of objects with largc hcight stcps,
isolated regions, holes 01' shaded parts, The main principle of the so-callcd temporal
phasc unwrapping is that each pixel is used as an individual detector. The evolution of its intensity along the time axis is timc-frcqucncy analyzed to retrieve the
wantcd phase. An interesting particular casc is that of the so-callcd "dynamic phase
shifting" method, which, based on wavelet analysis, conscquontly allows to perform
measurements on non-stationary events, The group of Prof. Jacquot in Lausanne first
developecl the main routines for this process, We've furt her developed post-processing
routines to enable its application to shape rneasuremcnt and 3D deforrnation analysis.
We proposed also new model-based calibration routines for the estimation of the
set-up parameters: similarly to what is routinely proccssed in the photogrammctry
community nonlinear optimizations arc used to fit the model parameters to the results
obtained during specific calibration rneasurements.
I30th the system and the prograrnmcs are finally experimcntally validated on an
easily rnodeled,
3D~3C
loading case: the torsion of an hollow cylinder.
N. Goudemand, .Iuly 5, 2005
IMES-ETH Zurich