12 July 2018 Using energy consistency to improve phase retrievals with discrete Fourier transform cropping
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Abstract
A new error metric, known as the Parseval error metric, was developed for phase retrieval algorithms for wavefront sensing that use a cropped discrete Fourier transform to deal with local minima of the sum-squared error metric that have high-frequency phase artifacts that incorrectly place energy outside the crop window. This was done by defining an energy consistency error metric based on a modified version of Parseval’s theorem, and then adding it with a relative weighting factor to the sum-squared error metric to form the Parseval error metric. Simulations were performed to examine the effect of the Parseval error metric compared to the sum-squared error metric alone and to downsampling the data PSF instead of cropping. We found that the cropping methods had better wavefront fits compared to the downsampled method, and the Parseval error metric had better retrieval success rates over the other two methods, although with greater computational requirements.
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Joseph S. Tang, Joseph S. Tang, James R. Fienup, James R. Fienup, "Using energy consistency to improve phase retrievals with discrete Fourier transform cropping", Proc. SPIE 10698, Space Telescopes and Instrumentation 2018: Optical, Infrared, and Millimeter Wave, 106986K (12 July 2018); doi: 10.1117/12.2307849; https://doi.org/10.1117/12.2307849
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