Minnaert function

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 ( \alpha ), 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. 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 , 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.

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 ( \alpha ), 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. 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 , 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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