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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 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.

Authors:
ORCiD logo
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:
Published Article
Journal Name:
Optics Letters
Additional Journal Information:
Journal Name: Optics Letters Journal Volume: 43 Journal Issue: 19; Journal ID: ISSN 0146-9592
Publisher:
Optical Society of America
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},
number = 19,
volume = 43,
place = {United States},
year = {2018},
month = {9}
}

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

Citation Metrics:
Cited by: 3 works
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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:

Multi-slice ptychographic tomography
journal, February 2018


Ptychographic transmission microscopy in three dimensions using a multi-slice approach
journal, January 2012

  • Maiden, A. M.; Humphry, M. J.; Rodenburg, J. M.
  • Journal of the Optical Society of America A, Vol. 29, Issue 8
  • DOI: 10.1364/JOSAA.29.001606

Ptychographic microscope for three-dimensional imaging
journal, January 2014

  • Godden, T. M.; Suman, R.; Humphry, M. J.
  • Optics Express, Vol. 22, Issue 10
  • DOI: 10.1364/OE.22.012513

Algebraic Reconstruction Techniques (ART) for three-dimensional electron microscopy and X-ray photography
journal, December 1970


Sampling the 2-D Radon transform
journal, October 1981

  • Rattey, P.; Lindgren, A.
  • IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. 29, Issue 5
  • DOI: 10.1109/TASSP.1981.1163686

The Reconstruction of a Three-Dimensional Structure from Projections and its Application to Electron Microscopy
journal, June 1970

  • Crowther, R. A.; DeRosier, D. J.; Klug, A.
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 317, Issue 1530
  • DOI: 10.1098/rspa.1970.0119

Movable Aperture Lensless Transmission Microscopy: A Novel Phase Retrieval Algorithm
journal, July 2004


Certain Topics in Telegraph Transmission Theory
journal, April 1928


Dynamische Theorie der Kristallstrukturanalyse durch Elektronenbeugung im inhomogenen Primärstrahlwellenfeld
journal, November 1970

  • Hegerl, R.; Hoppe, W.
  • Berichte der Bunsengesellschaft für physikalische Chemie, Vol. 74, Issue 11
  • DOI: 10.1002/bbpc.19700741112

X-ray ptychography with extended depth of field
journal, January 2016

  • Tsai, Esther H. R.; Usov, Ivan; Diaz, Ana
  • Optics Express, Vol. 24, Issue 25
  • DOI: 10.1364/OE.24.029089

Ptychographic X-ray computed tomography at the nanoscale
journal, September 2010

  • Dierolf, Martin; Menzel, Andreas; Thibault, Pierre
  • Nature, Vol. 467, Issue 7314
  • DOI: 10.1038/nature09419

Developments in synchrotron x-ray computed microtomography at the National Synchrotron Light Source
conference, September 1999

  • Dowd, Betsy A.; Campbell, Graham H.; Marr, Robert B.
  • SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, SPIE Proceedings
  • DOI: 10.1117/12.363725

Digital composition of images with increased depth of focus considering depth information
journal, January 1985

  • Sugimoto, Satoshi A.; Ichioka, Yoshiki
  • Applied Optics, Vol. 24, Issue 14
  • DOI: 10.1364/AO.24.002076

Cell refractive index tomography by digital holographic microscopy
journal, January 2006

  • Charrière, Florian; Marian, Anca; Montfort, Frédéric
  • Optics Letters, Vol. 31, Issue 2
  • DOI: 10.1364/OL.31.000178

On the extended depth of focus algorithms for bright field microscopy
journal, August 2001


Tomographic image reconstruction from a limited number of projections
journal, December 1984


Learning approach to optical tomography
journal, January 2015

  • Kamilov, Ulugbek S.; Papadopoulos, Ioannis N.; Shoreh, Morteza H.
  • Optica, Vol. 2, Issue 6
  • DOI: 10.1364/OPTICA.2.000517

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


Hard-X-Ray Lensless Imaging of Extended Objects
journal, January 2007


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


In situ click chemistry generation of cyclooxygenase-2 inhibitors
journal, February 2017


Fourier Images: I - The Point Source
journal, May 1957


A Fast Sinc Function Gridding Algorithm for Fourier Inversion in Computer Tomography
journal, December 1985


Extended depth of focus in optical microscopy: Assessment of existing methods and a new proposal
journal, September 2012

  • Piccinini, Filippo; Tesei, Anna; Zoli, Wainer
  • Microscopy Research and Technique, Vol. 75, Issue 11
  • DOI: 10.1002/jemt.22104

Communication in the Presence of Noise
journal, January 1949


High-Resolution Multislice X-Ray Ptychography of Extended Thick Objects
journal, February 2014


Opportunities and limitations for combined fly-scan ptychography and fluorescence microscopy
conference, September 2015

  • Deng, Junjing; Vine, David J.; Chen, Si
  • SPIE Optical Engineering + Applications, SPIE Proceedings
  • DOI: 10.1117/12.2190749

    Works referencing / citing this record:

    Multimodal x-ray nanotomography
    journal, April 2020


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