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 ($\lambda$).

:$\text = \frac = \pi~A_M~\mu_0^k~\mu^$
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,{{Cite journal, url=http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1941ApJ....93..403M&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf, bibcode=1941ApJ....93..403M, title=The reciprocity principle in lunar photometry, last1=Minnaert, first1=M., journal=The Astrophysical Journal, year=1941, volume=93, page=403, doi=10.1086/144279 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

Observational astronomy
Photometric systems