Phase Diversity Technique with Sparse Regularization in Liquid Crystal Adaptive Optics System

Phase diversity (PD) technique is an effective method for wavefront sensing and image restoration in adaptive optics (AO). Classical PD with Tikhonov regularization can achieve proper wavefront estimation but constantly results in overly smooth images. Nonlocal centralized sparse representation (NCSR) based on nonlocal self-similarity and the sparsity model is combined with PD to obtain high-resolution images. The proposed method contains two steps: the first step is obtaining wavefront from ordinary PD with Tikhonov regularization, and the second step is deblurring the image with NCSR other than Tikhonov regularization. Numerical simulations show that the peak signal-to-noise ratios and structural similarity index metrics of deblurred images by the proposed method are higher than those by the traditional method. This work also studies the influence of weak noise. Initially, the proposed method is applied to a liquid crystal AO system, where the highest spatial resolutions that can be clearly distinguished are 1.59x diffraction limitation with AO on, 1.41x diffraction limitation with traditional PD, and 1.26x diffraction limitation with the proposed method. The proposed approach can be widely used for AO postprocessing in ground-based telescopes, fluorescence microscopes, and other applications. (c) 2018 Society of Photo-Optical Instrumentation Engineers (SPIE)