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 (α) and the photometric latitude ($\varphi$) and the photometric longitude (λ).

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

where A_M is the Minnaert albedo, k is an empirical parameter, I is the scattered radiance in the direction $(\alpha,\varphi,\lambda)$, πF 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 ^[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.

References

1. ^ http://dx.doi.org/10.1016/S0019-1035(03)00075-7
2. ^ http://dx.doi.org/10.1016/j.icarus.2006.05.006
3. ^ http://dx.doi.org/10.1080/01431160500104194
4. ^ http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1941ApJ....93..403M&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf

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