Experimental demonstration of a fast analytical method for modeling photon propagation in diffusive media with arbitrary geometry

Quantitative measurements of diffusive media, in spectroscopic or imaging mode, rely on the generation of appropriate forward solutions, independently on the inversion scheme employed. For complicated boundaries, the use of numerical methods is usually pursued due to implementation simplicity, but this results in great computational needs. Even though some analytical expressions are available, an analytical solution to the diffusion equation that deals with arbitrary volumes and boundaries is needed. We use here an analytical approximation, the Kirchhoff Approximation or the tangent-plane method, and put it to test with experimental data in a cylindrical geometry. We examine the experimental performance of the technique, as a function of the optical properties of the medium and demonstrate how it greatly speeds up the computation time when performing 3D reconstructions.