Distributed Wavefront Reconstruction for Adaptive Optics Systems

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We are currently facing an increasing amount of challenges in the area of photonics as more and more applications in need for active “photon control” sprout in different fields of science. Adaptive Optics (AO) is the subject which deals with measuring, reconstructing, and reshaping the phase of a photon wavefront in real-time and can, thus, provide the framework for controlling the photons in areas such as medicine, astronomy and telecommunications, among others. The objective of this graduation project is to create a novel distributed method for wavefront reconstruction, integrate the method in an AO loop, and analyse its properties. This method will use the intensity distribution measured by the wavefront sensor instead of the classical slope approximation (obtained using a centroid algorithm). Using the complete intensity distribution gives us more information than the slope approximation and therefore, a more accurate reconstruction is expected. Moreover, we will estimate the wavefront using B-splines basis functions. These splines are defined locally which makes them suitable for the application of distributed reconstruction methods. The content of this thesis is divided into two distinct parts. In the first part, we analyse the different components of an AO system with special emphasis on the state-of-the-art phase retrieval methods. Furthermore, the B-splines framework is presented alongside distributed optimization techniques with special emphasis on the Alternating Direction Method of Multipliers (ADMM). The second part of the thesis uses the theoretical information from the first chapters to support the development of one centralized and two distributed algorithms for solving phase-retrieval problems using pupil-plane sensors. The results from these methods, together with the results from a compressive sampling method which decreases the quantity of measurements used, are presented in the last chapters. It was verified in simulation experiments that the average reconstruction error achieved by the novel centralized method surpasses the classical approaches which use slope measurements for aberrations with an RMS value smaller than the wavelength. It is also shown that the variance of the reconstruction error using the novel method is reduced by two orders of magnitude. Regarding the two distributed methods (unstructured and structured ADMM applications), it is shown that the unstructured method has a very low convergence rate which renders this method unpractical for real-time applications. The structured method showed much more promising results given that it was able to converge to within a 5% tolerance of the optimal centralized solution after 50 ? 150 iterations. This method can also be implemented in a completely decentralized manner which is suitable for a GPU/FPGA implementation.