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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

  • Editor: Stephen A. Burns
  • Vol. 23, Iss. 9 — Sep. 1, 2006
  • pp: 2119–2131

Perturbation theory for the diffusion equation by use of the moments of the generalized temporal point-spread function. II. Continuous-wave results

Angelo Sassaroli, Fabrizio Martelli, and Sergio Fantini  »View Author Affiliations


JOSA A, Vol. 23, Issue 9, pp. 2119-2131 (2006)
http://dx.doi.org/10.1364/JOSAA.23.002119


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Abstract

We investigate the performance of the method proposed in Part I of this paper in several situations of interest in diffuse optical imaging of biological tissues. Monte Carlo simulations were extensively used to validate the approximate scaling relationship between higher-order and first-order self moments of the generalized temporal point-spread function in semi-infinite and slab geometry. More specifically we found that in a wide range of cases the scaling parameters c 1 , c 2 , c 3 [see Eq. (36) of Part I] lie in the intervals (1.48, 1.58), (3.1, 3.7), and (8.5, 11.5), respectively. The scaling relationships between higher-order and first-order self moments are useful for the calculation of the perturbation of a single defect in a straightforward way. Although these relationships are more accurate for inclusions of linear size less than 6 mm , their performance is also studied for larger inclusions. A good agreement, to within 10 % , was found between the perturbations of single and multiple defects calculated with the proposed method and those obtained by Monte Carlo simulations. We also provide formulas for the calculation of the moments up to the fourth order for which it is clear how lower-order moments can be used for the calculation of higher-order moments.

© 2006 Optical Society of America

OCIS Codes
(170.3660) Medical optics and biotechnology : Light propagation in tissues
(170.5280) Medical optics and biotechnology : Photon migration
(290.7050) Scattering : Turbid media
(300.1030) Spectroscopy : Absorption

ToC Category:
Medical Optics and Biotechnology

History
Original Manuscript: October 25, 2005
Revised Manuscript: March 8, 2006
Manuscript Accepted: March 25, 2006

Virtual Issues
Vol. 1, Iss. 10 Virtual Journal for Biomedical Optics

Citation
Angelo Sassaroli, Fabrizio Martelli, and Sergio Fantini, "Perturbation theory for the diffusion equation by use of the moments of the generalized temporal point-spread function. II. Continuous-wave results," J. Opt. Soc. Am. A 23, 2119-2131 (2006)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-23-9-2119


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References

  1. D. A. Boas, "A fundamental limitation of linearized algorithms for diffuse optical tomography," Opt. Express 1, 404-413 (1997). [CrossRef] [PubMed]
  2. M. R. Ostermeyer and S. L. Jacques, "Perturbation theory for diffuse light transport in complex biological tissues," J. Opt. Soc. Am. A 14, 255-261 (1997). [CrossRef]
  3. S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, "A finite element approach to modelling photon transport in tissue," Med. Phys. 20, 299-309 (1993). [CrossRef] [PubMed]
  4. H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and M. S. Patterson, "Optical image reconstruction using frequency-domain data: simulations and experiments," J. Opt. Soc. Am. A 13, 253-266 (1996). [CrossRef]
  5. G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 4th ed. (Academic, 1995), p. 934.
  6. A. Sassaroli, F. Martelli, and S. Fantini, "Perturbation theory for the diffusion equation by use of the moments of the generalized point-spread function. I. Theory," J. Opt. Soc. Am. A 23, 2105-2118 (2006). [CrossRef]
  7. R. Graaf and K. Rinzema, "Practical improvements on photon diffusion theory: application to isotropic scattering," Phys. Med. Biol. 46, 3043-3050 (2001). [CrossRef]
  8. A. Sassaroli, F. Martelli, D. Imai, and Y. Yamada, "Study on the propagation of ultrashort pulse light in cylindrical optical phantoms," Phys. Med. Biol. 44, 2747-2763 (1999). [CrossRef] [PubMed]
  9. D. Contini, F. Martelli, and G. Zaccanti, "Photon migration through a turbid slab described by a model based on diffusion approximation. I. Theory," Appl. Opt. 36, 4587-4599 (1997). [CrossRef] [PubMed]
  10. R. Aronson, "Radiative transfer implies a modified reciprocity relation," J. Opt. Soc. Am. A 14, 486-490 (1997). [CrossRef]

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