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9 November 2010 Algorithms for phase diversity wavefront sensing
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Phase diversity wavefront sensing is a methodology for estimating wavefront aberrations by solving an unconstrained optimization problem from multiple images whose pupil phases differ from one another with a known amount. Due to the large number of unknowns, an efficient numerical technique is required. In this paper, a cost function with appropriate stabilization is given by using least square estimate. Various optimization methods for minimizing the cost function are compared in numerical simulations when the wavefront is described by Zernike polynomials (modal method) and a set of individual pixel values (zonal method). The results show that, because of the less unknown parameters, modal method can achieve higher accuracy than zonal method by using the steepest descent method and the conjugate gradient method. In the solving process, the zonal method has a large number of unknown parameters, thereby it has a lower stability and it is easy to fall into a local extremum. Fortunately, the L-BFGS method can improve this problem efficiently. For its good performance in solving large scale optimization problems, the L-BFGS method is very suited to PD wavefront estimate.
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Fei Li and Changhui Rao "Algorithms for phase diversity wavefront sensing", Proc. SPIE 7853, Advanced Sensor Systems and Applications IV, 78532D (9 November 2010);

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