15 
Projector 
s o 
dt 
Tolerance 
dl 
Tolerance 
micr. 
micr. 
micr. 
micr. 
micr. 
Left 
7.2 
-32.3 
±28.5 
+ 32.3 
±28.3 
Right 
5.9 
+ 21.8 
±23.4 
+ 36.2 
±23.2 
The tolerances are exceeded in three out of four cases and mechanical adjust 
ment is necessary. The basic accuracy is considerably lower than in the new 
instrument. 
Flatness of Surfaces. 
The determination of flatness is a common problem in photogrammetry 
which has to be solved by measurements. Tolerances for the deformations of 
surfaces have to be established and must be checked. The measurements can 
never be made free from errors and therefore it is of importance to determine 
theoretically the tolerances for the deformations which may be caused by the 
irregular errors of the measurements only. In Hallert 1960 a some principles of 
such a tolerance determination have been discussed. The surface to be tested 
is assumed to be measured with a device of which the standard error of unit 
weight is known from special calibration measurements. The elevation differ 
ences of the surface are expressed in relation to a plane through three suitably 
located points. The standard errors of the elevation differences from this plane 
have been computed according to the laws of error propagation and then the 
differences are to be compared with their own standard errors. The /-test then 
gives the tolerances for the deviations from the ideal value zero which may be 
caused by the errors of measurement only. The elevation differences have to 
be larger than these tolerances in order to be regarded as significant. 
As shown in Fiallert 1960 a there is a variation of the standard errors over 
the surface. With a minor approximation a mean value of the standard errors 
over the surface can be used. This value is 
M s = 1.3JQ 
where 5 0 is the standard error of unit weight of the basic measurements. It 
must be determined from calibration measurements. 
The tolerances are then to be determined with respect to the degrees of free 
dom in the determination of this standard error of unit weight and for a 
specific level. If 25 points are used for the calibration there are 22 degrees of 
freedom. The level is usually chosen at 5 percent. A /-table then gives the t p - 
factor 2.1 and the tolerance limits consequently become 
+ 2. 7Sq