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Numerical Aberrations Compensation and Polarization Imaging in Digital Holographic Microscopy

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Numerical Aberrations Compensation and Polarization Imaging in Digital Holographic Microscopy NUMERICAL ABERRATIONS COMPENSATION AND POLARIZATION IMAGING IN DIGITAL HOLOGRAPHIC MICROSCOPY THÈSE NO 3455 (2006) PRÉSENTÉE À LA FACULTÉ SCIENCES ET TECHNIQUES DE L'INGÉNIEUR Laboratoire d'optique appliquée SECTION DE MICROTECHNIQUE ÉCOLE POLYTECHNIQUE FÉDÉRALE DE LAUSANNE POUR L'OBTENTION DU GRADE DE DOCTEUR ÈS SCIENCES PAR Tristan COLOMB ingénieur physicien diplômé EPF de nationalité suisse et originaire de Bagnes (VS) acceptée sur proposition du jury: Prof. Ph. Renaud, président du jury Prof. R.P. Salathé, directeur de thèse Prof. C. Depeursinge, rapporteur Prof. M. Gu, rapporteur Prof. H. Tiziani, rapporteur Prof. M. Unser, rapporteur Lausanne, EPFL 2006 En mémoire de Grand-maman, Pierrot et Simon Abstract In this thesis, we describe a method for the numerical reconstruction of the complete wavefront properties from a single digital hologram: the ampli- tude, the phase and the polarization state. For this purpose, we present the principle of digital holographic microscopy (DHM) and the numerical re- construction process which consists of propagating numerically a wavefront from the hologram plane to the reconstruction plane. We then define the different parameters of a Numerical Parametric Lens (NPL) introduced in the reconstruction plane that should be precisely adjusted to achieve a cor- rect reconstruction. We demonstrate that automatic procedures not only allow to adjust these parameters, but in addition, to completely compen- sate for the phase aberrations. The method consists in computing directly from the hologram a NPL defined by standard or Zernike polynomials without prior knowledge of physical setup values (microscope objective fo- cal length, distance between the object and the objective...). This method enables to reconstruct correct and accurate phase distributions, even in the presence of strong and high order aberrations. Furthermore, we show that this method allows to compensate for the curvature of specimen. The NPL parameters obtained by Zernike polynomial fit give quantitative measure- ments of micro-optics aberrations and the reconstructed images reveal their surface defects and roughness. Examples with micro-lenses and a metallic sphere are presented. Then, this NPL is introduced in the hologram plane and allows, as a system of optical lenses, numerical magnification, complete aberration com- pensation in DHM (correction of image distortions and phase aberrations) and shifting. This NPL can be automatically computed by polynomial fit, but it can also be defined by a calibration method called Reference Con- jugated Hologram (RCH). We demonstrate the power of the method by the reconstruction of non-aberrated wavefronts from holograms recorded specifically with high orders aberrations introduced by a tilted thick plate, or by a cylindrical lens or by a lens ball used instead of the microscope objective. Finally, we present a modified digital holographic microscope permit- ii ABSTRACT ting the reconstruction of the polarization state of a wavefront. The prin- ciple consists in using two reference waves polarized orthogonally that in- terfere with an object wave. Then, the two wavefronts are reconstructed separately from the same hologram and are processed to image the polar- ization state in terms of Jones vector components. Simulated and experi- mental data are compared to a theoretical model in order to evaluate the precision limit of the method for different polarization states of the object wave. We apply this technique to image the birefringence and the dichroism induced in a stressed polymethylmethacrylate sample (PMMA), in a bent optical fiber and in a thin concrete specimen. To evaluate the precision of the phase difference measurement in DHM design, the birefringence in- duced by internal stress in an optical fiber is measured and compared to the birefringence profile captured by a standard method, which had been developed to obtain high-resolution birefringence profiles of optical fibers. A 6 degrees phase difference resolution is obtained, comparable with stan- dard imaging polariscope, but with the advantage of a single acquisition allowing real-time reconstruction. Keywords: Computer Holography, Microscopy, Aberration Compensa- tion, Polarization Version abrégée Dans cette thèse, nous décrivons une méthode capable de reconstruire numériquement et complètement les propriétés d’un front d’onde à par- tir d’un unique hologramme digital: l’amplitude, la phase et l’état de po- larisation. Dans ce but, nous présentons le principe de la Microscopie par Holographie Digitale (DHM) et le processus de reconstrution qui consiste à propager numériquement un front d’onde à partir du plan de l’hologramme jusqu’au plan de reconstruction. Nous définissons ensuite les différents paramètres d’une Lentille Numérique Paramétrique (NPL), introduite dans le plan de reconstruction, qui doivent être précisément ajustés pour obtenir une reconstruction correcte. Nous démontrons que des procédures automa- tiques permettent non seulement d’ajuster ces paramètres mais de plus de compenser complètement les aberrations de phase. La méthode consiste à calculer directement, à partir de l’hologramme, une NPL définie par des polynômes standards ou de Zernike sans connaissance a priori des valeurs physiques du montage expérimental (focale de l’objectif de microscope, dis- tance entre l’objet et l’objectif...). Cette méthode permet de reconstruire les distributions de phase correctement et précisément, même en présence d’aberrations fortes ou d’ordres élevés. De plus, nous montrons que cette méthode permet de compenser la courbure de spécimens. Les paramètres de la NPL obtenus avec l’approche par les polynômes de Zernike fournissent des mesures quantitatives des aberrations de micro-optiques et les images reconstruites révèlent leur défauts de surface et leur rugosité. Des exemples avec des micro-lentilles et une sphère métallique sont présentés. Ensuite, cette NPL est introduite dans le plan de l’hologramme et per- met, comme un système de lentilles optiques, des décalages et des gran- dissements numériques paramétrables ainsi qu’une compensation totale des aberrations en DHM (correction des distorsions d’images et des aberra- tions de phase). Cette NPL peut être calculée automatiquement par une approche polynomiale, mais elle peut aussi être définie par une méthode de calibrage appellée Hologramme de Référence Conjugué (RCH). Nous démontrons la puissance de la méthode en reconstruisant des fronts d’onde non aberrés à partir d’hologrammes volontairement enregistrés avec des iv VERSION ABRÉGÉE aberrations d’ordre élevé introduites par une lame épaisse inclinée, par une lentille cylindrique ou par une lentille sphérique utilisées à la place d’un objectif de microscope. Enfin, nous présentons un microscope holographique digital modifié qui permet de reconstruire l’état de polarisation d’un front d’onde. Le principe consiste à utiliser deux ondes de référence polarisées orthogonalement qui interfèrent avec une onde objet. Ensuite, l’état de polarisation, exprimé en termes de composantes du vecteur de Jones, est calculé à partir des deux fronts d’onde reconstruits séparément à partir du même hologramme. Des mesures simulées et expérimentales sont comparées à un modèle théorique dans le but d’évaluer la limite de précision de la méthode pour différents états de polarisation de l’onde objet. Nous appliquons cette technique à l’imagerie de biréfringence et de dichroïsme induits dans un échantillon de polymethylmethacrylate (PMMA) soumis à une contrainte, dans une fibre optique courbée, ainsi que dans un échantillon fin de béton. Afin d’évaluer la précision sur la mesure de différence de phase pour un montage expérimental en microscopie, la biréfringence induite par les contraintes internes d’une fibre optique est mesurée et comparée au profil de biréfringence obtenu par une méthode standard, qui a été développée pour obtenir des hautes résolutions de pro- fils de biréfringence pour les fibres optiques. Une résolution de 6 degrés pour la différence de phase est obtenue, ce qui est comparable aux polar- iscopes standards avec l’avantage d’une unique acquisition et donc d’une reconstruction possible en temps réel. Mots clefs: Holographie digitale, Microscopie, Compensation d’aberration, Polarisation Acknowledgements A Long Time Ago in the MVD Group Far, Far Aware... I met a wise man named Prof. Christian Depeursinge who instructed me on the Force of optical engineering. His competence, his enthusiasm, and his many pertinent ideas gave to me, and to the other Rebels of digi- tal holography, the Force and the wisdom to fight the dark side of a thesis work. He was always there when a recorded hologram said: "Help me, Chris- tian Depeursinge, you are our only hope." His sympathy and his kindness is always like a light saber that illuminates the friendship of his group. Therefore, I would like to thank him a lot to have initiated and directed this thesis work. Then, I would like to thank my thesis advisor, and director of the Institute of Applied Optics, Prof. René-Paul Salathé, who pushed me to finish my training before facing the thesis examination. I am grateful to him for having given me the opportunity to achieve this thesis in excellent conditions. Thanks to Prof. M. Gu, Prof. H. Tiziani, Prof. M. Unser and Prof. P. Renaud for having accepted to participate in the jury of this thesis. I would now like to thank very much all the Rebellion members. First the Red Leader of digital holography, Dr. Etienne Cuche, who opened the way with his thesis and who proposed to me a semester project in 1999, which has stimulated my interest in digital holography; the Chewie of my office, Dr. Frédéric Montfort, for all the discussions about science or not, and especially for his bellowing about the culinary quality of the Vinci; the R2D2 of the experimental setups, always there to help, Jonas Kühn and the 3PO specialist of the belgian joke, Michel Saint-Ghislain. I will never forget the other office, (fortunately not the dark side), Florian Charrière for helping me to use the OPA Death Star, and Anca Marian for their availabilities and their invaluable advice. I only regret that Anca did not explain to us how she uses the Force to evaporate herself..
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