A direct solver for the phase retrieval problem in ptychographic imaging. (English) Zbl 07318078

Summary: Measurements achieved with ptychographic imaging are a special case of diffraction measurements. They are generated by illuminating small parts of a sample with, e.g., a focused X-ray beam. By shifting the sample, a set of far-field diffraction patterns of the whole sample is then obtained. From a mathematical point of view those measurements are the squared modulus of the windowed Fourier transform of the sample. Thus, we have a phase retrieval problem for local Fourier measurements. A direct solver for this problem was introduced by M. A. Iwen et al. [SIAM J. Imaging Sci. 9, No. 4, 1655–1688 (2016; Zbl 1352.49035)] and improved by M. Iwen et al. [“Phase retrieval from local measurements in two dimensions”, in: Y. M. Lu (ed.) et al., Wavelets and sparsity XVII. Proc. Vol. 10394. San Diego, CA: SPIE. Article ID 103940X (2017; doi:10.1117/12.2274355)]. Motivated by the applied perspective of ptychographic imaging, we present a generalization of this method and compare the different versions in numerical experiments. The new method proposed herein turns out to be more stable, particularly in the case of missing data.


15Bxx Special matrices
78Axx General topics in optics and electromagnetic theory
94Axx Communication, information
90Cxx Mathematical programming


Zbl 1352.49035
Full Text: DOI arXiv


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