OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 15, Iss. 8 — Aug. 1, 1998
  • pp: 2078–2088

Direct experimental verification of light transport theory in an optical phantom

K. Rinzema, L. H. P. Murrer, and W. M. Star  »View Author Affiliations

JOSA A, Vol. 15, Issue 8, pp. 2078-2088 (1998)

View Full Text Article

Acrobat PDF (359 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Starting from light transport theory, we present an ab initio calculation of the fluence rate that is due to an isotropic point source in an infinite, anisotropically scattering medium. To verify the results experimentally, a latex suspension with uniform particle size, corresponding to g=0.734, was prepared. In the suspension an isotropic light source and an isotropic light detector were placed, and the fluence rate as a function of distance was measured. We observed good agreement in absolute values between the calculated and the observed fluence rate over distances ranging from 1/4 to ~8 the total mean free path, which corresponds to a fluence rate varying over some five orders of magnitude. Furthermore, the calculated fluence was obtained from measured values of μs and μa and a calculated phase function without any kind of fitting, and thus the calculation was completely independent from the measurement. This is the first time that the fluence was measured quantitatively with an isotropic probe and found to agree within experimental error with transport theory. The experimental results indicate that, far from the source, the behavior is diffusionlike, even for low albedos, albeit with a corrected effective extinction coefficient.

© 1998 Optical Society of America

OCIS Codes
(290.0290) Scattering : Scattering

K. Rinzema, L. H. P. Murrer, and W. M. Star, "Direct experimental verification of light transport theory in an optical phantom," J. Opt. Soc. Am. A 15, 2078-2088 (1998)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. K. Rinzema, B. J. Hoenders, H. A. Ferwerda, and J. J. Ten Bosch, “Analytic calculation of the radiance in an anisotropically scattering turbid medium close to a source,” Pure Appl. Opt. 4, 629–642 (1995).
  2. A. Ishimaru, R. L. T. Cheung, and K. Shimizu, “Scattering and diffusion of a beam in randomly distributed scatterers,” J. Opt. Soc. Am. 73, 131–136 (1983).
  3. B. Davison and J. B. Sykes, “The spherical harmonics method for spherical geometries,” in Neutron Transport Theory, N. F. Mott and E. C. Ballard, eds. (Clarendon, Oxford, 1957), Sec. 11.1.
  4. M. Abramowitz and I. A. Stegun, “Bend functions of fractional order,” in Handbook of Mathematical Functions (Dover, New York, 1972), p. 437.
  5. I. S. Gradshteyn and I. M. Ryzhik, “8. Special functions,” in Tables of Integrals, Series, and Products, Yu. V. Geronimus and M. Yu. Tseytlin, eds. (Academic, San Diego, Calif., 1980), p. 1019.
  6. J. Mathews and R. L. Walker, “7. Special functions,” in Mathematical Methods of Physics, 2nd ed. (Addison-Wesley, Reading, Mass., 1970), p. 174.
  7. A. Ishimaru, “9. Diffusion approximation,” in Wave Propagation and Scattering in Random Media (Academic, San Diego, Calif., 1978), Vol. 1, p. 178.
  8. J. P. A. Marijnissen and W. M. Star, “Calibration of isotropic light dosimetry detectors based on scattering bulbs in clear media,” Phys. Med. Biol. 41, 1191–1208 (1996).
  9. M. S. Patterson, E. Schwartz, and B. C. Wilson, “Quantitative reflectance spectroscopy for the noninvasive measurement of photosensitizer concentration in tissue during photodynamic therapy,” in Photodynamic Therapy: Mechanisms, T. J. Dougherty, ed., Proc. SPIE 1065, 115–122 (1989).
  10. W. M. Star, J. P. A. Marijnissen, and M. J. C. V. Gemert, “Light dosimetry in optical phantoms and in tissues: I. multiple flux and transport theory,” Phys. Med. Biol. 33, 437–454 (1988).
  11. W. M. Star, “Diffusion theory of light transport,” in Optical-Thermal Response of Laser Irradiated Tissue, A. J. Welch and M. J. C. van Gemert, eds. (Plenum, New York, 1995), pp. 131–206.
  12. J. W. Goodwin, J. Hearn, C. C. Ho, and R. H. Ottewil, “Studies on the preparation of monodisperse polystyrene latices,” Colloid Polym. Sci. 252, 464–471 (1974).
  13. J. R. Zijp and J. J. Ten Bosch, “Pascal program to perform Mie calculations,” Opt. Eng. 32, 1691–1695 (1993).
  14. L. Wang and S. L. Jacques, “Error estimation of measuring total interaction coefficients of turbid media using colli-mated light transmission,” Phys. Med. Biol. 39, 2349–2354 (1994).
  15. H. C. Van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  16. S. T. Flock, B. C. Wilson, and M. J. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14, 835–841 (1987).
  17. J. P. A. Marijnissen and W. M. Star, “Quantitative light dosimetry in vitro and in vivo,” Lasers Med. Sci. 2, 235–242 (1987).
  18. H. J. Van Staveren, J. P. A. Marijnissen, M. C. G. Aalders, and W. M. Star, “Construction, quality control and calibration of spherical isotropic fibre-optic light diffusers,” Lasers Med. Sci. 10, 137–147 (1996).
  19. L. H. P. Murrer, J. P. A. Marijnissen, and W. M. Star, “Ex vivo light dosimetry and Monte Carlo simulations for endobronchial photodynamic therapy,” Phys. Med. Biol. 40, 1807–1817 (1995).
  20. W. M. Star and J. P. A. Marijnissen, “Calculating the response of isotropic light dosimetry probes as a function of the tissue refractive index,” Appl. Opt. 12, 2288–292 (1989).
  21. H. G. Kaper, “Application to the slab albedo problem. Part 1. Theory,” Internal Rep. TW-37, Mathematics Department, University of Gronigen, Gronigen, The Neth- erlands, 1967), pp. 7–10.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited