A direct solver for the phase retrieval problem in ptychographic imaging
Sissouno, Nada ; Boßmann, Florian ; Filbir, Frank ; Iwen, Mark ; Kahnt, Maik LU
; Saab, Rayan
; Schroer, Christian
and zu Castell, Wolfgang
(2020)
In Mathematics and Computers in Simulation
176.
p.292-300
- 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... (More)
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.
(Less)
- author
- Sissouno, Nada
; Boßmann, Florian
; Filbir, Frank
; Iwen, Mark
; Kahnt, Maik
LU
; Saab, Rayan
; Schroer, Christian
and zu Castell, Wolfgang
- organization
- publishing date
- 2020-10
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Diffraction imaging, Image reconstruction, Phase retrieval, Ptychography
- in
- Mathematics and Computers in Simulation
- volume
- 176
- pages
- 9 pages
- publisher
- Elsevier
- external identifiers
-
- scopus:85076237585
- ISSN
- 0378-4754
- DOI
- 10.1016/j.matcom.2019.11.003
- language
- English
- LU publication?
- yes
- id
- 9926a41d-fd98-456d-a6c8-24ed5dabba82
- date added to LUP
- 2019-12-22 11:49:36
- date last changed
- 2023-12-04 06:05:17
@article{9926a41d-fd98-456d-a6c8-24ed5dabba82,
abstract = {{<p>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.</p>}},
author = {{Sissouno, Nada and Boßmann, Florian and Filbir, Frank and Iwen, Mark and Kahnt, Maik and Saab, Rayan and Schroer, Christian and zu Castell, Wolfgang}},
issn = {{0378-4754}},
keywords = {{Diffraction imaging; Image reconstruction; Phase retrieval; Ptychography}},
language = {{eng}},
pages = {{292--300}},
publisher = {{Elsevier}},
series = {{Mathematics and Computers in Simulation}},
title = {{A direct solver for the phase retrieval problem in ptychographic imaging}},
url = {{http://dx.doi.org/10.1016/j.matcom.2019.11.003}},
doi = {{10.1016/j.matcom.2019.11.003}},
volume = {{176}},
year = {{2020}},
}