X=Xx-P1x 
X Zx-P2eX e Y e 1.0E-6 
X 2x-P3eX e Y e Y e 1.0E-6 
X 2 x- P4 e SIN(X e 1/90.) 
X 2 X - P5 e SIN(Y e 1/90.) 
X 2 x- P6 « COS(X e 1/90.) 
X 2 X - P7 « SIN(Y e 71/90.) 
X 2 x- P8 «e COS(X e 1/45.) 
X 2 X - P9 «e SIN(Y e 1/45.) 
X 2 x- P10 e SIN(X e 71/45.) 
X 2 X - P11 «e SIN(Y e 7/45.) 
X 2 x- P12 « COS(X e 1/22.5) 
X z X- P13 «e COS(Y e 71/22.5) 
X' 2 x - P14 e (X - INT(X/12.288) - 6.144) 
  
Table 1: set of 
formulas for the 
separation of 
Systematic errors 
  
  
  
  
  
  
The set of formulas shown in table 1 has been used for 
the separation of systematic errors. A corresponding set 
of formulas has been used also for y-component. This 
strategy is corresponding to the determination of 
systematic image errors in the block adjustment with 
selfcalibration by additional parameters. The same 
statistical tests like used in program BLUH have been 
made (Jacobsen 1982 and 1984). 
The scanner was tested several times over a longer time 
period. Up to the replacement of one friction drive the 
systematic errors have not changed. But the change of 
  
the friction drive by the Institute has had a strong 
influence to the geometry as visible in the comparison of 
figure 3 and 4. Before the replacement the original 
discrepancies at the transformed reseau points have 
been +4.7um (+4.2um without the influence of the manual 
measurement). This value can be splitted into a random 
part of +2.9jm and a systematic part of +3.0um. After the 
change, the total effect has reached +6.8um based on an 
automatically point determination of 11 507 points, which 
can be explained as +6.3um systematic part and 2.7um 
random part. (see figure 4). The large size of the 
systematic errors have been caused by lubricant on the 
reference rod for the x-direction. After cleaning the rod, 
the total mean square error was drastically reduced to 
+3.3um at 11708 reseau crosses. This small size again 
can be splitted into +2.6pm systematic error (figure 6) 
and +2.0um random error (figure 5). Of course the 
systematic error can be used for an improvement of 
determined image coordinates, but in the case of such a 
small size, corresponding to the accuracy of analytical 
plotters, the meaning is not so important. 
Together with the determination of the systematic errors, 
the rotation of the sensor line against the scan direction 
and the fitting of the swath width to the spacing between 
neighbored scans can be computed by the parameter 14. 
It was possible to reduce the remaining error to 
approximately £1um. 
  
  
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Figure 3: T results of the RM1 calibration 1 [vector scale 10um] 
random part 
systematic part 
  
  
by lubricant on rod 
Y results of the RM1 calibration after replacing the friction drive + 
Figure 4: discrepancies influenced Figure 5: random part after cleaning 
Figure 6: final systematic errors 
  
  
  
  
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