Phase Retrieval Using Neural Networks

The wavefront sensing and control (WFSC) is developed for NASA James Webb Space Telescope (JWST) mission (B. H. Dean, D. L. Aronstein, J. S. Smith, R. Shiri, and D. S. Acton, Proc. SPIE 6265:626511, 2006). The phase retrieval (phase retrieval: PR) is one of the key algorithms in WFSC. There are two general categories of PR algorithms (B. H. Dean, Proc. IEEE. Aerospace Conference. 2007): iterative-transform (D. L. Misell, J Phys. D6: L6–L9, 1973; R. W. Gerchberg, W. O. Saxton, OPTIK. 34: 275, 1971; W. O. Saxton, OPTIK. 35: 237–246, 1972) and parametric approach (R. A. Gonsalves, P. Considine, J. Opt. Soc. Am. 66: 961–964, 1976; W. H. Southwell, J. Opt. Soc. Am. A3: 396–399, 1977). In most scenarios, the PR algorithm takes advantage of both categories, iterative-transform for retrieval high spatial frequency and parametric for retrieval high dynamic range. However, the parametric approach sometimes returns local minimum due to the bad starting parameters set, which is very common in optimization algorithm such as nonlinear optimization algorithm and genetic algorithm. In this paper, the neural networks are used for parametric approach, which return the global minimum and cost less time. A new PR algorithm block is also proposed and verified by experiments. Unlike other algorithms, the defocus values of PSFs are not necessary, which are also difficult to be determined when dealing with large wavefront errors (wavefront error: WFE) system. Instead, the PSF images which are taken before or after the focal plane (focal plane: FP) are the inputs for this algorithm. The experiment results which include both the high spatial frequency and high dynamic range capability of PR are presented in this paper.