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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 15, Iss. 5 — May. 1, 1998
  • pp: 1371–1382

Theory of a fixed scatterer embedded in a turbid medium

Koichi Furutsu  »View Author Affiliations

JOSA A, Vol. 15, Issue 5, pp. 1371-1382 (1998)

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Diffuse photon density waves are currently used to probe turbid media for optical anomalies such as tumors in tissue. A basic theory is established for detection of a fixed scatterer embedded in a turbid medium, including the effects of the medium’s boundaries. Several diffuse expressions are obtained for a scattered wave both reflected and transmitted through a turbid layer, as well as within the layer, including important cases of vertically incident light and vertical observation by optical fibers. The importance of the scatterer’s effective cross section when it is embedded in a random medium is emphasized. Specific results are obtained with a simple model of a scatterer.

© 1998 Optical Society of America

OCIS Codes
(100.6950) Image processing : Tomographic image processing
(170.3660) Medical optics and biotechnology : Light propagation in tissues
(170.3880) Medical optics and biotechnology : Medical and biological imaging
(170.4580) Medical optics and biotechnology : Optical diagnostics for medicine
(170.5270) Medical optics and biotechnology : Photon density waves
(170.6960) Medical optics and biotechnology : Tomography
(170.7050) Medical optics and biotechnology : Turbid media

Original Manuscript: July 10, 1997
Revised Manuscript: December 3, 1997
Manuscript Accepted: December 11, 1997
Published: May 1, 1998

Koichi Furutsu, "Theory of a fixed scatterer embedded in a turbid medium," J. Opt. Soc. Am. A 15, 1371-1382 (1998)

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  1. D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Detection and characterization of optical inhomogeneities with diffuse photon density waves: a signal-to-noise analysis,” Appl. Opt. 36, 75–92 (1997). [CrossRef] [PubMed]
  2. H. Jiang, K. D. Paulsen, U. L. Osterberg, M. S. Patterson, “Frequency-domain optical image reconstruction in turbid media: an experimental study of single-target detectability,” Appl. Opt. 36, 52–63 (1997). [CrossRef] [PubMed]
  3. S. A. Walker, S. Fantini, E. Gratton, “Image reconstruction by backprojection from frequency-domain optical measurements in highly scattering media,” Appl. Opt. 36, 170–179 (1997). [CrossRef] [PubMed]
  4. H. Wabnitz, H. Rinneberg, “Imaging in turbid media by photon density waves: spatial resolution and scaling relations,” Appl. Opt. 36, 64–74 (1997). [CrossRef] [PubMed]
  5. C. Schotland, “Continuous-wave diffusion imaging,” J. Opt. Soc. Am. A 14, 275–279 (1997). [CrossRef]
  6. J. B. Fishkin, E. Gratton, “Propagation of photon-density waves in strongly scattering media containing an absorbing semi-infinite plane bounded by a straight edge,” J. Opt. Soc. Am. A 10, 127–140 (1993). [CrossRef] [PubMed]
  7. B. J. Tromberg, L. O. Svaasand, T. Tsay, R. C. Haskell, “Properties of photon density waves in multiple-scattering media,” Appl. Opt. 32, 607–616 (1993). [CrossRef] [PubMed]
  8. P. N. den Outer, Th. M. Nieuwenhuizen, A. Lagendijk, “Location of objects in multiple-scattering media,” J. Opt. Soc. Am. A 10, 1209–1218 (1993). [CrossRef]
  9. D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994). [CrossRef] [PubMed]
  10. K. Furutsu, “Transport theory and boundary-value solutions. I. The Bethe–Salpeter equation and scattering matrices,” J. Opt. Soc. Am. A 2, 913–931 (1985); “Transport theory and boundary-value solutions. II. Addition theorem of scattering matrices and applications,” J. Opt. Soc. Am. A 2, 932–944 (1985); K. Furutsu, Random Media and Boundaries—Unified Theory, Two-Scale Method, and Applications, Vol. 14 of Springer Series in Wave Phenomena (Springer-Verlag, New York, 1993), p. 270. [CrossRef]
  11. K. Furutsu, “Boundary conditions of the diffusion equation and applications,” Phys. Rev. A 39, 1386–1401 (1989). [CrossRef] [PubMed]
  12. K. Furutsu, “Fixed scatterer in a random medium: shadowing, enhanced backscattering, and the inner structure of the Bethe–Salpeter equation,” Appl. Opt. 32, 2706–2721 (1993). [CrossRef] [PubMed]
  13. The diffusion constant D is given by Eqs. (B16) independent of the absorption cross section: K. Furutsu, “Diffusion equation derived from space–time transport equation,” J. Opt. Soc. Am. 70, 360–366 (1980). [CrossRef]
  14. Equations (B3)–(B5) of Ref. 11.
  15. K. Furutsu, “Transport theory and boundary-value solutions. II. Addition theorem of scattering matrices and applications,” J. Opt. Soc. Am. A 2, 932–944 (1985), Sec. 3 and App. D; Eqs. (5.7)–(5.9) of Ref. 12. [CrossRef]
  16. R. A. J. Groenhuis, H. A. Ferwerda, J. J. T. Bosch, “Scattering and absorption of turbid materials determined from reflection measurements. 1. Theory,” Appl. Opt. 22, 2456–2462 (1983). [CrossRef] [PubMed]
  17. R. C. Haskell, L. O. Svaasand, T. T. Tsay, T. C. Feng, M. S. McAdams, B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11, 2727–2741 (1994). [CrossRef]
  18. A. H. Hielscher, S. L. Jacques, L. Wang, F. K. Tittle, “The influence of boundary conditions on the accuracy of diffusion theory in time-resolved reflectance spectroscopy of biological tissues,” Phys. Med. Biol. 40, 1957–1975 (1995). [CrossRef] [PubMed]
  19. A. Kienle, M. S. Patterson, “Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium,” J. Opt. Soc. Am. A 14, 246–254 (1997). [CrossRef]
  20. Equations (5.3)–(5.11) of Ref. 11.
  21. The detailed theory is given in K. Furutsu, “Transport theory and boundary-value solutions. II. Addition theorem of scattering matrices and applications,” J. Opt. Soc. Am. A 2, 932–944 (1985). [CrossRef]
  22. Ref. 11, Sec. 4.

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