The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B5. Beijing 2008
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The nested models all produce satisfying results concerning the
data of the range experiments. The mean intensity can be
predicted with a precision of 1% for both scanners.
For the Riegl scanner a bi-cubic model was found to provide
best results. For each range the intensity is described as a cubic
polynomial of the product of target reflectivity and cosine of
the incidence angle. This function can be seen as the transfer
(amplification) function from optical power to the digital
intensity values. In all the experiments this function proved to
be strictly monotonously growing. It is, therefore, invertible,
allowing to infer reflectivity from range and intensity. Also, no
oscillatory behaviour could be detected. The model is therefore
suitable and fulfils the requirements of Sec. 3.2. For the Optech
scanner, the cubic model is best for the range experiment.
Concerning the angle experiment, the prediction is different for
the two scanners. Testing the model for the Riegl scanner is an
extrapolation, as lower mean intensities were obtained than in
the range experiments. Still, the estimation of the intensity on
the basis of the known reflectivity and the estimated incidence
angle was possible with the same accuracy. This confirms that
the model proposed fits well to the data and its temporal
stability should be investigated next. For the Optech data the
intensity in the angle experiments can be predicted not as good.
While predicted intensities can be compared to observed ones,
it has more applications to estimate the reflectivity p E (or k, the
target cross section, ...) from the intensities. As noted above,
for a given range r g 4 is always monotonous and thus invertible.
In Table 8 the distribution of estimated reflectivity residuals e p
= P~Pe, computed from mean range, incidence angle, and
intensity, is shown. It should be considered that the model
parameters were derived from the range experiment and then
also applied to the angle series to evaluate these parameters.
experiment
g4
mean e 0
std. e D
min., max. e D
Riegl, range
Cubic
0.0004
0.0271
-0.0699, 0.0897
Riegl, angle
Cubic
0.0026
0.0549
-0.1628,0.1089
Riegl, range
Log.
-0.0221
0.1273
-0.5412,0.1209
Riegl, angle
Log.
0.0291
0.1325
-0.3442, 0.2273
Optech, range
Cubic
-0.0001
0.0119
-0.0278, 0.0298
Optech, angle
Cubic
0.0234
0.0609
-0.1069,0.2028
Optech, range
Linear
0.0000
0.0277
-0.0582,0.0419
Optech, angle
Linear
0.0204
0.0469
-0.0568,0.1600
Optech, range
Scale
-0.0046
0.0287
-0.0696, 0.0526
Optech, angle
Scale
-0.0072
0.0466
-0.1012, 0.0851
Table 8: Residuals of reflectivity estimated from r, a, and /.
For the Riegl data it holds that the cubic model fits much better
for the inverse task than does the logarithmic model. Also, the
extrapolation to low intensity values observed in the angle
experiment obviously has a more severe influence. For the
given distance range of [2m,45m] the reflectivity of smooth
surfaces can, however, be estimated from the range and
intensity data with a systematic error of 2% and a standard
deviation of 6%. This assumes that the angle of incidence can
be estimated precisely. The numbers for the estimation of k are
similar. With the approach of Pfeifer et al. (2007) this inversion
was possible with a standard deviation of 23% only.
For the Optech data the values of the cubic model are similar to
those of the Riegl data. However, the other two models fit also
comparably good. For the angle experiment the linear and the
scale model fit even better, and thus should be used for the
inversion. In the distance range of [4m,40m] the reflectivity of
smooth surface can, therefore, be estimated from the range and
intensity data with a systematic error of maximum 2% and a
standard deviation of 5%.
7. CONCLUSIONS
The purpose of terrestrial laser scanners is currently mainly in
acquiring geometry. It was shown that the intensity values
provided alongside the range are not realizations of the Lidar
equation in its simple form (Eq. 1, Eq. 3). The inherent
assumptions (coaxial system, etc.) do not hold. However, the
components of these laser scanners work consistently and allow
reconstructing also target properties like reflectivity, if the
scattering properties are known. It was shown that this is
possible in the range of the shortest measurable distances to
approximately 50m for the specific devices used, namely a
Riegl LMS-Z420i and an Optech ILRIS 3D. The reflectivity of
Lambertian targets could be reconstructed with a precision of
about 6% and a bias in the order of 2%. This demonstrates the
great potential for using these devices in monitoring
applications, where the backscatter strength depends on
material properties. Laser scanning should therefore be
considered a 4D measurement process, with each coordinate
holding object information.
The standard deviation of the intensity values and the plane fit
results should be analysed next. Also, larger distances should be
investigated. Likewise, the temporal stability of the function
parameters has not been studied. Verifying the stability would
allow calibrating once, with no need to use the reference targets
for subsequent applications/experiments of the intensity values.
Finally, also the properties of phase shift scanners should be
studied with respect to “their” intensity values. Eventually,
under the assumption that the “increasing intensity with range”
behaviour originates in the changing overlap of emitter and
receiver field of view, also the energy distribution within each
footprint becomes important and should be investigated. The
final aim is, of course, verifying the findings over natural
surfaces.
ACKNOWLEDGMENTS
Part of this project was supported by the Vienna University of
Technology innovative project "The Introduction of ILScan
technology into University Research and Education". We are
especially grateful to M. Vetter for the experiment support.
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Briese, Hofle, Lehner, Wagner, Pfennigbauer, Ullrich, 2008.
Calibration of full-waveform airborne laser scanning data for
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Farin, 2002. Curves and Surfaces in CAGD (5th ed). Academic
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