Steady-state reflectance spectroscopy in the P 3 approximation

The Green’s function of the steady-state radiative-transport equation is derived in the P3 approximation for isotropic sources. It is demonstrated that the P3 approximation models the radiance in highly absorbing media or close to sources more accurately than does diffusion theory. Boundary conditions consistent with the P3 approximation are also developed for semi-infinite media bounded by a nonscattering medium. Expressions for the reflectance remitted from media interrogated by a normally incident pencil beam are derived and fitted to simulated and experimental reflectance data from media having optical properties typical of biological tissue. The reconstructed optical properties are accurate to within ±10% in absorption and scattering for source–detector separations as small as 0.43 mm and albedos as low as 0.59. Methods for simplifying these expressions given some a priori knowledge of the scattering phase function are discussed.

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