Minnaert Function

The Minnaert function is a photometric function used to interpret astronomical observations and remote sensing data for the Earth. This function expresses the radiance factor (RADF) as a function the phase angle and the photometric latitude and the photometric longitude .

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

where is the Minnaert albedo, is an empirical parameter, is the scattered radiance in the direction, 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.

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, 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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