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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 37, Iss. 10 — Apr. 1, 1998
  • pp: 1935–1944

Photon Density Waves Scattered from Cylindrical Inhomogeneities: Theory and Experiments

Scott A. Walker, David A. Boas, and Enrico Gratton  »View Author Affiliations


Applied Optics, Vol. 37, Issue 10, pp. 1935-1944 (1998)
http://dx.doi.org/10.1364/AO.37.001935


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Abstract

We present an analytical solution for the scattering of diffuse photon density waves from an infinite circular, cylindrical inhomogeneity embedded in a homogeneous highly scattering turbid medium. The analytical solution, based on the diffusion approximation of the Boltzmann transport equation, represents the contribution of the cylindrical inhomogeneity as a series of modified Bessel functions integrated from zero to infinity and weighted by different angular dependencies. This series is truncated at the desired precision, similar to the Mie theory. We introduce new boundary conditions that account for specular reflections at the interface between the background medium and the cylindrical inhomogeneity. These new boundary conditions allow the separate recovery of the index of refraction of an object from its absorption and reduced scattering coefficients. The analytical solution is compared with data obtained experimentally to evaluate the predictive capability of the model. Optical properties of known cylindrical objects are recovered accurately. However, as the radius of the cylinder decreases, the required measurement signal-to-noise ratiorapidly increases. Because of the new boundary conditions, an upperlimit can be placed on the recovered size of cylindrical objects with radii below 0.3 cm if they have a substantially different index of refraction from that of the background medium.

© 1998 Optical Society of America

OCIS Codes
(120.5710) Instrumentation, measurement, and metrology : Refraction
(160.4760) Materials : Optical properties
(170.5280) Medical optics and biotechnology : Photon migration

Citation
Scott A. Walker, David A. Boas, and Enrico Gratton, "Photon Density Waves Scattered from Cylindrical Inhomogeneities: Theory and Experiments," Appl. Opt. 37, 1935-1944 (1998)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-37-10-1935


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References

  1. M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of optical properties,” Appl. Opt. 28, 2331–2336 (1989).
  2. J. S. Maier and E. Gratton, “Frequency-domain methods in optical tomography: detection of localized absorbers and a backscattering reconstruction scheme,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance and R. R. Alfano, eds., Proc. SPIE 1888, 440–451 (1993).
  3. D. A. Boas, M. A. Oleary, B. Chance, and 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).
  4. G. Gratton, M. Fabiani, D. Friedman, M. A. Franceschini, S. Fantini, P. M. Corballis, and E. Gratton, “Rapid changes of optical parameters in the human brain during a tapping task,” J. Cognitive Neurosci. 7, 446–456 (1994).
  5. D. A. Benaron and D. K. Stevenson, “Optical time-of-flight and absorbance imaging of biologic media,” Science 259, 1463–1466 (1993).
  6. 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).
  7. J. B. Fishkin and 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).
  8. S. Fantini, M. A. Franceschini, and E. Gratton, “Semi-infinite-geometry boundary problem for light migration in highly scattering media: a frequency-domain study in the diffusion approximation,” J. Opt. Soc. Am. B 11, 2128–2138 (1994).
  9. D. A. Boas, M. A. Oleary, B. Chance, and 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).
  10. R. Aronson, “Boundary conditions for diffusion of light,” J. Opt. Soc. Am. A 12, 2532–2539 (1995).
  11. R. C. Haskell, L. O. Svaasand, T.-T. Tsay, and B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11, 2727–2741 (1994).
  12. F. P. Bolin, L. E. Preuss, R. C. Taylor, and R. J. Ference, “Refractive index of some mammalian tissues using a fiber optic cladding method,” Appl. Opt. 28, 2297–2302 (1989).
  13. S. L. Jacques, C. A. Alter, and S. A. Prahl, “Angular dependence of HeNe laser light scattering by human dermis,” Lasers Life Sci. 1, 309–333 (1987).
  14. J. D. Jackson, Classical Electrodynamics (Wiley, New York), Chap. 16.
  15. S. A. Walker, S. Fantini, and E. Gratton, “Image reconstruction using back-projection from frequency domain optical measurements in highly scattering media,” Appl. Opt. 35, 170–179 (1996).
  16. S. Fantini, M. A. Franceschini, J. B. Fishkin, B. Barbieri, and E. Gratton, “Quantitative determination of the absorption spectra of chromophores in strongly scattering media: a light-emitting-diode based technique,” Appl. Opt. 33, 5204–5213 (1994).
  17. J. M. Beechem, E. Gratton, M. Ameloot, J. R. Knutson, and L. Brand, “The global analysis of fluorescence intensity and anisotropy decay data: second generation theory and programs,” in Topics in Fluorescence Spectroscopy, II, J. R. Lakowicz, ed. (Plenum, New York, 1991), Chap. 5, pp. 241–305.

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