5 
Deformation of the distorted model by manufacturing errors 
Proceeding from the mathematical-geometrical model of 
perspective projection, we have so far considered those 
deviations only that occur in the physical and optical realiza 
tion of such projection and represent system errors. These 
considerations based on the assumption that it might be 
technically possible to manufacture an optical system exactly 
to* the physical design concept. This assumption actually is 
wrong. Although optical instrument manufacturers are able to 
keep inaccuracies within tolerances as narrow as, a light 
wavelength, the accumulation of such inaccuracies in a multi- 
-component optical system will result in appreciable deforma 
tions of the imaging model described. Practical experiments 
with a photolens will therefore reveal a superposition of the 
different influences involved. Attempts at determining the 
effective imaging function for a certain photogrammetrie 
camera lens in one azimuth only from the optic axis will fail. 
If the test is repeated in several azimuths, results may 
contradict each other in a relatively high degree, especially 
fpr modern high-performance photogrammetrie lenses having 
low absolute distortion (Pig. 3). 
Asymmetric deformation 
Investigating the image of a grid of equal geometrical spacing 
arranged symmetrically about the optic axis will generally 
reveal dislocations of the image points, to which a radial 
and a tangential component, referred to the image centre, 
may be ascribed. As an effect of the radial component, imag 
ing rays incident at equal angles to the optic axis are asso 
ciated to different distances in the image plane (measured from 
the intersection point of the optic axis to those of the 
respective imaging rays), depending on the azimuth. The 
radial component corresponds, in effect, to an accidental 
tilt of the camera when taking the photograph of the test 
object. Consequently, it should be possible to compensate