Calculation of the reflection function of an optically thick scattering layer for a Henyey-Greenstein phase function.

Simple analytical methods are proposed for calculating the reflection function of a semi-infinite and conservative scattered layer, the value of which is needed to solve many atmospheric optics problems. The methods are based on approximations of the exact values obtained with a strict numerical method. For a Henyey-Greenstein phase function, knowledge of the zeroth and sixth higher harmonics appears to be sufficient for a quite accurate approximation of the angle range, which is acceptable for solution of direct and inverse problems in atmospheric optics when a plane atmosphere is assumed. An error estimation and a comparison with the exact solution are presented.