(
0
2
between 0.4 mm and 7.2 mm, as well as the change of the
position of the principal point relative to the image
coordinate system do not exceed 0.04 mm in the most
unfavourable case.
For the change of the calibrated focal length Ac, with
distance setting there exists with reference to Fig. 2
the following linear functional dependence on the prin-
cipal distance change Aa':
Ar! ;
Rep At den © za ude’ (1)
In Fig. 2 H and H' mean the nodal points of the lens
and P and P' the positions of the entrance and exit pu-
pils. The calibrated focal length is normally fixed in
such a way that for a certain image radius, viz. the
zero radius of distortion, the projection beam in the
image space is parallel to the principal ray in the
Object space passing through the centre of the entrance
pupil which is effective for this principal ray. For
' the UMK the zero radius of distortion was fixed to be
TE = 72 mm, which corresponds to an inclination angle
ot the principal ray of about 40 gon.
2.2.2. Distortion and other image deformations
The rotation-symmetric distortion varies with changing
distance setting according to
Artzı = Ar -B8', À rt, (2)
By calibrating the camera one obtains, however, only
the quantity Ari, For other distance settings with
image magnifications B' > O additions have to be
applied according to the second term in (1), which were
determined in the optical-geometrical calculation of
the lens. They refer to the primary colour e. As is
apparent from Fig. 3, the deviations for the primary
colours C and F are in the most unfavourable case at
i BF = 0,072 generally smaller than 1 gun and only in the
region of the image corners they reath values of 1.1 Jum
and 1.4 Jum, respectively .
As has already been pointed out in /3/ manufacturing
deviations for Ar}, are expected to be of the same
order of magnitude âs for Ar! due to the quasi-sym-
metric design of the Lamegon 8°/100, so that in view of
existing close manufacturing tolerances such deviations
remain below 1 um even for the largest image magnifica-
