A Computed Tomographic Imaging Spectrometer (CTIS) is an imaging spectrometer which can acquire a hyper-spectral data set in a single snapshot (one focal plane array integration time) with no moving parts. A specially designed dispersing element, which separates light from the three-dimensional object cube into a grid of two-dimensional prismatic diffraction orders, is the key element in the instrument. The capabilities of the CTIS instrument can be improved by employing a more optimized grating design.There were two main goals to this research: (1) to design a novel CTIS disperser that will improve CTIS capabilities over the previous 5x5 disperser and (2) to integrate the new disperser into the CTIS and evaluate its performance compared to the 5x5 disperser. Six new disperser ideas were evaluated based on their performance in a number of computer simulations to determine the most optimal dispersion pattern. A new CTIS disperser incorporating a novel radial design pattern was developed and tested. Reconstruction results of various spatial and spectral targets are presented. Capabilities of the new CTIS instrument incorporating the radial grating are compared to the previous instrument employing a 5x5 disperser. While both dispersers perform similarly for point-source objects, the radial grating performs better than the previous disperser for extended sources.

This dissertation is comprised of two separate topics within the domain of polarization optical engineering. The first topic is a Mueller matrix roots decomposition, and the second topic is polarization computer generated holography. The first four chapters of the dissertation are on the topic of the Mueller matrix roots decomposition. Recently, an order-independent Mueller matrix decomposition was proposed in an effort to organize the nine depolarization degrees of freedom. Chapter 1 discusses relevant Mueller matrix decomposition prior art and the motivation for this work. In chapter 2, the critical computational issues involved in applying this Mueller matrix roots decomposition are addressed, along with a review of the principal root and common methods for its calculation. The choice of the pth root is optimized at p = 10⁵, and computational techniques are proposed which allow singular Mueller matrices and Mueller matrices with a half-wave of retardance to be evaluated with the matrix roots decomposition. A matrix roots algorithm is provided which incorporates these computational results. In chapter 3, the Mueller matrix roots decomposition is reviewed and a set of Mueller matrix generators are discussed. The parameterization of depolarization into three families, each with three degrees of freedom is explained. Analysis of the matrix roots parameters in terms of degree of polarization maps demonstrates that depolarizers fall into two distinct classes: amplitude depolarization in one class, and phase and diagonal depolarization in another class. It is shown that each depolarization family and degree of freedom can be produced by averaging two non-depolarizing Mueller matrix generators. This is extended to provide further insight on two sample measurements, which are analyzed using the matrix roots decomposition. Chapter 4 discusses additional properties of the Mueller matrix roots generators and parameters, along with a pupil aberration application of the matrix roots decomposition. Appendix C, adapted from a conference proceedings paper, presents an application of the matrix roots depolarization parameters for estimating the orientation of a one-dimensionally textured object. The last two chapters are on the topic of polarization computer generated holography. In chapter 5, an interlaced polarization computer-generated hologram (PCGH) is designed to produce specific irradiance and polarization states in the image plane. The PCGH produces a tangentially polarized annular pattern with correlated speckle, which is achieved by a novel application of a diffuser optimization method. Alternating columns of orthogonal linear polarizations illuminate an interlaced PCGH, producing a ratio of polarization of 88% measured on a fabricated sample. In chapter 6, an etched calcite square-wave retarder is designed, fabricated, and demonstrated as an illuminator for an interlaced polarization computer generated hologram (PCGH). The calcite square-wave retarder enables alternating columns of orthogonal linear polarizations to illuminate the interlaced PCGH. Together, these components produce a speckled, tangentially polarized PCGH diffraction pattern with a measured ratio of polarization of 84% and a degree of linear polarization of 0.81. An experimental alignment tolerance analysis is also reported.

This work builds up on the greatest minds of Cambridge Holography: Adrian Cable, Edward Buckley, Jonathan Freeman, and Christoph Bay. Cable and Buckley, developed an OSPR algorithm which was the first to provide high-quality real-time hologram generation using general-purpose hardware while Freeman designed a method to correct arbitrary aberrations. As ingenious as the method was, the calculations were extensively lengthy. Addressing this issue, a variant of OSPR suited for correcting spatially-varying aberration is presented. The algorithm combines the approaches of Cable, Buckley and Freeman to provide real-time hologram generation while incorporating various corrections (aberration, distortion, and pixel shape envelope). A high-performance implementation on a mid-range GPU achieved hologram generation up to 12 fps. Following topic studied is an adaptive optical correction. This work attempts to construct a set of methods, forming an automated testbed for holographic projectors. Each model, after exiting the production line is placed on such testbed, having all of its imperfections characterized. Once calibrated, each model is able to display highest-quality image throughout its life-span. An application of this work to industry was carried in collaboration with Dr Phillip Hands (University of Edinburgh) and LumeJET. Three demonstrators are constructed intending for a cost-effective system for holographic lithography. They are characterized using the developed testbed. Using the supersampled Adaptive OSPR algorithm, the diffraction limit was surpassed 2.75 times allowing to increase the patterning area. This combines approaches of Cable, Buckley, Freeman and Bay to achieve a wide field-of-view and high pixel-count replay field using off-the-shelf components. This thesis is finished describing the work on 3D holography carried with Penteract28. It is shown that the 2D hologram in the presence of spatially-varying aberrations is mathematically equivalent to a 3D hologram. The same implementation of the algorithm can be used to provide real-time 3D hologram generation.

La révolution en cours des outils optogénétiques - des protéines photosensibles génétiquement induites qui peuvent activer, inhiber et enregistrer l'activité neuronale - a permis d'ouvrir une nouvelle voie pour relier l'activité neuronale et la cognition. Néanmoins, pour profiter au mieux de ces outils nous avons besoin de méthodes optiques qui peuvent projeter des schémas d'illumination complexes dans le cerveau. Pendant mon doctorat, j'ai travaillé sur deux nouveaux systèmes complémentaires pour la stimulation de l'activité neuronale. Le premier système combine des déflecteurs acousto-optiques et une illumination Gaussienne à faible ouverture numérique pour produire une photo activation rapide des outils optogénétiques. La capacité d'accès aléatoire du système permet de délivrer des séquences d'illumination spatialement et temporellement complexes qui simulent avec succès les schémas physiologiques de l'activité des fibres moussues dans des tranches de cerveaux. Ces résultats démontrent que les schémas de stimulation optogénétique peuvent être utilisés pour recréer l'activité en cours et étudier les microcircuits du cerveau dans un environnement physiologique. Alternativement, l'holographie générée par ordinateur (HGO) permet d'améliorer grandement les stimulations optogénétiques en répartissant efficacement la lumière sur plusieurs cibles cellulaires simultanément. Néanmoins, le confinement axial se dégrade pour des schémas d'illuminations larges. Afin de d'améliorer ce point, l’HGO peut être combinée avec une technique de focalisation temporelle qui confine axialement la fluorescence sans dépendre de l'allongement latéral. Les précédentes configurations maintiennent l'excitation non linéaire à un unique plan focal spatiotemporel. Dans cette thèse, je décris deux méthodes différentes qui permettent de dépasser ces limitations et de permettre la génération de schémas focalisés tridimensionnellement, à la fois spatialement et temporellement. / The ongoing revolution of optogenetic tools – genetically encoded light-sensitive proteins that can activate, silence and monitor neural activity – has opened a new pathway to bridge the gap between neuronal activity and cognition. However, to take full advantage of these tools we need optical methods that can deliver complex light patterns in the brain. During my doctorate, I worked on two novel and complementary optical systems for complex spatiotemporally neural activity stimulation. The first system combined acousto-optic deflectors and low numerical aperture Gaussian beam illumination for fast photoactivation of optogenetic tools. The random-access capabilities of the system allowed to deliver complex spatiotemporal illumination sequences that successfully emulated physiological patterns of cerebellar mossy fiber activity in acute slices. These results demonstrate that patterned optogenetic stimulation can be used to recreate ongoing activity and study brain microcircuits in a physiological activity context. Alternatively, Computer Generated Holography (CGH) can powerfully enhance optogenetic stimulation by efficiently shaping light onto multiple cellular targets simultaneously. Nonetheless, the axial confinement degrades for laterally extended illumination patterns. To address this issue, CGH can be combined with temporal focusing that axially confines fluorescence regardless of lateral extent. However, previous configurations restricted nonlinear excitation to a single spatiotemporal focal plane. In this thesis, I describe two alternative methods to overcome this limitation and enable three-dimensional spatiotemporal focused pattern generation.