108 
choice of the projection distance. As the 
depth of the test field increases, the correla- 
tion between the principal distance and the 
projection distance diminishes and the pre- 
cision requirements become more severe. 
This is of importance for close-range pho- 
togrammetry because the depth of focus is 
very narrow for imaging distances of 2—1 m 
or less (see Figure 1). Consequently, the 
depth extension of an object is severely 
restricted and the accuracy requirements on 
the parameters of inner orientation need not 
be so high. Therefore it seems unrealistic to 
demand special metric cameras for such 
short imaging distances. 
The computed tolerances are surprisingly 
large for narrow-angle cameras whereas they 
become very strict for wide-angle and super- 
wide-angle cameras. The precision of the 
principal distance should be on the order of 
+ 0.1 mm for the Hasselblad camera with 
Planar 1:3.5/100 (c = 100 mm, s = 27 x 27 
mm) whereas the tolerance for a wide-angle 
camera like the Zeiss TMK (c = 60 mm, s = 8 
x 10 cm) gets reduced to + 25 jm for film (0, 
+ 10 um). The corresponding values for glass 
plates (o, + 3 um) are smaller by a factor of 3 
and would be + 30 um for the Hasselblad and 
+ 8 um for the TMK. Therefore, it should 
be recommended that non-metric cameras 
are mainly applied with narrow opening 
angles and, consequently, long focal lengths. 
The precision requirements for wide-angle 
[um] T AH' 
500 
200 
150 
    
70 
50 
30 
15 
; =85# 
-105£ 
; 
Voo noo ET MA Var 82/2 
Fic. 3. Tolerances for the mean square coor- 
dinate error of the principal point according to a 
simulated camera calibration. The measuring 
precision in the picture has been assumed to be 
To = € 10 um. ais the angle under which the test 
field is seen from the camera. 
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1976 
cameras are on the order of + 10 to + 30 um 
for film and + 3 to + 10 um for plates. These 
tolerances are very narrow and it seems 
doubtful whether these values are always 
met by metric cameras. 
LENS DISTORTION 
The principal distance and the location of 
the principal point are liable to certain 
changes from photograph to photograph. 
These variations are caused by erroneous 
positioning of the plate or film during expo- 
sure. The lens distortion should not be influ- 
enced by this effect. Nevertheless the lens 
distortion determined by a camera calibra- 
tion might show considerable differences 
when the calibration procedure is repeated. 
This is due mainly to a superposition of the 
lens distortion with various other imaging 
errors such as atmospheric refraction, film 
shrinkage, or lack of flatness of the image 
plane. In general the symmetrical lens dis- 
tortion can be separated by a study of the 
reproducibility. The precision of the distor- 
tion curve should be at least of the same order 
as the measuring precision. 
An extension of the mathematical model 
for affinity or for the tangential and asym- 
metric lens distortion should not be neces- 
sary for small- or medium-format cameras! 7. 
The only exception would be for the princi- 
pal point of symmetry, and it is advisable to 
control its location in a camera calibration. 
This point is defined only for lenses with a 
noticeable distortion (more than + 5 to + 20 
pm). The precision of this point determined 
by a camera calibration varies from + 1 mm 
[u m]T AC 
500 
  
      
300 
200 
=105# 
        
1 AZ/Z 
20 Yio V; Va a 7 
Fic. 4. Tolerances for the principal distance.