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. 
REFERENCES 
Akca, 2007. Matching of 3D surfaces and their intensities. 
ISPRS-J, 62. 
Aschoff, Thies, Spiecker, 2004. Describing forest stands using 
terrestrial laser-scanning. IAPRS 36, 8/W2, Freiburg, Germany. 
Briese, Hofle, Lehner, Wagner, Pfennigbauer, Ullrich, 2008. 
Calibration of full-waveform airborne laser scanning data for 
object classification. SPIE 6950, Laser Radar Technology and 
Appl. XIII. 
Farin, 2002. Curves and Surfaces in CAGD (5th ed). Academic 
Press.