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A direct solver for the phase retrieval problem in ptychographic imaging

Author

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  • Sissouno, Nada
  • Boßmann, Florian
  • Filbir, Frank
  • Iwen, Mark
  • Kahnt, Maik
  • Saab, Rayan
  • Schroer, Christian
  • zu Castell, Wolfgang

Abstract

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 Iwen, Viswanathan and Wang in 2016 and improved by Iwen, Preskitt, Saab and Viswanathan in 2018. 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.

Suggested Citation

  • Sissouno, Nada & Boßmann, Florian & Filbir, Frank & Iwen, Mark & Kahnt, Maik & Saab, Rayan & Schroer, Christian & zu Castell, Wolfgang, 2020. "A direct solver for the phase retrieval problem in ptychographic imaging," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 176(C), pages 292-300.
    • Handle: RePEc:eee:matcom:v:176:y:2020:i:c:p:292-300
    DOI: 10.1016/j.matcom.2019.11.003
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    1. Frank Seiboth & Andreas Schropp & Maria Scholz & Felix Wittwer & Christian Rödel & Martin Wünsche & Tobias Ullsperger & Stefan Nolte & Jussi Rahomäki & Karolis Parfeniukas & Stylianos Giakoumidis & Ul, 2017. "Perfect X-ray focusing via fitting corrective glasses to aberrated optics," Nature Communications, Nature, vol. 8(1), pages 1-5, April.
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