The phase-integral method for radiative transfer problems with highly-peaked phase functions

Complete solutions to the radiative transfer equation, including both azimuth and depth dependence are provided by the discrete ordinate method of Chandrasekhar, but these solutions are often limited because of large computer requirements. This paper presents a “phase-integral” method which greatly reduces the number of discrete ordinates needed in the solution for highly-peaked phase functions. A composite quadrature method is shown to be effective in further reducing the number of discrete ordinates required for highly anisotropic phase functions. Examples are given to indicate convergence requirements and expected accuracy in the complete solution for Henyey-Greenstein and cloud-type phase functions.