y- 2279, 
> Py 
where p;; is the intensity value of the pixel located in row i and 
column j. 
Asymmetric effects can be reduced by adding a weighting 
factor equal to the intensity value of the pixel. Also a correct 
threshold value for the particular target size and level of 
asymmetry will eliminate the systematic errors (Trinder, 1989). 
The threshold value T is estimated from: 
T = 74 (SF)? A" (3) 
where SF is the 26-width of the spread function and A the 
target size. 
In the same investigation it is stated that if the targets are larger 
than 4x the 26 width of the spread function and the correct 
threshold value is used, the systematic errors of target pointing 
will be less than 0.02 pixel. This result corresponds to an 8 
bits/pixel quantisation and the reduced resolution in our system 
will deteriorate the results as mentioned earlier. 
To investigate the precision of the target location in our system 
a sequence of 32 measurements of the 108 targets on the 
calibration frame were taken. The results indicate a pointing 
precision of 0.170 pixel in x-direction and 0.225 pixel in y- 
direction. A possible explanation of the larger deviations in y 
is the reduced resolution in the y-direction because only one 
video-field is used. Otherwise the deviation in x should be the 
largest because of line-jittering. 
3.6 Calibration. 
The task of the calibration of the system is to estimate the 
interior and exterior orientation of the cámera. Since we are 
doing an on-the-job calibration, both orientations can be 
performed in the same adjustment. We must consider a system 
as consisting of two cameras with imaginary positions and 
rotations because of the mirrors and split-image arrangements. 
Figure 7 shows the geometry of the imaging system. 
The two halves of the sensor form the two images of the 
imaginary cameras. The interior orientation denotes the 
estimation of the parameters in the functional camera model. 
The functional model of the system describes the imaging of an 
object point past the mirrors, through the lens with its 
distortions and onto the sensor. The accuracy of the system 
depends strongly upon the model chosen and how well this 
model suites the real conditions. Kilpelä (1981) proposes a 
number of different parameter sets to be used to extend the 
pinhole model given by the perspective equations. Our 
formulation of the functional model is a variant of the "physical 
model" from that paper extended with parameters to help 
describe the mirror distortions. Our model then includes 
additional parameters for affinity, lack of orthogonality, radial 
and decentering distortions in addition to mirror distortions. 
Another possible method used to describe the influence of the 
mirrors is the use of mathematical surfaces, i.e. B-splines 
(Amdal, etal, 1990). This would possibly model the local 
anomalis in a better way, but require a larger set of datapoints 
in our calibration. 
   
  
   
  
  
  
   
  
  
  
  
   
   
  
   
  
  
  
  
  
   
  
  
  
  
  
  
  
  
  
   
  
  
  
  
  
  
  
  
   
  
  
  
  
  
   
  
  
   
   
    
  
  
  
  
  
  
  
   
imaginary 
€————————— camera |—— — — — —3À 
positions 
  
  
  
  
  
  
  
  
  
  
  
Figure 7. Geometry of the imaging system. 
The functional model used in our system is given in equations 
4 to 7, where: 
X,y : Observed image coordinates. 
Xo»Yo : Center of the frame memory. 
Xy : Undistorted image coordinates, corrected for 
distortion effects. 
X,Y,Z : Object coordinates of an imaged point. 
X,,Y,,Z, : Object coordinates of the origin (projection center) 
of the camera. 
f : Focal length of the camera. 
r : Distance from (x,y,) to (x,y.). 
r : Elements of the rotation matrix. 
b,..,b, : Parameters describing the distortions.