Probing the position-dependent optical energy fluence rate in 3D scattering samples

The accurate determination of the position-dependent energy fluence rate of light is crucial for the understanding of transport in anisotropically scattering and absorbing samples, such as biological tissue, seawater, atmospheric turbulent layers, and light-emitting diodes. While Monte Carlo simulations are precise, their long computation time is not desirable. Common analytical approximations to the radiative transfer equation (RTE) fail to predict light transport, and could even give unphysical results. Here, we experimentally probe the position-dependent energy fluence rate of light inside scattering samples where the widely used P_1 and P_3 approximations to the RTE fail. We study samples that contain anisotropically scattering and absorbing spherical scatterers, namely microspheres (r = 0.5 μm) with and without absorbing dye. To probe the position-dependent energy fluence rate, we detect the emission of quantum dots that are excited by the incident light and that are contained in a thin capillary. By scanning the sample using the capillary, we access the position dependence. We present a comprehensive analysis of experimental limitations and (systematic) errors. Our measured observations are compared to the results of analytical approximations of the solution of the radiative transfer equation and to Monte Carlo simulations. Our observations are found to agree well with the Monte Carlo simulations. The P_3 approximation with a correction for forward scattering also agrees with our observations, whereas the P_1 and the P_3 approximations deviate increasingly from our observations, ultimately even predicting unphysical negative energies.