364 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
Fig. 5. Example of the performance of the nonlinear preprocessing in the case of a low diffusivity of the 
target surface. 5.a: Image of the acquired pattern after the linear normalization; 5.b: Effect of the 
nonlinear preprocessing. 
Figs. 6 and 7 show the performance of the algorithm for profile reconstruction, in the case of the elaboration of the 
images in Figs. 4 and 5 respectively. In the experiment of Fig. 6 the geometric system parameters are L-5m and 
d=1m, while the profile in Fig. 7 has been calculated for L= 1m and d=0.3m. 
„AXIS MM 
X-AXI “An 
786 393 SN 
    
300 
300 
   
Z-AXIS mm 
150 
    
    
  
750 
42-4008 mm 
; 
e 
rM, 
; 
a ar 
2, 
I 
17) I Uy 
   
    
  
  
7, 22 ( 
I P 
AMA 
ORS 
  
  
  
      
      
    
        
   
  
  
     
P 
e Fo [ 4, ^ e 
TY TB 
"s IRI) 
OS + 
Q + us 
>> 
Fig. 6. Profile calculated by elaborating the Fig. 7. Profile calculated by elaborating the image of 
image of Fig. 4. Fig. 5. 
3.2. Analysis of the systematic errors and calibration of the system 
A study of the systematic errors has been performed (Biancardi et al., 1995). The influence of the inaccuracy in the 
estimation of parameters L, d and p on the measurement error has been investigated in order to (i) understand the 
criticality of the parameters involved in the measurement, (ii) provide some means to estimate the measurement error 
for a system of given set-up parameters, and finally (iii) provide suitable compensation procedures, to be used during 
the system calibration phase. The analysis performed shows that the height error of the coordinate z(x,y) is markedly 
influenced by the error made in the evaluation of the actual value of the period p used for projection, while the effect of 
errors on the estimate of parameters L and d, is two orders of magnitude smaller. This behavior suggests that, during 
the system calibration, it is possible to even markedly decrease the height error, simply by finely varying the estimate of 
p. 
Calibration is performed by using a master object, similar to that shown in Fig. 4. Thirty-six points have been selected 
on its surface. A Contact Measurement Machine (CMM) has been used to measure the master in correspondence to 
this set of points. A suitable procedure allows us to compare the profile of the object, as it is evaluated by the optical 
profilometer, with the measurements obtained by means of the CMM. In our system, parameters L and d are 
measured to the desired accuracy during the set-up phase of the system, before calibration. During the setup, the 
estimate of the parameter p is determined by a suitable algorithm. The resulting value is used as an input for the 
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop "From Pixels to Sequences", Zurich, March 22-24 1995 
  
f^ 
^