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Title: Relaxation of the Crowther criterion in multislice tomography

Abstract

For objects larger than the depth of focus of an imaging system, one must account for wavefield propagation effects within the object as is done in diffraction tomography, diffraction microscopy, and multislice ptychographic tomography. We show here that if the imaging method used reconstructs N a planes along each viewing direction, one can reduce the number of illumination directions required to fill Fourier space by a factor of 1/N a, relaxing the usual Crowther criterion for tomography. This provides a conceptual basis to explain two recent experiments where multiple axial planes were imaged per viewing direction, and tomographic images were obtained with good 3D spatial resolution even though fewer illumination directions were used than one would have expected from the Crowther criterion.

Authors:
ORCiD logo [1]
  1. Argonne National Lab. (ANL), Lemont, IL (United States); Northwestern Univ., Evanston, IL (United States)
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1476969
Alternate Identifier(s):
OSTI ID: 1474189; OSTI ID: 1493723
Grant/Contract Number:  
AC02-06CH11357
Resource Type:
Journal Article: Published Article
Journal Name:
Optics Letters
Additional Journal Information:
Journal Volume: 43; Journal Issue: 19; Journal ID: ISSN 0146-9592
Publisher:
Optical Society of America (OSA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Tomography

Citation Formats

Jacobsen, Chris. Relaxation of the Crowther criterion in multislice tomography. United States: N. p., 2018. Web. doi:10.1364/OL.43.004811.
Jacobsen, Chris. Relaxation of the Crowther criterion in multislice tomography. United States. doi:10.1364/OL.43.004811.
Jacobsen, Chris. Fri . "Relaxation of the Crowther criterion in multislice tomography". United States. doi:10.1364/OL.43.004811.
@article{osti_1476969,
title = {Relaxation of the Crowther criterion in multislice tomography},
author = {Jacobsen, Chris},
abstractNote = {For objects larger than the depth of focus of an imaging system, one must account for wavefield propagation effects within the object as is done in diffraction tomography, diffraction microscopy, and multislice ptychographic tomography. We show here that if the imaging method used reconstructs Na planes along each viewing direction, one can reduce the number of illumination directions required to fill Fourier space by a factor of 1/Na, relaxing the usual Crowther criterion for tomography. This provides a conceptual basis to explain two recent experiments where multiple axial planes were imaged per viewing direction, and tomographic images were obtained with good 3D spatial resolution even though fewer illumination directions were used than one would have expected from the Crowther criterion.},
doi = {10.1364/OL.43.004811},
journal = {Optics Letters},
issn = {0146-9592},
number = 19,
volume = 43,
place = {United States},
year = {2018},
month = {9}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1364/OL.43.004811

Citation Metrics:
Cited by: 3 works
Citation information provided by
Web of Science

Figures / Tables:

Fig. 1 Fig. 1: Schematic representation of the Crowther criterion in conventional tomography. In conventional tomography, each slice y of the object along the direction ŷ of the rotation axis is mapped onto one row of a detector. One then obtains one-dimensional pure projection images of the object with Nt transverse pixelsmore » of width ∆t in the transverse direction (A), and a depth of precisely one pixel at zero spatial frequency in the axial direction (because there is no way to distinguish between different axial positions in a pure projection). For an angle θ = 0°, the Fourier transform of this image yields an array with Nx = Nt pixels in the transverse or ux direction and Nz = 1 pixels in the axial or uz direction in trasverse-axial Fourier space (B). As the object is rotated, so is the information obtained in Fourier space, so the (ux, uz) Fourier space is filled in as shown in (C). The Crowther criterion of Eq. 3 is effectively a statement that one must provide complete, gap-free coverage of all pixels around the periphery in transverse-axial Fourier space.« less

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Works referenced in this record:

Reconstruction of an object from the modulus of its Fourier transform
journal, January 1978


The scattering of electrons by atoms and crystals. I. A new theoretical approach
journal, October 1957


    Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.