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8.1.2 Reflectance Behaviour of Planetary Regolith Surfaces
When the inner planets of the solar system formed, all of them underwent internal
differentiation processes which led to the formation of a core mainly consisting of
iron and nickel, a mantle consisting of dense silicate rock, and a silicic crust. In the
absence of an atmosphere, the rocky surfaces were shattered by meteorite impacts
over billions of years. At the same time, they were eroded in a less spectacular but
also fairly efficient manner by the particles of the solar wind, e.g. highly energetic
protons, which cause slow chemical changes in the material directly exposed to
them. As a consequence, the uppermost layer of an atmosphereless planetary body,
which mainly consists of silicate minerals, is made up by a material termed 're-
golith' which is highly porous and is composed of fine grains. This has been shown
directly by the drilling experiments performed during some of the Apollo missions
to the Moon (McKay et al.,
1991
).
A reflectance function for planetary regolith surfaces is introduced by Hapke
(
1981
) according to
cos
θ
e
)
1
B(α)
p(α)
H(
cos
θ
i
)H (
cos
θ
e
)
.
(8.1)
w
cos
θ
i
4
π(
cos
θ
i
+
R
H81
(θ
i
,θ
e
,α)
=
+
−
1
+
The parameter
w
corresponds to the 'single-scattering albedo', i.e. the reflectivity of
a single surface grain. The function
p(α)
specifies the phase angle-dependent scat-
tering behaviour of a single particle. The function
B(α)
describes the 'opposition
effect', a strong increase in the intensity of the light reflected from the surface for
phase angles smaller than about a few degrees. According to Hapke (
1986
,
2002
),
the opposition effect has two major sources. The shadow-hiding opposition effect
is due to the fact that regolith surfaces are porous, and under moderate and large
phase angles the holes between the grains are filled by shadows. These shadows dis-
appear for small phase angles, leading to an increased intensity of the light reflected
from the surface (Hapke,
1986
). The coherent backscatter opposition effect is due to
coherent reflection of light at the surface particles under low phase angles (Hapke,
2002
). The function
B(α)
can be expressed as
B
0
=
B(α)
tan
(α/
2
)/h
,
(8.2)
1
+
where
B
0
governs the strength and
h
the width of the peak (Hapke,
1986
). If the
opposition effect were exclusively due to shadow hiding, one would expect a value
of
B
0
between 0 and 1. However, values of
B
0
larger than 1 are commonly allowed
to additionally take into account the coherent backscatter opposition effect (Warell,
2004
), as it is difficult to separate the two contributions.
For the particle angular scattering function
p(α)
,McEwen(
1991
) uses the phase
function introduced by Henyey and Greenstein (
1941
) involving a single asymme-
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