this is actually the starting point for Hapke’s theory. What this value is physically, is
unclear and its description as a single scattering albedo is highly misleading and
should be avoided.
On the other hand, Hapke parameters are a very useful way of describing a data
set as they can be used to fit the bidirectional reflectance distribution function
(BRDF) to high accuracy (e.g. Pommerol et al. 2019). This is being used now in
databases such as DACE (Data and Analysis Center for Exoplanets)
1 to provide the
BRDF of materials measured in the laboratory to a wider community. The geometric
albedo and hemispherical albedos can also be determined to high accuracy
(e.g. Table 2.1).
Fornasier et al. (2016) determined the surface phase function of the nucleus of
67P by fitting OSIRIS observations of the nucleus. The long duration of the
rendezvous allowed observations of individual areas in many observing geometries
leading to well-constrained results. A reflectance factor curve for a surface element is
shown in Fig. 2.19. Here, the emission angle has been set to zero and the reflectance
plotted against the phase angle. Note that there is a factor of 10 decrease in the
observed reflectance from opposition geometry (α ¼ e ¼ i ¼ 0
) to the terminator
geometry (α ¼ i ¼ 90
, e ¼ 0
).
There are several other photometric functions that have been used in the literature
over the years. These are usually much simpler in form and have their uses where
data are sparse.
The Minnaert function is now probably only significant for historical reasons. It
takes the form
ρ F α, e, i
ð
Þ¼π A M μ
k M
0 μ
k M À1
ð2:76Þ
where
Fig. 2.19 Reflectance
curve of a surface element of
67P/C-G computed from the
Hapke parameters derived
by Fornasier et al. (2016).
The emission angle is set to
zero and i ¼ α
1 https://dace.unige.ch/dashboard/
2.6 Surface Reflectance
63
unclear and its description as a single scattering albedo is highly misleading and
should be avoided.
On the other hand, Hapke parameters are a very useful way of describing a data
set as they can be used to fit the bidirectional reflectance distribution function
(BRDF) to high accuracy (e.g. Pommerol et al. 2019). This is being used now in
databases such as DACE (Data and Analysis Center for Exoplanets)
1 to provide the
BRDF of materials measured in the laboratory to a wider community. The geometric
albedo and hemispherical albedos can also be determined to high accuracy
(e.g. Table 2.1).
Fornasier et al. (2016) determined the surface phase function of the nucleus of
67P by fitting OSIRIS observations of the nucleus. The long duration of the
rendezvous allowed observations of individual areas in many observing geometries
leading to well-constrained results. A reflectance factor curve for a surface element is
shown in Fig. 2.19. Here, the emission angle has been set to zero and the reflectance
plotted against the phase angle. Note that there is a factor of 10 decrease in the
observed reflectance from opposition geometry (α ¼ e ¼ i ¼ 0
) to the terminator
geometry (α ¼ i ¼ 90
, e ¼ 0
).
There are several other photometric functions that have been used in the literature
over the years. These are usually much simpler in form and have their uses where
data are sparse.
The Minnaert function is now probably only significant for historical reasons. It
takes the form
ρ F α, e, i
ð
Þ¼π A M μ
k M
0 μ
k M À1
ð2:76Þ
where
Fig. 2.19 Reflectance
curve of a surface element of
67P/C-G computed from the
Hapke parameters derived
by Fornasier et al. (2016).
The emission angle is set to
zero and i ¼ α
1 https://dace.unige.ch/dashboard/
2.6 Surface Reflectance
63