# Minnaert function

The Minnaert function is a photometric function used to interpret astronomical observations [1][2] and remote sensing data for the Earth.[3] This function expresses the radiance factor (RADF) as a function the phase angle ($\alpha$) and the photometric latitude ($\varphi$) and the photometric longitude ($\lambda$).

$\text{RADF} = \frac{I}{F} = \pi~A_M~\mu_0^k~\mu^{k-1}$

where $A_M$ is the Minnaert albedo, $k$ is an empirical parameter, $I$ is the scattered radiance in the direction $(\alpha,\varphi,\lambda)$, $\pi F$ is the incident radiance, and

$\mu_0 = \cos\varphi~\cos(\alpha-\lambda) ~;~~ \mu = \cos\varphi~\cos\lambda ~.$

The phase angle is the angle between the light source and the observer with the object as the center.

Minnaert's contribution is the introduction of the parameter $k$, having a value between 0 and 1,[4] originally for a better interpretation of observations of the Moon. In remote sensing the use of this function is referred to as Minnaert topographic correction, a necessity when interpreting images of rough terrain.