El propósito de este trabajo es describir un modelo físico del proceso de formación de imágenes en los telescopios astronómicos dotados de sistemas de óptica adaptativa para compensar los efectos de la turbulencia atmosférica. El análisis se centra en los sistemas de compensación parcial, aunque gran parte de los resultados son aplicables a todos los sistemas. En primer lugar, se desarrolla un modelo para la estadística del frente de onda corregido. Esta estadística está completamente determinada por la función de estructura; por tanto, se analiza esta función y se introducen y calculan los conceptos de longitud de correlación y de parámetro generalizado de Fried. Además se obtienen aproximaciones de la función de estructura, de la función de transferencia óptica y de la función imagen de un punto.A partir del modelo de la estadística del frente de onda, se generaliza el modelo de formación de imágenes de Goodman al caso de corrección parcial. Se describe la estadística de la intensidad luminosa en el plano imagen; la distribución exacta se aproxima por la distribución de Rice, debido a la analogía física entre el caso de compensación parcial y la suma de un fondo coherente más un patrón de speckle (p.ej. holografía). La estadística de fotones se obtiene como la transformada de Poisson de la distribución de la intensidad. Este modelo de formación de imágenes se utiliza para desarrollar dos aplicaciones. En la primera, se halla la varianza residual real de la fase, lo que permite calibrar los sistemas de óptica adaptativa cuando las fuentes de error son importantes. En la segunda, se analizan diversas técnicas de detección de exoplanetas. Finalmente los resultados teóricos se comparan con valores simulados y con datos experimentales, obtenidos utilizando un montaje experimental que se ha desarrollado para generar frentes de onda parcialmente compensados. El modulador de fase es una pantalla de cristal líquido extraída de un proyector de video comercial. El dispositivo se ha calibrado y se han estudiado sus limitaciones. Se concluye que las predicciones teóricas coinciden con exactitud con los datos simulados y experimentales. / The aim of this work is to describe a physical model of the image formation process in astronomical telescopes that use adaptive optics systems to compensate atmospheric turbulence. The analysis is focused on partially compensating systems, though a lot of the results are applicable to all the systems. First, a model of the corrected wavefront statistics has been developed. The statistics is completely determined by the structure function. This last function has been analyzed, and the concepts of correlation length and of Fried generalized parameter have been introduced and calculated. Furthermore, approximated expressions for the structure function, the optical transfer function and the point spread function have been derived. Using the wavefront model, the Goodman imaging model has been generalized to the partial compensation case. The light intensity statistics at the image plane in partial compensation has been described; the exact intensity distribution has been approximated by a modified Rician distribution, because of the physical analogy between the partial compensation case and the addition of a coherent background and a speckle pattern (e.g. holography). The photon statistics is obtained as the Poisson transform of the intensity distribution. The imaging model is used in the development of some practical applications. First, the residual phase variance in actual compensated wavefronts is obtained, which allows the calibration of the AO systems. Second, several methods to search for exoplanets are analyzed. Finally, theoretical results are compared with simulated data and with experimental values, obtained from an experimental setting that we have developed to generate partially compensated wavefronts. The phase modulator is a lyquid crystal display that has been extracted from a commercial video projector. The display has been calibrated and its performance limits have been studied. Theoretical predictions fit well both with simulated and experimental data.

<p> The performance of long-range imaging systems often suffers due to the presence of atmospheric turbulence. One way to alleviate the degradation caused by atmospheric turbulence is to apply post-processing mitigation algorithms, where a high-quality frame is reconstructed from a single degraded image or a sequence of degraded frames. The image processing algorithms for atmospheric turbulence mitigation have been studied for decades, yet some critical problems remain open.</p> <p><br></p> <p>This dissertation addresses the problem of image reconstruction through atmospheric turbulence from three unique perspectives: 1) Reconstruction with the presence of moving objects using an improved classical image processing pipeline. 2) A fast simulation scheme for efficiently generating large-scale turbulence-degraded datasets for training deep neural networks. 3) A deep learning-based single-frame reconstruction method using Vision Transformer. </p>

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Non-destructive imaging modalities for evaluating the internal properties of materials can be formulated as physics-driven inverse problems. Model-based Iterative reconstruction (MBIR) methods that integrate a forward model of the imaging system and a prior model of the object being imaged can provide superior reconstruction quality relative to conventional methods. However, making MBIR feasible for practical applications faces two key challenges. First, we require efficient computational methods for MBIR that allow large-scale reconstructions in real-time. Second, we must develop forward models that accurately capture the physics and geometry of the imaging system, and, support the use of advanced denoisers that enhance image quality as prior models.<br><br>This thesis attempts to address the aforementioned challenges and is divided into three main chapters, each corresponding to a different inverse imaging application. <br><br>In the first chapter of this thesis, we propose a novel 4D model-based iterative reconstruction (MBIR) algorithm for low-angle coherent-scatter X-ray Diffraction (XRD) tomography that can substantially increase the SNR. Our forward model is based on a Poisson photon counting model that incorporates a spatial point-spread function, detector energy response and energy-dependent attenuation correction. Our prior model uses a Markov random field (MRF) together with a reduced spectral bases set determined using non-negative matrix factorization. Our algorithm efficiently computes the Bayesian estimate by exploiting the sparsity of the measurement data. We demonstrate the ability of our method to achieve sufficient spatial resolution from sparse photon-starved measurements and also discriminate between materials of similar densities with real datasets.<br><br>In the second chapter of this thesis, we propose a multi-agent consensus equilibrium (MACE) algorithm for distributing both the computation and memory of <br>MBIR for Computed Tomographic (CT) reconstruction across a large number of parallel nodes. In MACE, each node stores only a sparse subset of views and a small portion of the system matrix, and each parallel node performs a local sparse-view reconstruction, which based on repeated feedback from other nodes, converges to the global optimum. Our distributed approach can also incorporate advanced denoisers as priors to enhance reconstruction quality. In this case, we obtain a parallel solution to the serial framework of Plug-n-play (PnP) priors, which we call MACE-PnP. In order to make MACE practical, we introduce a partial update method that eliminates nested iterations and prove that it converges to the same global solution. Finally, we validate our approach on a distributed memory system with real CT data. We also demonstrate an implementation of our approach on a massive supercomputer that can perform large-scale reconstruction in real-time. <br><br>In the third chapter of this thesis, we propose a method that makes MBIR feasible for real-time single-shot holographic imaging through deep turbulence. Our method uses surrogate optimization techniques to simplify and speedup the reflectance and phase-error updates in MBIR. Further, our method accelerates computation of the surrogate-updates by leveraging cache-prefetching and SIMD vector processing units on a single CPU core. We analyze the convergence and real CPU time of our method using simulated datasets, and demonstrate its dramatic speedup over the original MBIR approach. <br>