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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Steven A. Burns
  • Vol. 24, Iss. 9 — Sep. 1, 2007
  • pp: 2516–2526

Stability of phase-contrast tomography

Glenn R. Myers, Timur E. Gureyev, and David M. Paganin  »View Author Affiliations

JOSA A, Vol. 24, Issue 9, pp. 2516-2526 (2007)

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Phase-contrast tomography (PCT) allows three-dimensional imaging of objects that display insufficient contrast for conventional absorption-based tomography. We prove that PCT is stable with respect to high-frequency noise in experimental phase-contrast data, unlike conventional tomography, which is known to be mildly unstable. We use known properties of the three-dimensional x-ray transform and transport-of-intensity equation to construct a matrix representation of the forward PCT operator. We then invert this formula to show that, under natural boundary conditions, the PCT reconstruction operator exists and leads to a unique solution. We show that the singular values s n of the reconstruction operator have asymptotic behavior s n = O ( n āˆ’ 3 āˆ• 2 ) , guaranteeing the mathematical stability of the reconstruction process.

© 2007 Optical Society of America

OCIS Codes
(100.3010) Image processing : Image reconstruction techniques
(100.3190) Image processing : Inverse problems
(100.5070) Image processing : Phase retrieval
(100.6890) Image processing : Three-dimensional image processing
(100.6950) Image processing : Tomographic image processing
(340.7440) X-ray optics : X-ray imaging

ToC Category:
Image Processing

Original Manuscript: October 3, 2006
Revised Manuscript: March 28, 2007
Manuscript Accepted: April 12, 2007
Published: July 11, 2007

Glenn R. Myers, Timur E. Gureyev, and David M. Paganin, "Stability of phase-contrast tomography," J. Opt. Soc. Am. A 24, 2516-2526 (2007)

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