Kirchhoff approximation for diffusive waves - art. no. 051917

Quantitative measurements of diffuse media, in spectroscopic or imaging mod e. rely on the generation of appropriate forward solutions, independently o f the inversion scheme employed. For complex boundaries, the use of numeric al methods is generally preferred due to implementation simplicity, but usu ally results in great computational needs, especially in three dimensions. Analytical expressions are available, but are limited to simple geometries such as a diffusive slab, a sphere or a cylinder. An analytical approximati on, the Kirchhoff approximation, also called the tangent-plane method is pr esented for the case of diffuse light. Using this approximation, analytical solutions of the diffusion equation for arbitrary boundaries and volumes c an be derived. Also, computation time is minimized since no matrix inversio n is involved. The accuracy of this approximation is evaluated on compariso n with results from a rigorous numerical technique calculated for an arbitr ary geometry. Performance of the approximation as a function of the optical properties and the size of the medium is examined and it is demonstrated t hat the computation time of the direct scattering model is reduced at least by two orders of magnitude.