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Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 45, Iss. 19 — Jul. 1, 2006
  • pp: 4765–4775

Consideration of a spread-out source in problems of near-infrared optical tomography

Vadim Y. Soloviev and Lada V. Krasnosselskaia  »View Author Affiliations

Applied Optics, Vol. 45, Issue 19, pp. 4765-4775 (2006)

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When the light propagates in media where absorption is not negligible and∕or scattering is weak, a contribution to the energy density coming from ballistic photons cannot be neglected. A point source effectively spreads out over a scattering volume and its spatial distribution is described by the source function. We consider a boundary value problem of light propagation in half-space for such a source on the basis of the telegraph equation. A solution is found by convolution of Green's function with the source function. The final result shows a significant difference in the behavior of the radiant energy density between the solution obtained for a distributed source and the diffusion approximation. Our results agree well with the Monte Carlo simulations over a broad range of scattering and∕or absorption conditions. The obtained results are of practical importance in luminescence optical tomography because an erroneous shape of the energy density function may lead to an incorrect estimate of the light source depth after image reconstruction. The range of applications of the diffusion approximation is also discussed.

© 2006 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
(290.0290) Scattering : Scattering
(290.7050) Scattering : Turbid media

Original Manuscript: January 12, 2005
Revised Manuscript: August 23, 2005
Manuscript Accepted: November 17, 2005

Virtual Issues
Vol. 1, Iss. 8 Virtual Journal for Biomedical Optics

Vadim Y. Soloviev and Lada V. Krasnosselskaia, "Consideration of a spread-out source in problems of near-infrared optical tomography," Appl. Opt. 45, 4765-4775 (2006)

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  1. S. R. Arridge, M. Cope, and D. T. Delpy, "The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis," Phys. Med. Biol. 37, 1531-1560 (1992). [CrossRef] [PubMed]
  2. D. A. Boas, M. A. O'Leary, B. Chance, and A. G. Yodh, "Scattering of diffuse photon density waves by spherical inhomogeneties within turbid media: Analytical solution and applications," Proc. Natl. Acad. Sci. USA 91, 4887-4891 (1994). [CrossRef] [PubMed]
  3. S. R. Arridge, "Optical tomography in medical imaging," Inverse Probl. 15, R41-R93 (1999). [CrossRef]
  4. A. D. Kim, "Light propagation in biological tissues containing an absorbing plate," Appl. Opt. 43, 555-563 (2004). [CrossRef] [PubMed]
  5. A. D. Kim and J. B. Keller, "Light propagation in biological tissue," J. Opt. Soc. Am. A 20, 92-98 (2003). [CrossRef]
  6. A. D. Kim and M. Moscoso, "Beam propagation in sharply peaked forward scattering media," J. Opt. Soc. Am. A 21, 797-803 (2004). [CrossRef]
  7. A. D. Klose, U. Netz, J. Beuthan, and A. H. Heilscher, "Optical tomography using time-independent equation of radiative transfer--Part 1: forward model," J. Quant. Spectrosc. Radiat. Transfer 72, 691-713 (2002). [CrossRef]
  8. A. D. Klose and A. H. Heilscher, "Optical tomography using time-independent equation of radiative transfer--Part 2: inverse model," J. Quant. Spectrosc. Radiat. Transfer 72, 715-732 (2002). [CrossRef]
  9. R. Elaloufi, R. Carminati, and J.-J. Greffet, "Diffusive-to-ballistic transition in dynamic light transition through thin scattering slabs: a radiative transfer approach," J. Opt. Soc. Am. A 21, 1430-1437 (2004). [CrossRef]
  10. K. Ren, G. S. Abdoulaev, G. Bal, and A. H. Hielscher, "Algorithm for solving the equation of radiative transfer in the frequency domain," Opt. Lett. 29, 578-580 (2004). [CrossRef] [PubMed]
  11. L. H. Wang, S. L. Jacques, and L. Q. Zheng, "MCML-Monte Carlo modeling of light transport in multilayered tissues," Comput. Methods Programs Biomed. 47, 131-145 (1995). [CrossRef] [PubMed]
  12. X. Wang, G. Yao, and L.-H. Wang, "Monte Carlo model and single-scattering approximation of polarized light propagation in turbid media containing glucose," Appl. Opt. 41, 792-801 (2002). [CrossRef] [PubMed]
  13. X. Wang, L. V. Wang, C.-W. Sun, and C.-C. Yang, "Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments," J. Biomed. Opt. 8, 608-617 (2003). [CrossRef] [PubMed]
  14. M. Xu, W. Cai, M. Lax, and R. R. Alfano, "Photon migration in turbid media using a cumulant approximation to the radiative transfer," Phys. Rev. E 65, 066609 (2002). [CrossRef]
  15. M. Xu, W. Cai, M. Lax, and R. R. Alfano, "Photon-transport forward model for imaging in turbid media," Opt. Lett. 26, 1066-1068 (2001). [CrossRef]
  16. M. Xu, W. Cai, and R. R. Alfano, "Multiple passage of the light through an absorption inhomogeneity in optical imaging of turbid media," Opt. Lett. 29, 1757-1759 (2004). [CrossRef] [PubMed]
  17. W. Cai, M. Xu, and R. R. Alfano, "Analytical form of the particle distribution based on the cumulant solution of the elastic Boltzmann transport equation," Phys. Rev. E. 71, 041202 (2005). [CrossRef]
  18. D. J. Durian and J. Rundick, "Photon migration at short times and distances and in cases of strong absorption," J. Opt. Soc. Am. A 14, 235-245 (1997). [CrossRef]
  19. V. Soloviev, D. Wilson, and S. Vinogradov, "Phosphorescence lifetime imaging in turbid media: the forward problem," Appl. Opt. 42, 113-123 (2003). [CrossRef] [PubMed]
  20. V. Y. Soloviev, D. F. Wilson, and S. A. Vinogradov, "Phosphorescence lifetime imaging in turbid media: the inverse problem and experimental image reconstruction," Appl. Opt. 43, 564-574 (2004). [CrossRef] [PubMed]
  21. V. V. Sobolev, A Treatise on Radiative Transfer (Van Nostrand, 1963).
  22. S. Chandrasekhar, Radiative Transfer (Dover, 1960).
  23. N. N. Lebedev, Special Functions and Their Applications (Dover, 1972).
  24. M. V. Fedoryuk, Asimptotika: Integraly, Summy i Ryady (Nauka, 1987), in Russian.
  25. F. W. Olver, Asymptotics and Special Functions (Academic, 1974).

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