A modified spectral method for simulating arbitrary directional radiative intensity in participating media with graded refractive index

Accurate simulation of the arbitrary directional radiative intensity in participating media with graded refractive index (GRI) is important for solving the inverse radiation problem. The conventional spectral method (SM) can be applied to solve the radiative transfer problem of graded index media with limit-fixed discrete directions, which cannot obtain arbitrary directional radiative intensities required in inverse estimation. From the conventional SM, a modified spectral method (MSM) is proposed to simulate the arbitrary directional radiative intensity of participating media with GRI accurately. The detailed derivation process of MSM is illustrated and verified by solving the radiative transfer problem involving three different kinds of GRI distributions. All results show that the arbitrary directional radiative intensity can be calculated accurately based on the fixed directional radiative intensities of SM. Furthermore, the GRI distribution was reconstructed accurately by using the stochastic particle swarm optimization with noisy data and the MSM as forward method.