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.
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