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
SN - 0378-4754
VL - 176
SP - 292
EP - 300
JO - Mathematics and Computers in Simulation
JF - Mathematics and Computers in Simulation
ER -