A protocol for searching the most probable phase-retrieved maps in coherent X-ray diffraction imaging by exploiting the relationship between convergence of the retrieved phase and success of calculation

Yuki Sekiguchi, Saki Hashimoto, Amane Kobayashi, Tomotaka Oroguchi, Masayoshi Nakasako

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3 Citations (Scopus)

Abstract

Coherent X-ray diffraction imaging (CXDI) is a technique for visualizing the structures of non-crystalline particles with size in the submicrometer to micrometer range in material sciences and biology. In the structural analysis of CXDI, the electron density map of a specimen particle projected along the direction of the incident X-rays can be reconstructed only from the diffraction pattern by using phase-retrieval (PR) algorithms. However, in practice, the reconstruction, relying entirely on the computational procedure, sometimes fails because diffraction patterns miss the data in small-angle regions owing to the beam stop and saturation of the detector pixels, and are modified by Poisson noise in X-ray detection. To date, X-ray free-electron lasers have allowed us to collect a large number of diffraction patterns within a short period of time. Therefore, the reconstruction of correct electron density maps is the bottleneck for efficiently conducting structure analyses of non-crystalline particles. To automatically address the correctness of retrieved electron density maps, a data analysis protocol to extract the most probable electron density maps from a set of maps retrieved from 1000 different random seeds for a single diffraction pattern is proposed. Through monitoring the variations of the phase values during PR calculations, the tendency for the PR calculations to succeed when the retrieved phase sets converged on a certain value was found. On the other hand, if the phase set was in persistent variation, the PR calculation tended to fail to yield the correct electron density map. To quantify this tendency, here a figure of merit for the variation of the phase values during PR calculation is introduced. In addition, a PR protocol to evaluate the similarity between a map of the highest figure of merit and other independently reconstructed maps is proposed. The protocol is implemented and practically examined in the structure analyses for diffraction patterns from aggregates of gold colloidal particles. Furthermore, the feasibility of the protocol in the structure analysis of organelles from biological cells is examined.A protocol for objectively and automatically identifying the most probable electron density map from phase-retrieval calculations in coherent X-ray diffraction imaging is proposed.

Original languageEnglish
Pages (from-to)1024-1038
Number of pages15
JournalJournal of Synchrotron Radiation
Volume24
Issue number5
DOIs
Publication statusPublished - 2017 Sep 1

Fingerprint

retrieval
Imaging techniques
X ray diffraction
Carrier concentration
Diffraction patterns
diffraction
diffraction patterns
x rays
figure of merit
tendencies
X ray lasers
X rays
organelles
Free electron lasers
Materials science
materials science
biology
structural analysis
free electron lasers
Structural analysis

Keywords

  • coherent X-ray diffraction imaging
  • phase retrieval calculation
  • structure analysis of non-crystalline particles
  • X-ray free-electron laser

ASJC Scopus subject areas

  • Radiation
  • Nuclear and High Energy Physics
  • Instrumentation

Cite this

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title = "A protocol for searching the most probable phase-retrieved maps in coherent X-ray diffraction imaging by exploiting the relationship between convergence of the retrieved phase and success of calculation",
abstract = "Coherent X-ray diffraction imaging (CXDI) is a technique for visualizing the structures of non-crystalline particles with size in the submicrometer to micrometer range in material sciences and biology. In the structural analysis of CXDI, the electron density map of a specimen particle projected along the direction of the incident X-rays can be reconstructed only from the diffraction pattern by using phase-retrieval (PR) algorithms. However, in practice, the reconstruction, relying entirely on the computational procedure, sometimes fails because diffraction patterns miss the data in small-angle regions owing to the beam stop and saturation of the detector pixels, and are modified by Poisson noise in X-ray detection. To date, X-ray free-electron lasers have allowed us to collect a large number of diffraction patterns within a short period of time. Therefore, the reconstruction of correct electron density maps is the bottleneck for efficiently conducting structure analyses of non-crystalline particles. To automatically address the correctness of retrieved electron density maps, a data analysis protocol to extract the most probable electron density maps from a set of maps retrieved from 1000 different random seeds for a single diffraction pattern is proposed. Through monitoring the variations of the phase values during PR calculations, the tendency for the PR calculations to succeed when the retrieved phase sets converged on a certain value was found. On the other hand, if the phase set was in persistent variation, the PR calculation tended to fail to yield the correct electron density map. To quantify this tendency, here a figure of merit for the variation of the phase values during PR calculation is introduced. In addition, a PR protocol to evaluate the similarity between a map of the highest figure of merit and other independently reconstructed maps is proposed. The protocol is implemented and practically examined in the structure analyses for diffraction patterns from aggregates of gold colloidal particles. Furthermore, the feasibility of the protocol in the structure analysis of organelles from biological cells is examined.A protocol for objectively and automatically identifying the most probable electron density map from phase-retrieval calculations in coherent X-ray diffraction imaging is proposed.",
keywords = "coherent X-ray diffraction imaging, phase retrieval calculation, structure analysis of non-crystalline particles, X-ray free-electron laser",
author = "Yuki Sekiguchi and Saki Hashimoto and Amane Kobayashi and Tomotaka Oroguchi and Masayoshi Nakasako",
year = "2017",
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TY - JOUR

T1 - A protocol for searching the most probable phase-retrieved maps in coherent X-ray diffraction imaging by exploiting the relationship between convergence of the retrieved phase and success of calculation

AU - Sekiguchi, Yuki

AU - Hashimoto, Saki

AU - Kobayashi, Amane

AU - Oroguchi, Tomotaka

AU - Nakasako, Masayoshi

PY - 2017/9/1

Y1 - 2017/9/1

N2 - Coherent X-ray diffraction imaging (CXDI) is a technique for visualizing the structures of non-crystalline particles with size in the submicrometer to micrometer range in material sciences and biology. In the structural analysis of CXDI, the electron density map of a specimen particle projected along the direction of the incident X-rays can be reconstructed only from the diffraction pattern by using phase-retrieval (PR) algorithms. However, in practice, the reconstruction, relying entirely on the computational procedure, sometimes fails because diffraction patterns miss the data in small-angle regions owing to the beam stop and saturation of the detector pixels, and are modified by Poisson noise in X-ray detection. To date, X-ray free-electron lasers have allowed us to collect a large number of diffraction patterns within a short period of time. Therefore, the reconstruction of correct electron density maps is the bottleneck for efficiently conducting structure analyses of non-crystalline particles. To automatically address the correctness of retrieved electron density maps, a data analysis protocol to extract the most probable electron density maps from a set of maps retrieved from 1000 different random seeds for a single diffraction pattern is proposed. Through monitoring the variations of the phase values during PR calculations, the tendency for the PR calculations to succeed when the retrieved phase sets converged on a certain value was found. On the other hand, if the phase set was in persistent variation, the PR calculation tended to fail to yield the correct electron density map. To quantify this tendency, here a figure of merit for the variation of the phase values during PR calculation is introduced. In addition, a PR protocol to evaluate the similarity between a map of the highest figure of merit and other independently reconstructed maps is proposed. The protocol is implemented and practically examined in the structure analyses for diffraction patterns from aggregates of gold colloidal particles. Furthermore, the feasibility of the protocol in the structure analysis of organelles from biological cells is examined.A protocol for objectively and automatically identifying the most probable electron density map from phase-retrieval calculations in coherent X-ray diffraction imaging is proposed.

AB - Coherent X-ray diffraction imaging (CXDI) is a technique for visualizing the structures of non-crystalline particles with size in the submicrometer to micrometer range in material sciences and biology. In the structural analysis of CXDI, the electron density map of a specimen particle projected along the direction of the incident X-rays can be reconstructed only from the diffraction pattern by using phase-retrieval (PR) algorithms. However, in practice, the reconstruction, relying entirely on the computational procedure, sometimes fails because diffraction patterns miss the data in small-angle regions owing to the beam stop and saturation of the detector pixels, and are modified by Poisson noise in X-ray detection. To date, X-ray free-electron lasers have allowed us to collect a large number of diffraction patterns within a short period of time. Therefore, the reconstruction of correct electron density maps is the bottleneck for efficiently conducting structure analyses of non-crystalline particles. To automatically address the correctness of retrieved electron density maps, a data analysis protocol to extract the most probable electron density maps from a set of maps retrieved from 1000 different random seeds for a single diffraction pattern is proposed. Through monitoring the variations of the phase values during PR calculations, the tendency for the PR calculations to succeed when the retrieved phase sets converged on a certain value was found. On the other hand, if the phase set was in persistent variation, the PR calculation tended to fail to yield the correct electron density map. To quantify this tendency, here a figure of merit for the variation of the phase values during PR calculation is introduced. In addition, a PR protocol to evaluate the similarity between a map of the highest figure of merit and other independently reconstructed maps is proposed. The protocol is implemented and practically examined in the structure analyses for diffraction patterns from aggregates of gold colloidal particles. Furthermore, the feasibility of the protocol in the structure analysis of organelles from biological cells is examined.A protocol for objectively and automatically identifying the most probable electron density map from phase-retrieval calculations in coherent X-ray diffraction imaging is proposed.

KW - coherent X-ray diffraction imaging

KW - phase retrieval calculation

KW - structure analysis of non-crystalline particles

KW - X-ray free-electron laser

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