In: Wagner W., Székely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Voi. XXXVIII, Part 7B 
IS, Vol. XXXVIII, Part 7B 
59 
ra by Size Class 
(m m ) 
ì by Size Class 
im) 
¡jectra for gravels of 
pes viewed at 30° from 
ation 
the radiant interactions 
Tadiosity describes the 
e elements, and in the 
;ed and reflected energy. 
:o any dimension, as a 
ì appropriate for high- 
. Input digital elevation 
sily measured with laser 
ty for a number of facets 
i,j = \,2...n (4) 
element i, /?, is thermal 
t, p is reflectivity of the 
ce element j to surface 
ce elements. The second 
scattering components— 
mong surface elements, 
s determining the form- 
m factor is given by 
where F„ is the form factor from surface element j to surface 
ji j 
element i, 9 is the projection angle between the normal of a 
surface element and the line, linking the pair of elements 
together, A,- is the area of element i, and d is the distance 
between two elements (Figure 4). 
The model simulates temperature and radiance variations due to 
roughness around some mean temperature over the course of a 
day. It is illumination and view angle-dependent, and while not 
explicitly spectral, it is wavelength-dependent and can be run 
for a series of spectra to simulate spectral changes. In this 
model, the mean temperature over time is determined by a 
simple heat diffusion model driven by environmental data. 
Mixed materials result in mixed spectra, and this can be 
simulated by assigning different properties to facets but 
assuming there is no difference of temperature.. 
Figure 5 shows a measured digital elevation model (DEM) of a 
rock surface in part a., shown graphically in part c. The DEM 
covers an area of 0.5 m by 0.85 m at sample spacing of 1 cm. 
Part b shows the change of simulated emissivity averaged over 
the area throughout the day. The roughness effect is largest 
when the sun is at moderate elevations. The DEM can then be 
multiplied by constants to rescale the roughness of the data. 
Part c shows the resulting calculation of broad-band emissivity 
over a range of RMS values. 
The concept radiatively interacting surface elements can be 
extended to shapes and larger surfaces such as cracks, holes, 
and comers of surfaces. In these cases, terminology such as 
“cavity effects” and ’’adjacency effects” are used. In fact, 
imaging spectrometer instruments show that even small cracks 
and holes become aspectral regardless of the spectra of the 
materials large when view factors exist. 
Figure 6 shows observations and a simulation of the effects of 
two depressions (cavities) about 2 cm deep in a norite rock 
(plagioclase and hypersthene ± olivine). The norite has 
overlapping reststrahlen bands from 8.5 to 10.0 pm. Parts a and 
b show a photograph and a thermal IR spectral image of the 
rock. The thermal image was made with a Telops Inc, Hyper- 
Cam imaging FTIR spectrometer (Telops, 2010). Part c shows a 
micro-DEM of the rock smoothed to a 2 mm grid. Part d shows 
spectra taken from the image inside and outside the depressions. 
Finally, part e shows the simulated emissivity of the rock. In the 
depressions, the spectrum is shallower and higher than on the 
surface, becoming significantly more like a blackbody than the 
outer surface. 
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£ 
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LU 
Emissivity 
Figure 5. Simulated change of broad-band emissivity for a 
measured surface; the cavities in the rock become more like 
a blackbody than the outer surface; see text more 
explanation of the individual parts. 
4. 
Figure 4. Schematic plot of the terms used in the form 
factor equation (Eq. 5).