## 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.

Original language | English |
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Pages (from-to) | 292-300 |

Number of pages | 9 |

Journal | Mathematics and Computers in Simulation |

Volume | 176 |

Early online date | 2019 Nov 16 |

DOIs | |

Publication status | Published - 2020 Oct |

## Subject classification (UKÄ)

- Computational Mathematics
- Other Physics Topics

## Keywords

- Diffraction imaging
- Image reconstruction
- Phase retrieval
- Ptychography