METRIC OR NON-METRIC CAMERAS 
for a nearly distortion-free lens (Topogon 
with ancillary lens and a maximum distortion 
of about 5 um) to + 0.2 mm for the Planar 1: 
2.8/80 mm lens (maximum distortion about 
0.4 mm). The definition and the reproduci- 
bility of the principal point of symmetry 
should not cause any problems in a pre- 
calibrated camera as the tolerances are con- 
sequently rather large. 
REPRODUCIBILITY OF THE ELEMENTS OF 
INNER ORIENTATION 
The investigations have shown that the 
tolerances for the parameters of inner orien- 
tation are not uniform and that they depend 
on various factors. Especially for long focal 
lengths the tolerances are very large and it 
seems possible that these values could be 
met even by non-metric cameras. In a photo- 
graphic camera the position of the image 
plane is defined by optical conditions. If the 
photographic material deviates from its pre- 
scribed position, then the image quality 
might deteriorate. For the estimation of tol- 
erances again the circle of confusion can 
similarly be used as for determination of the 
depth of focus. For this computation the 
largest possible aperture stop should be 
taken into account. For the Hasselblad cam- 
era with the Planar 1 : 2.8/80 mm lens a circle 
of confusion of 30 um is already reached by 
a displacement of the image plane of 84 um 
for the aperture of 1:2.8. In this case an 
object point at the nominal focusing distance 
would be out of focus. From a statistical point 
of view this deviation should not be reached 
in 95 per cent or even 99 per cent of the cases. 
The calculated tolerances for the principal 
distance have been standard errors (with a 
significance level of 68 per cent). Conse- 
quently, the standard error for the position- 
ing of the picture plane should be only one- 
half or even one-third of the computed tol- 
erance: that means + 30 to = 40 um. 
A positioning error of the image plane in 
general also will affect the location of the 
principal point (see Figure 5). With some 
simplifications the displacement of the prin- 
cipal point can be computed. For the deriva- 
tion of a mathematical relation it is assumed 
that the photographic material is completely 
flat and pressed with its edge against the 
frame of the camera. Due to imperfections of 
the contact surface the plate has a varying 
distance (Ad,,Ad;) to the upper and lower 
edge of the camera. From these differential 
values the error of the principal point and the 
principal distance can be computed. 
109 
Ac = Ady + Adi 
aA 
AH = € (Ad, - Ad) (3) 
The distance between the two contact 
points is s and should coincide with the 
diagonal of the plate format. For the compu- 
tation of the variances the differential values 
Ad, and Ad, have to be replaced by their 
standard deviation mg. According to the law 
of error propagation one gets the following 
relations: 
m, TA my = s 7 (A) 
Thus 
my = 2: me (5) 
The computation becomes more complex 
if itis taken into account that the film or plate 
in the camera does not form a plane but has 
the shape ofa cylinder or an arbitrary, higher- 
order surface. Therefore the formula can give 
only a rough approximation and indicates a 
certain ratio between the reproducibility of 
the principal point and the principal dis- 
tance. For the Hasselblad camera equipped 
with the Planar 1:2.8/80 lens one would ex- 
pect an accuracy ofthe principal point of + 60 
to + 80 um according to the assumed vari- 
ance of the principal distance of + 30 to + 40 
um. This computation coincides fairly well 
with the practical experiences in camera cali- 
bration*$ (see Table 1, Columns 5,8). The 
  
  
d gi ul, wd 
ada | "mam En Lal i ; L : J 
bec rp wow adi 
——L 5 a 
pue mm V 
Fue ET au 
| NE 
i= s > 
  
Fic. 5. Falsification of the principal point and 
the principal distance by an erroneous position- 
ing of the photo plate (AH, Ac errors of the 
principal point and the principal distance; Ad,, 
Ad, displacement of the edge of the plate from 
the camera frame, and a tilt of the plate).