In order to determine the corrections to the image coordinates of an arbitrary 
point, (x, z) the equations (1) and (2) are used, in which the expressions (8) 
through (13) are substituted. The geometrical quality of the corrections can 
be obtained from application of the general law of error propagation to (1) 
and (2). 
Hence 
2\2 
x^ (c* + xy^ 
Qdxdx Qxqxq ~^2,Qcc "b ^ Ôkk ^2 Qipcp 3 ^2 
■Qo 
2 (c 2 + x 2 ) 
»H Qx 
(22) 
2 2 
X z 
Qdzdz=Qz 0 z 0 + 'pQcc + X Qkk+- c 2 
■Q, 
+ ^l Q 
» ' 2 ^0 
2(c 2 + z 2 ) 
,+- Qz 
(23) 
After substituting the expressions (17) through (21) and using the weight 
number 1 for the measured coordinates to be corrected, the following weight 
numbers of the corrected coordinates are obtained 
_3 x 
QvxVx = 2 + 4a 
3 z‘ 
'2 + 4 a 
3x 2 x 2 z 2 z 2 
8a 2 4a 4 8a 2 
(24) 
3z 2 x 2 z 2 x 2 
8a 2 4a 4 8a 2 
(25) 
The standard errors of the corrected image coordinates are then found from 
s jc = SoV6^Z ^ 26 ) 
S Z = S 0 yQv z v z ( 27 ) 
The expressions (26) and (27) can be plotted graphically for a presentation 
of the distribution of the standard errors. 
A mean value can be determined for x from 
M 
Sx 
So_ 
(X2-Xi)(z 2 -Zi) 
Z 2 
Q VxVx dxdz 
z 1 
A mean value can be determined similarly for z. 
(28) 
After integration the mean value over the area 2 a times 2 a is found to be 
M Sx =1.22s 0 = M Sz (29) 
Similarly the geometrical quality of the interpolated image coordinates can be 
determined for any arbitrary number and location of the stars. The standard 
error decreases with an increase in the number of stars, but the successive