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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 30, Iss. 7 — Jul. 1, 2013
  • pp: 1460–1463

Simple solution to the Fresnel–Kirchoff diffraction integral for application to refraction-enhanced radiography

J. A. Koch, O. L. Landen, L. J. Suter, and L. P. Masse  »View Author Affiliations

JOSA A, Vol. 30, Issue 7, pp. 1460-1463 (2013)

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We present a simple solution to the Fresnel–Kirchoff diffraction integral that is appropriate for x-ray radiography of strongly absorbing and phase-shifting objects in the geometrical optics regime, where phase contrast enhancements can be considered to be caused by refraction by a semi-opaque object. We demonstrate its accuracy by comparison to brute-force numerical ray trace and diffraction calculations of a representative simulated object, and show excellent agreement for spatial scales corresponding to Fresnel numbers greater than unity. The result represents a significant improvement over approximate formulas typically used in analysis of refraction-enhanced radiographs, particularly for radiography of transient phenomena in objects that strongly refract and show significant absorption.

© 2013 Optical Society of America

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(100.5070) Image processing : Phase retrieval
(110.1650) Imaging systems : Coherence imaging
(110.2990) Imaging systems : Image formation theory
(340.7440) X-ray optics : X-ray imaging

ToC Category:
Diffraction and Gratings

Original Manuscript: March 20, 2013
Revised Manuscript: June 10, 2013
Manuscript Accepted: June 10, 2013
Published: June 28, 2013

J. A. Koch, O. L. Landen, L. J. Suter, and L. P. Masse, "Simple solution to the Fresnel–Kirchoff diffraction integral for application to refraction-enhanced radiography," J. Opt. Soc. Am. A 30, 1460-1463 (2013)

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