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We consider the radiative transfer of a finite width collimated beam incident normally on a plane-parallel slab composed of a uniform absorbing and scattering medium. This problem is fundamental for modeling and interpreting non-invasive measurements of light backscattered by a multiple scattering medium. Assuming that the beam width is the smallest length scale in the problem, we introduce a perturbation method to determine the asymptotic expansion for the solution of this problem. Using this asymptotic expansion, we determine the leading asymptotic behavior of the reflectance. This result includes the influence integral, which gives the influence of the phase function on the leading asymptotic behavior of the reflectance. We validate this asymptotic theory using a novel implementation of the Monte Carlo method that is fully vectorized to run efficiently in MATLAB. We evaluate the usefulness of this asymptotic behavior for different phase functions and show that it provides valuable insight into the influence of the phase function on spatially resolved non-invasive measurements of light backscattered by a multiple scattering medium.
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Radiance backscattered by a strongly scattering medium in the high spatial frequency limit
We study the radiative transfer of a spatially modulated plane wave incident on a half-space composed of a uniformly scattering and absorbing medium. For spatial frequencies that are large compared to the scattering coefficient, we find that first-order scattering governs the leading behavior of the radiance backscattered by the medium. The first-order scattering approximation reveals a specific curve on the backscattered hemisphere where the radiance is concentrated. Along this curve, the radiance assumes a particularly simple expression that is directly proportional to the phase function. These results are inherent to the radiative transfer equation at large spatial frequency and do not have a strong dependence on any particular optical property. Consequently, these results provide the means by which spatial frequency domain imaging technologies can directly measure the phase function of a sample. Numerical simulations using the discrete ordinate method along with the source integration interpolation method validate these theoretical findings.
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- Award ID(s):
- 1840265
- PAR ID:
- 10369601
- Publisher / Repository:
- Optical Society of America
- Date Published:
- Journal Name:
- Journal of the Optical Society of America A
- Volume:
- 39
- Issue:
- 7
- ISSN:
- 1084-7529; JOAOD6
- Format(s):
- Medium: X Size: Article No. 1193
- Size(s):
- Article No. 1193
- Sponsoring Org:
- National Science Foundation
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