P_N approximation for frequency-domain measurements in scattering media

Presented here are expressions for the P_N approximation for light propagation in scattering media in the frequency domain. To elucidate parametric dependencies, the derivation uses normalization of the resulting expressions to either the total interaction coefficient or the reduced total interaction coefficient. For the latter case, a set of reduced phase function coefficients are introduced. Expression of the P_N approximation as a conventional eigenvalue problem facilitates computation of the eigenvalues or attenuation coefficients. This approach is used to determine the attenuation coefficients in the asymptotic regime over the full values of the scattering albedo and reduced scattering albedo (0 to 1) and all positive values of the asymmetry factor (0 to 1). Frequencydomain measurements yield a sensitivity to turbid media optical properties for reduced scattering albedos as small as 0.2. P_N calculations are used to assess the magnitude of errors associated with the P_1 and P_3 approximations over a range of scattering albedo, phase function, and modulation frequency.