Scattering phase function ($P(\Theta )$)

A scattering phase function describes the angular distribution of single-scattered power. One common convention is $\int Pd\Omega =4\pi$, so that $P/(4\pi )$ is a probability density over outgoing solid angle. For unpolarized Rayleigh scattering, $P=3(1+{\cos }^2\Theta )/4$. It is distinct from the oscillatory-integral meaning of phase function.

The scattering asymmetry parameter is the mean scattering-angle cosine, $g=(4\pi {)}^{-1}\int P\cos \Theta d\Omega$ in the $4\pi$ normalization. Forward/backward symmetry gives $g=0$; positive $g$ indicates a net forward preference. In a two-stream transport approximation, the reduced scattering optical depth is $(1-g)\tau$.