could successfully be applied for description of the radial part of 
the function. 
For a least - squares adjustment, error equations are written as follows 
Le V4 51 (cos o); €4 * J4 Cp 
or Mi ài C1 * D. Cp = Li 
The unknown parameter c, signifies a factor, which adapts the cosine 
function to the microdefis tometer profile, whereas c, describes the 
linear part of the light fall - off as a function of the y - coordinate. 
For each image 100 error equations exist to determine the two unknowns C1 
  
  
  
  
  
  
  
| and C5. 
| Function l - cosa l/cosi-1 1 - cose 1/cosa-1 1 - Cos 
| el 1,0892 | 0,8665 | 0,8458 1 0,6229 | 0,7000 
| Cy 0,0019 0,0019 0,0019 0,0019 0,0019 
f = 1:5,6| m, (D) + 0,0282 | + 0,0197 | + 0,0297 1 + 0,0185 | + 0,0312 
cq 0,8822 0,6963 0,6858 0,5000 0,5683 
Co 0,0014 0,0014 0,0014 0,0014 0,0014 
f=1:8|m (D)| + 0,0193 | + 0,0203 | + 0,0195 | + 0,0210 | + 0,0198 
  
  
  
  
  
  
Table 1: Results from least - squares adjustments 
  
  
  
The results of the adjustment are summarized in Table 1. m, is the 
| weighted root mean square error, computed from the residuals which con- 
sequently signifies the accuracy of the procedure. Hence for f : 5,6 we get 
- 1 
D, = ( 
| - 1) 0,6229 + y 0,0019 
| COS a ) [ mm] 
and for f = 1 : 8 we get 
D - (1 - cos 0°) 0,8822 + y [mj 00014 
a 
as the best fit. The root mean square errors of c, are all below 
+ 0,0035, those of C, are all below + 0,00006. Thére exist no correlation 
between the unknowns. 
Obviously there is a steeper light fall - off for f = 1 : 5,6 than for 
f = 1 : 8, but the difference is only about D = 0,05 at the maximum 
(a = 25 9). Even less is the difference between the particular functions: 
AD = 0,02 for f 1: 5,6 and AD = 0,015 for f.« 1: 8, both at a = 17 0. 
For many practical applications an appropriate mean function will be 
sufficient.