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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 19, Iss. 3 — Mar. 1, 2002
  • pp: 558–566

Inverse problem in optical diffusion tomography. II. Role of boundary conditions

Vadim A. Markel and John C. Schotland  »View Author Affiliations


JOSA A, Vol. 19, Issue 3, pp. 558-566 (2002)
http://dx.doi.org/10.1364/JOSAA.19.000558


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Abstract

We consider the inverse problem of reconstructing the absorption and diffusion coefficients of an inhomogeneous highly scattering medium probed by diffuse light. The role of boundary conditions in the derivation of Fourier–Laplace inversion formulas is considered. Boundary conditions of a general mixed type are discussed, with purely absorbing and purely reflecting boundaries obtained as limiting cases. Four different geometries are considered with boundary conditions imposed on a single plane and on two parallel planes and on a cylindrical and on a spherical surface.

© 2002 Optical Society of America

OCIS Codes
(170.0170) Medical optics and biotechnology : Medical optics and biotechnology
(170.3010) Medical optics and biotechnology : Image reconstruction techniques
(170.3660) Medical optics and biotechnology : Light propagation in tissues
(170.6960) Medical optics and biotechnology : Tomography

History
Original Manuscript: December 8, 2000
Revised Manuscript: August 13, 2001
Manuscript Accepted: August 13, 2001
Published: March 1, 2002

Citation
Vadim A. Markel and John C. Schotland, "Inverse problem in optical diffusion tomography. II. Role of boundary conditions," J. Opt. Soc. Am. A 19, 558-566 (2002)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-19-3-558


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References

  1. V. A. Markel, J. C. Schotland, “The inverse problem in optical diffusion tomography. I.  Fourier-Laplace inversion formulas,” J. Opt. Soc. Am. A 18, 1336–1347 (2001). [CrossRef]
  2. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, San Diego, Calif., 1978), Vol. 1.
  3. J. Ripoll, M. Nieto-Vesperinas, “Index mismatch for diffuse photon density waves at both flat and rough diffuse–diffuse interfaces,” J. Opt. Soc. Am. A 16, 1947–1957 (1999). [CrossRef]
  4. R. Aronson, “Boundary conditions for diffuse light,” J. Opt. Soc. Am. A 12, 2532–2539 (1995). [CrossRef]
  5. An explicit characterization of admissible scattering data for which integral equation (38) is solvable is difficult to state. An implicit characterization consists of the closure of the image under the integral operator defined by Eq. (38) of all functions with compact support in L2.
  6. V. A. Markel, J. C. Schotland, “Inverse scattering for the diffusion equation with general boundary conditions,” Phys. Rev. E 64, R035601 (2001). [CrossRef]
  7. J. C. Schotland, V. A. Markel, “Inverse scattering with diffusing waves,” J. Opt. Soc. Am. A 18, 2767–2777 (2001). [CrossRef]

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