Radiative Transfer on Mesoscopic Spatial Scales

Accurate predictions of light transport produced by illumination of turbid media such as biological tissues, cloudy atmospheres, terrestrial surfaces, and soft matter is essential in many applications including remote sensing, functional optical imaging, realistic image synthesis, and materials characterization. The inability to model light transport on mesoscopic scales limits the spatial resolution and information content that can be extracted from optical measurements. While effective approaches exist to model light transport in singly- and diffusely-scattering regimes, modeling light propagation over the mesoscopic spatial scales remains an important challenge. Radiative transfer on these scales must account for the complete 5-dimensional spatial and angular distributions of the radiant field.;Here, we present novel stochastic and analytic methods to analyze and predict light propagation in turbid media generated by collimated illumination on mesoscopic scales. We also consider coupled transport problems, resulting from illumination and detection, to facilitate measurement design and inverse problems. Specifically, we introduce a coupled Forward-Adjoint Monte Carlo (cFAMC) method that leverages generalized optical reciprocity to enable the computation of spatially-resolved distributions of light interrogation for specific source-detector pairs. cFAMC can aid the design of optical diagnostic measurements by tailoring the light field to interrogate specific sub-volumes of interest. We use cFAMC to examine the effects of angular resolution on the resulting interrogation distributions and analyze a diagnostically-relevant compact fiber probe design for the detection of epithelial precancer.;While Monte Carlo simulation is considered a gold standard method to solve the equation of radiative transfer (ERT), it is computationally expensive. Thus, methods to obtain ERT solutions at lower computational cost are valuable. We introduce a general analytical framework to solve the ERT which employs the complete Spherical Harmonic Expansion to order N and utilizes Fourier decomposition (SHEFN) of the transverse spatial variables. We provide an exhaustive analytical analysis to develop a rapid and robust computational framework. We also introduce a sequential order smoothing method to improve accuracy, particularly for low-order approximations. The SHEFN predictions are verified using Monte Carlo simulations for oblique Gaussian beam illumination of a turbid half-space. We also extend SHEFN for cases of stratified media and adjoint radiative transfer.