## Statistical Properties of the Penetration of Photons into a Semi-Infinite Turbid Medium: A Random-Walk Analysis

Applied Optics, Vol. 37, Issue 16, pp. 3558-3563 (1998)

http://dx.doi.org/10.1364/AO.37.003558

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### Abstract

Statistical properties of the expected amount of time spent by a photon at different depths of a semi-infinite turbid medium are derived with formalism based on the continuous-time random walk. The formalism is applied to the study of both cw and time-gated experiments. Earlier analytical results relating to cw experiments are reproduced with a single approximation, rather than the more complicated approach used in earlier research based on the discrete-time random walk. The distribution of the occupancy of different depths in a time-gated experiment is found to have a convenient scaling form.

[Optical Society of America ]

**OCIS Codes**

(030.6600) Coherence and statistical optics : Statistical optics

(170.0170) Medical optics and biotechnology : Medical optics and biotechnology

(170.5280) Medical optics and biotechnology : Photon migration

**Citation**

George H. Weiss, "Statistical Properties of the Penetration of Photons into a Semi-Infinite Turbid Medium: A Random-Walk Analysis," Appl. Opt. **37**, 3558-3563 (1998)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-37-16-3558

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### References

- B. B. Das, F. Liu, and R. R. Alfano, “Time-resolved fluorescence and photon migration studies in biomedical and model random media,” Rep. Prog. Phys. 60, 227–292 (1997).
- J. C. Hebden, S. R. Arridge, and D. T. Delpy, “Optical imaging in medicine: I. Experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997).
- S. R. Arridge and J. C. Hebden, “Optical imaging in medicine: II. Modelling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
- R. F. Bonner, R. Nossal, S. Havlin, and G. H. Weiss, “Model for photon migration in turbid biological media,” J. Opt. Soc. Am. A 4, 423–432 (1987).
- A. H. Gandjbakhche and G. H. Weiss, “Random walk and diffusion-like models of photon migration in turbid media,” in Progress in Optics E. Wolf, ed. (North-Holland, Amsterdam, 1995), Vol. 34, pp. 333–401.
- L. T. Perelman, J. Wu, I. Itzkan, and M. S. Feld, “Photon migration in turbid media using path integrals,” Phys. Rev. Lett. 72, 1341–1344 (1994).
- I. Ishimaru, “Diffusion of light in turbid media,” Appl. Opt. 28, 2210–2215 (1989).
- D. J. Durian and J. Rudnick, “Photon migration at short times and distances and in cases of strong absorption,” J. Opt. Soc. Am. A 14, 235–245 (1997).
- E. W. Montroll and G. H. Weiss, “Random walks on lattices. II,” J. Math. Phys. 6, 167–181 (1965).
- G. H. Weiss, Aspects and Applications of the Random Walk (North-Holland, Amsterdam, 1994).
- G. H. Weiss, J. M. Porrà, and J. Masoliver, “The continuous-time random walk description of photon motion in an isotropic medium,” Opt. Commun. 14, 268–276 (1998).
- G. H. Weiss, R. Nossal, and R. F. Bonner, “Statistics of penetration depth of photons re-emitted from irradiated tissue,” J. Mod. Opt. 36, 349–359 (1989).
- W. J. Cui, N. Wang, and B. Chance, “Study of photon migration depths with time-resolved spectroscopy,” Opt. Lett. 16, 1632–1635 (1991).
- T. L. Troy, D. L. Page, and E. M. Sevick-Muraca, “Optical properties of normal and diseased breast tissues: prognosis for optical mammography,” J. Biomed. Opt. 1, 342–345 (1996).
- A. H. Gandjbakhche, R. F. Bonner, and R. Nossal, “Scaling relationships for anisotropic random walks,” J. Stat. Phys. 69, 35–53 (1992).
- M. J. Lighthill, Fourier Analysis and Generalised Functions (Cambridge U Press, Cambridge, UK, 1958).
- A. H. Gandjbakhche, R. Nossal, and R. F. Bonner, “Resolution limits for optical transillumination of abnormalities deeply imbedded in tissues,” Med. Phys. 21, 185–191 (1994).
- V. Chernomordik, R. Nossal, and A. H. Gandjbakhche, “Point spread functions of photons in time-resolved transillumination experiments using simple scaling arguments,” Med. Phys. 23, 1857–1861 (1996).

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