The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B5. Beijing 2008 
initial orientation of the scanner head, has been evaluated in 
±4.0 and ±9.2 mgon for (p and 0 angles, and ±3.0 mm for r, 
respectively. These results do not outline very large differences 
w.r.t. absolute repeatability, considering also the different size 
of data samples. 
4.3 Empirical error propagation modeling 
During the data analysis only a systematic error in range 
direction has been evidenced. Thus, in this sub-section the error 
is modelled in function of range (4-35 m) and of 3-D incidence 
angle. 
The off-plane bias from the target centre and the plane 
interpolating the background surface around the RRT is 
considered as an error in range. In a first step this is modelled 
only in function of range (r) by means of the following 
quadratic function: 
Ar r = K 2 r 2 ± K x r + K 0 (2) 
where Ar r is the correction for the range. Thanks to data coming 
from Test Ex3.1, coefficients of formula (2) have been 
evaluated as K ( f=2-\0' 4 m, ATy=l .2-1 O' 3 , and K 2 =-3-1 O' 5 m* 1 . After 
the application of formula (2) to the same data with the 
computed coefficients, residual errors (see Figure 7) featuring 
about zero mean, a std.dev of ±2.2 mm, and a maximum 
absolute value of 5.1 mm have been obtained. 
In a second time the error has been modelled in function of 3-D 
incidence angle (a), by applying the linear correction: 
Ar a = K,r (3) 
where Ar a is the correction for the range. Thanks to data 
coming from Test Ex3.2, coefficient of formula (3) has been 
estimated as Æy=-1-10' 4 m. After the application of corrections 
coming from both formulas (2) and (3) to the dataset Ex3.2, 
residuals (see Figure 10) featuring zero mean, a std.dev of ±0.8 
mm, and a maximum absolute value of 1.7 mm have been 
obtained. 
The expression for the final corrected range r c is then given by 
the sum of both contributes Ar r and Ar a \ 
r c = r + (Ar r + Ar a ) (4) 
To validate the corrective model (4) and the estimated 
parameters for Riegl LMS-Z420/ instrument with an 
independent dataset, measurements taken on RRTs during Test 
Ex2.2 have been used. The computed range corrections r c have 
been applied to all measured targets, and results compared to 
GCP reference coordinates. Results have been summarized in 
table 12, where three algorithms for automatic RRT 
measurement have been compared: “riscan” algorithm 
implemented by Riegl Riscan Pro and “fuzzypos” described in 
Sub-sec. 4.1. Moreover, a modified version of “intersect” 
algorithm has been applied (“intersect2”), which makes use of 
the orthogonal distance between background surface and RRT 
to correct the measured range, instead of using r c . 
In general the estimated range corrections r c improve the 
accuracy of georeferencing for both “riscan” and “fuzzypos” 
algorithms. RMSE on 3-D coordinates of RRTs are better of 16 
and 10%, respectively, w.r.t. to non-corrected measurements 
(compare to table 3). However, even better results have been 
achieved by using “intersect2” method. 
Figure 11. Linear function interpolate the offset plane-point for 
different 3-D incidence angle. The blue points are the residual 
on range after correction 
Algorithm 
RMSE of 
3-D 
residuals 
on targets 
|mm| 
Estimated georeferencing parameters (a) 
Rotations of 1RS fmgonj 
Position of 
1RS centre 
fmmj 
n 
0 
K 
intersect2 
3.1 
5.4 
8.2 
4.3 
0.8 
riscan 
4.2 
6.8 
10.7 
5.9 
0.9 
fuzzypos 
3.5 
5.7 
8.9 
4.9 
0.8 
Table 12. Target residuals after scan georeferencing on GCPs 
and std.dev.s of georeferencing parameters; in this case ranges 
have been corrected by using model (4) 
5. CONCLUSIONS 
In the paper different aspects concerning retro-reflective target 
(RRT) measurement by TLS have been analysed. In detail, here 
the application of Riegl LMS-Z420/ has been investigated, but 
results could be extended to other ToF instruments. 
Main achievements can be summarized in three items. Firstly, 
different algorithms for automatic RRT measurement have been 
compared. Techniques based on point clustering have featured 
the best, because they are able to take into account differences 
in range measurements concerning the background surface and 
the RRT itself. On the other hand, the target size should be 
properly selected. 
Secondly, the repeatibility of RRT measurement is very good 
(under ±1 mm), property that can be exploited in monitoring 
applications where the TLS can be accurately repositioned (or 
kept stable) on the same stand-point. The use of a steal pillar is 
recommended. 
Thirdly, all tests have shown a systematic error in range 
measurement. This is for the most part due to the range TLS- 
RRT, and to the 3-D incidence angle. Modelling of this error 
has allowed to improve the accuracy of georeferencing up to 
10-16%, depending on the algorithm adopted for target 
measurement. Alternatively, good results can be achieved by