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We consider the classic Fourier phase retrieval problem of reconstructing a function H from intensity measurements \(|\mathscr {F}^{-1} H|^2\) in a finite-dimensional setting. In particular, we consider the case of differential measurements and investigate in which form classic results for the continuous case, such as the transport of intensity equation (TIE), transfer to the practically relevant finite-dimensional case. Finally, we discuss the implications of our results on numerical reconstruction methods.

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On Fourier Phase Retrieval by Differential Intensity Measurements in Finite Dimensions

  • 会议论文

  • 发表日期：

    2025年

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  • Simon Hubmer,
  • Stefan Kindermann

摘要

We consider the classic Fourier phase retrieval problem of reconstructing a function H from intensity measurements \(|\mathscr {F}^{-1} H|^2\) in a finite-dimensional setting. In particular, we consider the case of differential measurements and investigate in which form classic results for the continuous case, such as the transport of intensity equation (TIE), transfer to the practically relevant finite-dimensional case. Finally, we discuss the implications of our results on numerical reconstruction methods.