Directional radiative intensity calculation in one-dimensional media by spherical harmonics method

Directional radiative intensity calculation is very useful for inverse analysis since it can provide abundant useful information inside radiative systems. In this work, spherical harmonics method (PN approximation) is utilized to calculate directional radiative intensity. Meanwhile, in order to improve the computational accuracy of radiative intensity, a method named PN-path integral method which is based on PN approximation is developed. Both methods are applied to calculate radiative intensity with high directional resolution in one-dimensional media. Different radiative systems with varying optical thickness, scattering phase function, scattering albedo, and boundary emissivity are considered. Results show that radiative intensity calculated directly by PN approximation has very low accuracy with errors of several tens of percentages in most cases. The accuracy does not improve much by increasing the order of approximation. In contrast, the developed PN-path integral method can calculate radiative intensity with very high accuracy. The errors are less than 5% in most cases by P1-path integral method and can be further reduced by using P3-path integral method. The PN-path integral method also inherits the advantage of PN approximation with high computation efficiency.