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Ta b l e 8 . 1
Flank slope and
height values for several mare
domes, determined using the
shadow-based method of
Ashbrook (
1961
)
Slope (
◦
)
Dome
Height (m)
C11
0.6
60
A2 (Arago
α
)
1.5
310
H7
1.5
100
M11
3.0
150
M12 (Milichius
π
)
2.7
230
such that the determined height difference value merely represents a lower limit to
the true dome height.
Ashbrook (
1961
) shows that under the assumption of a spherical shape of the
dome surface, the average value of the flank slope corresponds to the solar eleva-
tion angle when the shadow length equals one quarter of the dome diameter. The
observer determines the moment in time, corresponding to a solar elevation angle
˜
μ
,forwhich
l
μ
. The Ash-
brook method has primarily been devised for visual observations. The assumption
of spherical dome shape, however, represents a significant restriction to its applica-
bility. Here it was used to determine the heights of domes C11, A2, H7, M11, and
M12 (cf. Table
8.1
).
Photometric three-dimensional surface reconstruction methods are more gener-
ally applicable to the determination of the morphometric properties of lunar domes.
In a first step, the photoclinometric approach (cf. Sect.
3.2.2.1
) is taken, which con-
sists of computing depth profiles along image rows. For all regarded domes, the
terrain is gently sloping, i.e.
=
D/
4 is given, leading to a dome height
h
=
(D/
2
)
tan
˜
|
|
|
|
1, the illumination is highly oblique, and
the scene is illuminated nearly exactly from the east or the west, corresponding
to
q
s
=
p
,
q
0. The lunar-Lambert reflectance (
8.6
) thus depends much more strongly
on the surface gradient
p
in the east-west direction than on the gradient
q
in the
north-south direction, such that we may initially set
q
0. Note that this approxi-
mation is exact for cross sections in the east-west direction through the summit of
a feature, while it is otherwise a reasonable approximation. A constant albedo
ρ
is
assumed, which is justified for all examined domes, as they are virtually indistin-
guishable from their surroundings in Clementine 750 nm images. The value of
ρ
is
chosen such that the average surface slope over the region of interest is zero. Under
these assumptions, (
3.16
) is solved for the surface gradient
p
uv
for each pixel with
intensity
I
uv
.
The result of photoclinometry is used as an initialisation to the shape from shad-
ing scheme according to Horn (
1989
) described in Sect.
3.2.2.2
. The ground-based
CCD images are affected by a slight blur due to atmospheric seeing. Hence, the ob-
served image
I
uv
is assumed to be a convolution of the true image with a Gaussian
point spread function (PSF)
G
σ
(cf. Chap.
4
). The PSF radius
σ
is determined from
the intensity profile of shadows cast by steep mountains, e.g. crater rims, where
an abrupt transition from illuminated surface to darkness is expected. Convolving a
synthetically generated abrupt change in intensity with a Gaussian PSF and compar-
ing the result with the intensity profile observed in the image allows for an estima-
=
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