2 
tance s' to the image point P* from the point of intersection 
of the projection axis with the image plane is found by the 
simple equation 
s' = c • tan . (1 ) 
■ki the described imaging model of mathematical perspective 
projection, c is a constant applicable to any angle of inciden 
ce. 
Already in computing an optical imaging system it will be 
found that constant c in eq. ( 1 ) has to be substituted by 
O = P (Tp. (2) 
If c increases with increasing angles of incidence, all image 
points will be displaced outwards (away from the principal 
point H’) to an extent depending on the angle of incidence. 
Any straight line not intersecting the optic axis will 
necessarily appear in the image plane as a curve deflected 
towards the principal point. If, in the opposite case, c 
would decrease with increasing field angles, the images of ana 
logous object straightlines should be deflected in the opposi 
te way. The image of a square located symmetrically to the 
optic axis will in the first case have the shape of a pin 
cushion, in the second case that of a barrel. This pheno 
menon can be explained also by assuming a magnification vary 
ing with the ray's angle of incidence relative to the optic 
axis. Barrel distortion will occur at a collecting lens 
having its aperture diaphragm in front of it (Pig. 1). 
Refraction of the principal rays incident in the marginal 
zones, i.e. at a large angle from the optic axis, is pro 
portionally greater, which locally reduces the magnification. 
Similarly f pincushion distortion can be explained by a 
limiting aperture behind the lens (Pig. 2 ). In the case of 
axial-parallel rays extending from a test object, again 
those incident near the lens rim are refracted by a greater 
angle and consequently cannot pass the aperture. The aperture