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
), the photometric latitude (
φ
) and the photometric longitude (
λ
).
RADF
=
I
F
=
π
A
M
μ
0
k
μ
k
−
1
where
A
M
is the Minnaert albedo,
k
is an empirical parameter,
I
is the scattered radiance in the direction
(
α
,
φ
,
λ
)
,
π
F
is the incident radiance, and
μ
0
=
cos
φ
cos
(
α
−
λ
)
;
μ
=
cos
φ
cos
λ
.
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.
