Phase functions as solutions of integral equations

A phase function is an important characteristic of a scattering medium. A method to derive new analytic phase functions is proposed. The relation between a phase function and an angle-averaged single-scattering intensity, derived earlier [M. L. Shendeleva, J. Opt. Soc. Am. A 30, 2169 (2013)], is considered as an integral equation for a phase function. This equation is classified as an Abel integral equation of the first kind, whose solution is known. Two phase functions newly derived with this method are presented