In: Wagner W„ Székely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B 
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al., 2007). It was a parametric approach using either simple 
(three parameters) or generalized Gaussian (four parameters) or 
a Lognormal function to model extracted relevant peaks as 
echoes. Since the discrete return data used in our analysis 
represent the peaks of partial signal returns, we assumed that 
the entire reflected laser pulse energy could be decomposed 
into a sum of components while each one would be represented 
by a single discrete return: 
/( x ) = Zfri) 0) 
;=1 
Here n = 4 for four returns or 3 for three returns. For modeling 
of each function fj in our analysis we used only a simple three- 
parametric Gaussian: 
f, = a, exp 
2o-, 2 J 
(2) 
Figure 6 gives a graphic representation of our approach, where 
the peak of each discrete return is modeled by a simple 
Gaussian (2) while a, p, and <j were used as fitting parameters 
so that the amplitude of each peak would be proportional to the 
recorded intensity value. Furthermore, we assumed that the 
superposition (1) of all four simple Gaussian functions 
representing the waveforms of the discrete partial returns would 
represent the total optical receiver power P n which can be 
modeled through the lidar equation (Measures, 1984). 
Considering partial signal returns P„ the intensity of each one 
was modeled using the lidar equation in the form derived by 
Jelalian (1992): 
p P t D rQ T 2 Çf 
l ' 4 nS 1 atm R i 4 
(3) 
Here: 
Pi is the received signal power for /-return 
P, is the transmitted laser pulse power 
D r is the diameter of the lidar receiver aperture 
Q is the optical efficiency of the lidar system 
3 is the laser beam divergence 
T atm is the atmospheric transmittance factor 
Ri is the range from the sensor to /-target 
<Ji is the effective backscattering cross section of /-target 
Here the reflective properties of each target for each partial 
return P t are described by the backscattering cross-section o;-, 
which is proportional to the target reflectance p, and the /- 
fraction of the total received power P r in each return: 
<T, = k,p,A, (4) 
Here Aj is the area of the target illuminated by the /-fraction of 
the laser footprint, which created the discrete return f. and k t is 
the fitting parameter, characterizing scattering properties of /- 
target, which could be calibrated using redundant 
measurements. 
A similar approach, based on waveform generalization of the 
lidar equation (Jutzi and Stilla, 2006) and Gaussian 
decomposition, was applied to the analysis of full waveform 
data by Wagner and co-authors (Wagner et al., 2006; Wagner et 
al., 2008). 
Figure 6. Graphic representation of the modeling approach 
for ALTM Orion data. 
Figure 7. Illustration of the modeling for cornfield data 
collected by ALTM Orion-M (Figure 4). 
Figure 8. Illustration of the modeling for high-canopy 
vegetation data collected by ALTM 3100 (Figure 1). 
Based on the approach described by equations (1-4) and using 
the known characteristics of the emitted laser pulse and lidar 
system hardware, it was possible to model waveform of each 
discrete return (Figure 7-8) and estimate the effective 
reflectivity of complex vegetation targets like cornfields and 
coniferous trees. This work is still in progress and requires