Validity of a closed-form diffusion solution in P1 approximation for reflectance imaging with an oblique beam of arbitrary profile.

Determination of optical parameters of turbid media from reflectance image data is an important class of inverse problems due to its potential for noninvasive characterization of materials and biological tissues, which demands rapid modeling tools to generate calculated images. We treat the problem of reflectance imaging with homogeneous semi-infinite turbid media as a boundary-value problem of diffusion type in the P1 approximation to the radiative transfer equation. A closed-form solution has been obtained for an oblique incident beam of arbitrary profile and its accuracy has been examined against a Monte Carlo method and measured data. We find that the diffusion solution provides a sufficiently accurate tool to rapidly calculate reflectance images for samples of large or moderate scattering albedo illuminated by a beam of arbitrary profile as long as the anisotropy factor remains less than 0.7 and single scattering albedo larger than 0.8. The closed-form solution can thus be used as a part of a forward modeling toolbox to determine optical parameters from reflectance image data in combination with other method such as the Monte Carlo simulation.