TY - JOUR

T1 - A direct solver for the phase retrieval problem in ptychographic imaging

AU - Sissouno, Nada

AU - Boßmann, Florian

AU - Filbir, Frank

AU - Iwen, Mark

AU - Kahnt, Maik

AU - Saab, Rayan

AU - Schroer, Christian

AU - zu Castell, Wolfgang

PY - 2020/10

Y1 - 2020/10

N2 - 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.

AB - 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.

KW - Diffraction imaging

KW - Image reconstruction

KW - Phase retrieval

KW - Ptychography

U2 - 10.1016/j.matcom.2019.11.003

DO - 10.1016/j.matcom.2019.11.003

M3 - Article

AN - SCOPUS:85076237585

VL - 176

SP - 292

EP - 300

JO - Mathematics and Computers in Simulation

JF - Mathematics and Computers in Simulation

SN - 0378-4754

ER -