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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 15, Iss. 10 — Oct. 1, 1998
  • pp: 2670–2677

Diffraction tomographic imaging with photon density waves: an explicit solution

Stephen J. Norton and Tuan Vo-Dinh  »View Author Affiliations

JOSA A, Vol. 15, Issue 10, pp. 2670-2677 (1998)

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An explicit formula is derived for reconstructing tissue inhomogeneities from scattered photon-density waves. When intensity-modulated light is used as a source, such waves obey a Helmholtz equation with a complex wave number. A process of analytical continuation in the spatial-frequency domain is used to make this wave number real, whereupon inversion formulas based on conventional diffraction tomography are applied to invert the data to yield an image. In this way an explicit solution to the inverse problem can be derived within the Born approximation. Here the spatially varying quantity imaged is a linear combination of the transport scattering and absorption coefficients. Data are assumed measured at one modulation frequency, but multiple modulation frequencies could in principle be used to generate independent images of the scattering and absorption coefficients.

© 1998 Optical Society of America

OCIS Codes
(100.3010) Image processing : Image reconstruction techniques
(100.3190) Image processing : Inverse problems
(170.3660) Medical optics and biotechnology : Light propagation in tissues
(170.3880) Medical optics and biotechnology : Medical and biological imaging
(170.5270) Medical optics and biotechnology : Photon density waves
(170.5280) Medical optics and biotechnology : Photon migration

Original Manuscript: February 2, 1998
Revised Manuscript: June 29, 1998
Manuscript Accepted: June 6, 1998
Published: October 1, 1998

Stephen J. Norton and Tuan Vo-Dinh, "Diffraction tomographic imaging with photon density waves: an explicit solution," J. Opt. Soc. Am. A 15, 2670-2677 (1998)

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