Physical models and Monte Carlo estimates for spatial and angular derivatives of the specific intensity

Authors:
Preprint
Publisher website
Google Scholar
Abstract
Monte Carlo methods are highly capable at solving complex radiative transfer and coupled-physics problems and are used as reference solutions in many fields (e.g. solar processes,astrophysics and climate research). However, computing sensitivities of observables to geometricparameters, or computing spatial and angular derivatives of the radiative intensity, are difficultwhen employing Monte Carlo methods. Starting from the radiative transfer equation and its usualboundary conditions, this work aims to derive two new Monte Carlo algorithms for estimatingarbitrary spatial and angular derivatives of the radiative intensity. We apply the new estimatorsfor the spatial and angular derivatives in several test configurations involving homogeneousand non-homogeneous scattering and absorbing media, as well as black, diffuse and specularboundaries. Our approach provides direct access to spatial and angular derivatives of radiativeintensity, which are critical for applications such as analyzing inhomogeneous solar radiancein photovoltaic systems or optimizing satellite camera angles. By enabling these derivativecalculations, our work expands the utility of Monte Carlo methods, paving the way for advancedoptimization and inversion techniques in radiative transfer applications.