where the following is given information; 
x°, y$ : observed sensor coordinate of a LED 
(target point) on the Light Pen, 
f . calibrated focal length of CCD camera, 
3D coordinates of a LED (target point) 
on the Light Pen in the local 
coordinate system of the Light Pen, 
. camera calibration corrections to the 
dx, dy 
primary sensor observations, 
and these six parameters are estimated in the adjustment; 
X,5 Yo ZS: origin of the camera coordinate 
system (perspective center of camera) 
as referenced to the Pen coordinate 
system (three unknown coordinates), 
three unknown rotation angles defined 
by the nine elements in the rotation 
matrix, 
With six LEDs on the Pen, there is a redundancy of six 
observations (twelve observations, six unknowns) for each 
measured object point. Equation 1 is linearized and solved 
in iterations, using the redundant observations to perform 
a least squares adjustment (bundle adjustment) on the 
sensor observations. The camera position as referenced 
to the local coordinates system of the Pen is estimated in 
the adjustment. The reverse transformation, that is the Pen 
position as referenced to the camera coordinate system, 
is then easily found. 
Approximate values for the unknown parameters, which 
are necessary for the iterative solution approach, are 
found using simplified computations together with "rules 
of thumb". 
The points on the Light Pen do not contain enough 
information to perform a successful camera calibration 
through the bundle adjustment. Therefore, to obtain a 
favorable accuracy, the SCS has to rely on precalibrated 
(laboratory calibrated) cameras. 
4. Accuracy Characteristics 
An important feature of any metrology system is the mea- 
surement accuracy. To indicate the accuracy potential of 
the SCS and also to find a favorable Light Pen geometry, 
simulation studies have been done. The studies have 
primarily been focused on measurement precision 
(repeatability). 
The 3D point determination is based upon the 
observations of a given pen geometry in only one camera, 
and not on the intersection of rays between cameras with 
known relative orientation. Therefore, the accuracy 
characteristics is quite different for the SCS compared to 
a dual- or multi-camera system. Higher accuracy is 
achieved in the XY plane (lateral and vertical axes which 
are parallel to the CCD sensor inside the camera) than in 
Z direction (along the depth axis which is perpendicular to 
the CCD sensor). Accuracy is a function of camera 
characteristics, camera to object distance and geometry 
of the Light Pen. In the simulation studies, the sensor 
observations have a noise level (0 value) of 0.015 pixels. 
The simulated Light Pen is equipped with six LEDs and 
has a total length (y) of 800 mm, and a depth (z) of 200 
mm. 
Table 1 shows simulated repeatability results for different 
camera to object distances. 
  
  
  
  
  
  
  
  
  
  
  
Distance [mm] | o X [mm] | o Y [mm] | e Z [mm] 
2000 0.013 0.013 0.05 
4000 0.026 0.026 0.18 
6000 0.037 0.033 0.41 
8000 0.052 0.052 0.79 
10000 0.066 0.066 1:25 
15000 0.091 0.091 2.65 
  
  
Table 1: Simulated repeatability results for SCS 
To verify the simulation results several experimental mea- 
surement test have been done. Table 2 shows the results 
from a repeatability test for various camera to object 
distances. 
  
  
  
  
  
  
Distance [mm] | o X [mm] | © Y [mm] | e Z [mm] 
2000 0.006 0.005 0.05 
4000 0.020 0.016 0.13 
6000 0.025 0.025 0.26 
8000 0.037 0.038 0.54 
10000 0.111 0.058 0.87 
  
  
  
  
  
  
Table 2: Experimental repeatability results for SCS 
There is a good correlation between the simulated and the 
experimental results. With the exception of one of the 
results for the longest distance, the experimental results 
are slightly better than the simulated. This indicates that 
the simulated o level of 0.015 pixel on the sensor 
observation is too high for optimal conditions. 
An other experimental measurement test was done to find 
the accuracy of surface measurements. 50 points were 
measured on a certified plane (plane better than 0.001 
mm) of size 200 mm X 500 mm. The optical axis of the 
camera was aligned to be approximately parallel with the 
plane. The SCS measurements were fitted to a 
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