A semi-analytic technique to speed up successive order of scattering model for optically thick media

A semi-analytic technique has been developed to speed up the integration of radiative transfer over optically thick media for the successive order of scattering (SOS) method. Based on the characteristics of the internal distribution of scattering intensity, this technique uses piecewise analytic eigenfunctions to fit internal scattering intensities and integrates them analytically over optical depth. This semi-analytic approach greatly reduces the number of sub-layers required for accurate radiative transfer calculation based on the SOS method. Results show that an accuracy of 1% for both flux and radiance (polar angle less than 67∘) can be achieved with a significantly small number of layers. This technique is accurate and efficient and makes the SOS method applicable for optically thick scattering media.