Background Removal for Ptychography via Wigner Distribution Deconvolution
Abstract.
Ptychography is a computational imaging technique that aims to reconstruct the object of interest from a set of diffraction patterns. Each of these is obtained by a localized illumination of the object, which is shifted after each illumination to cover its whole domain. Because in the resulting measurements the phase information is lost, ptychography gives rise to solving a phase retrieval problem. In this work, we consider ptychographic measurements contaminated by a background signal. Such a background is caused by imperfections in the experimental setup and appears as a signal that is added to the diffraction patterns. The background is assumed to be independent of the shift of the object, i.e., it is the same for all diffraction patterns. Two algorithms are provided, for arbitrary objects and for so-called phase objects that do not absorb the light but only scatter it. For the second type, a uniqueness of reconstruction is established for almost every object. Our approach is based on the Wigner distribution deconvolution, which lifts the object to a higher-dimensional matrix space where the recovery can be reformulated as a linear problem. The background only affects a few equations of the linear system that are therefore discarded. The lost information is then restored using redundancy in the higher-dimensional space.
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Acknowledgments.
The authors would like to thank Johannes Hagemann, Tim Salditt, Christian Schroer, and Maximilian Töllner for providing valuable insights into the physics of imaging experiments. Furthermore, the authors are grateful for the helpful comments on this work by Benedikt Diederichs and Frank Filbir.
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History
Submitted: 27 February 2024
Accepted: 16 July 2024
Published online: 23 September 2024
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Deutsche Forschungsgemeinschaft (DFG): KR 4512/1-1, KR 4512/2-2
Helmholtz Association: ZT-I-0025, ZT-I-PF-4-018, ZT-I-PF-5-28, ZT-I-PF-4-024
Funding: The work of the authors was supported by the Helmholtz Association under contracts ZT-I-0025 (Ptychography 4.0), ZT-I-PF-4-018 (AsoftXm), ZT-I-PF-5-28 (EDARTI), and ZT-I-PF-4-024 (BRLEMMM). The second author acknowledges further financial support by German Research Foundation (DFG) grants KR 4512/1-1 and KR 4512/2-2.
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