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Modeling, Design and Optimization of Computer- Generated Holograms with Binary Phases

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Modeling, Design and Optimization of Computer- Generated Holograms with Binary Phases Modeling, design and optimization of computer- generated holograms with binary phases Thèse Jing Wang Doctorat en physique Philosophiæ doctor (Ph. D.) Québec, Canada © Jing Wang, 2019 Modeling, design and optimization of computer- generated holograms with binary phases Thè se JING WANG Sous la direction de : Yunlong Sheng Résumé L’hologramme généré par ordinateur (HGO) a été démontré à jouer un rôle important depuis son invention par Lohmann dans les années 1960 dans de nombreuses applications telles que l’ingénierie du front d'onde, l’éclairage structuré et l’affichage optique, etc. Dans le travail de thèse ci-présent, la modélisation, la conception et l’optimisation d’HGO avec des phases binaires sont étudiées. Nous avons examiné un système pratique de projection d’image avec certaines spécifications de travail, par exemple, une distance de travail de 40 cm, une profondeur de champ de 10 cm et un angle de diffraction de 53 degré pour une longueur d’onde de travail de 632 nm, et ensuite conçu et optimisé un hologramme de phase binaire en passant par une recherche directe binaire pour ce système d’image. L’hologramme a été fabriqué par la lithographie à faisceau d’électrons. Pour atteindre l’angle de diffraction requis, nous avons discuté de l’architecture optique dans le système de projection d’image holographique. L’HGO conçu et le système de projection d’image holographique ont été validés expérimentalement par reconstruction optique. Étant donné que les pixels finiront par se regrouper pour former des ouvertures polygonales en hologramme, qui peut être vu clairement dans le processus de recherche directe binaire, nous avons proposé une nouvelle approche pour la conception directe des ouvertures polygonales basée sur la disposition triangulaire en HGO de grande taille en pixels. La diffraction de l’ouverture a été calculée par la transformation analytique d’Abbe. L’image reconstruite peut être exprimée comme une addition cohérente de motifs de diffraction à partir de tous les bords droits d’orientations et de longueurs différentes. Une optimisation en deux étapes comprenant l’algorithme génétique avec la recherche locale de codage des phases binaires des ouvertures, suivie par la recherche directe de co-sommets flottants des ouvertures triangulaires élémentaires a été développée. Nous avons en outre proposé une disposition d’ouverture quadrilatérale, qui fournit plus de degrés de liberté et peut former des ouvertures polygonales plus diverses en hologrammes. L’algorithme génétique parallèle avec la recherche locale a été adopté dans une première étape pour assigner des phases binaires, et la recherche directe a ensuite été utilisée pour III optimiser des emplacements de co-sommets d'ouvertures quadrilatérales lors de la deuxième étape. Trois schémas différents pour l'algorithme en deux étapes ont été discutés pour fournir des moyens flexibles afin d’équilibrer la performance de l’optimisation et la durée nécessaire. IV Abstract The computer-generated hologram (CGH) has been demonstrated to play an important role, since its invention by Lohmann in 1960s, in many applications such as wavefront engineering, structured illumination and optical display, etc. In this thesis, the modeling, design and optimization of CGH with binary phases are studied. We considered a practical projection image system with certain working specification, e.g. working distance of 40 cm, depth of field of 10 cm and a diffraction angle of 53 degree for 632 nm working wavelength, and then designed and optimized a binary-phase hologram by direct binary search for this image system. The hologram was fabricated by E-beam lithography. To achieve the required diffraction angle, we discussed the optical architecture in holographic projection image system. The designed CGH and holographic projection image system were validated experimentally by optical reconstruction. Since the pixels will eventually cluster to form polygonal apertures in hologram, which can be seen clearly during the process of direct binary search, we proposed a new approach to directly design polygonal apertures based on triangular layout in CGH of a large number of pixels. The diffraction of aperture was calculated by analytical Abbe transform. The reconstructed image can be expressed as a coherent addition of diffraction patterns from all the straight edges of different orientations and lengths. A two-step optimization including genetic algorithm with local search for encoding binary phases of apertures, followed by direct search for floating covertices of the elementary triangular apertures was developed. We further proposed a quadrilateral aperture layout, which provides more degrees of freedom and can form more diverse polygonal apertures in holograms. The parallel genetic algorithm with local search was adopted to assign binary phases in the first step, and direct search was then used to optimize of locations of covertices of quadrilateral apertures in the second step. Three different schemes for the two-step algorithm were discussed to provide flexible ways to balance the optimization performance and time cost. V Contents Résumé ................................................................................................................................. III Abstract .................................................................................................................................. V Contents ................................................................................................................................ VI List of figures ........................................................................................................................ X List of tables ...................................................................................................................... XIII Abbreviations .................................................................................................................... XIV Acknowledge .................................................................................................................... XVII Foreword ......................................................................................................................... XVIII General introduction ............................................................................................................... 1 Historical events of holography .......................................................................................... 1 Computer-generated holography and conventional optical holography ............................. 2 Categories of CGHs ............................................................................................................ 3 Current research of CGHs ................................................................................................... 4 Design procedures of CGHs ............................................................................................... 5 The motivation .................................................................................................................... 6 Organization of thesis ......................................................................................................... 7 Chapter 1 Theory, algorithms and fabrications of holograms ................................................ 9 1.1 Fundamental of holography .......................................................................................... 9 1.2 Scalar diffraction theory ............................................................................................. 12 1.2.1 Wave equation ...................................................................................................... 12 1.2.2 Spatial frequency transfer function ...................................................................... 13 1.2.3 Fresnel diffraction and Fraunhofer diffraction ..................................................... 14 VI 1.3 Conventional algorithms for CGHs design ................................................................. 15 1.3.1 Direct Binary Search ............................................................................................ 16 1.3.2 Simulated Annealing ............................................................................................ 16 1.3.3 Genetic algorithm ................................................................................................. 17 1.3.4 Iterative Fourier Transform Algorithm ................................................................ 17 1.4 Industrial schemes for CGH design ............................................................................ 18 1.4.1 Dot matrix hologram ............................................................................................ 18 1.4.2 Holographic printer .............................................................................................. 19 1.5 Fabrication technologies of holograms ....................................................................... 21 1.5.1 Diamond machining ............................................................................................. 21 1.5.2 Photolithography .................................................................................................. 22 1.5.3 Direct laser writing ............................................................................................... 22 1.5.4 Electron beam lithography ................................................................................... 23 Chapter 2 Design of holograms by direct binary
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