To model bidirectional measurements, a numerical method for computing the incoherent light scattered by a diffusing medium is presented. The results are expressed as a function of the incident and the observer angles (θ<sub>i</sub>, φ<sub>i</sub>) and (θ<sub>f</sub>, φ<sub>f</sub>), in contrast to the <i>N</i>-flux method, which gives no information about the azimuthal distribution. To solve the multiple-scattering equations, an auxiliary function, expanded on the spherical harmonics, is introduced in the diffusion equation. A set of integral equations on the coefficients are obtained that are well suited for the numerical resolution. The boundary conditions are included in the linear operator of the integral equation, so that each boundary condition is associated with a specific equation. As an illustration, the method is applied to numerical simulations of maps of the light scattered by a thick refractive diffusing layer of refractive index n = 1.5, for two directive phase functions and for several incident collimated-beam angles.
© 2002 Optical Society of America
Mady Elias and Georges Elias, "New and fast calculation for incoherent multiple scattering," J. Opt. Soc. Am. A 19, 894-901 (2002)