The Minnaert function is a photometric function used to interpret astronomical observations and remote sensing data for the Earth. It was named after the astronomer Marcel Minnaert. This function expresses the radiance factor (RADF) as a function the phase angle ( α {\displaystyle \alpha } ), the photometric latitude ( φ {\displaystyle \varphi } ) and the photometric longitude ( λ {\displaystyle \lambda } ).

RADF = I F = π   A M   μ 0 k   μ k − 1 {\displaystyle {\text{RADF}}={\frac {I}{F}}=\pi ~A_{M}~\mu _{0}^{k}~\mu ^{k-1}}

where A M {\displaystyle A_{M}} is the Minnaert albedo, k {\displaystyle k} is an empirical parameter, I {\displaystyle I} is the scattered radiance in the direction ( α , φ , λ ) {\displaystyle (\alpha ,\varphi ,\lambda )} , π F {\displaystyle \pi F} is the incident radiance, and

μ 0 = cos ⁡ φ   cos ⁡ ( α − λ )   ;     μ = cos ⁡ φ   cos ⁡ λ   . {\displaystyle \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.

The assumptions made are:

• the surface is illuminated by a distant point source.
• the surface is isotropic and flat.

Minnaert's contribution is the introduction of the parameter k {\displaystyle k} , having a value between 0 and 1, 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.