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Disposing of certain number of collimators to materialize the principal beams (passing 
through pupil Z centre) to the different concerned inclinations. In the Fig. 15, where all the 
dimensions have been magnified, two inclinations are considered : 15? and 30? to infinity and to 
close range respectively, then first let us suppose lens L having no aberration. 
Position and dimension of the image are obtained in both cases by means of simple 
geometrical constructions. 
Now a very important detail makes clearly different the two considered cases. In fact 
when the object is to infinity, both centres (0 of the lens and z of the pupil) see the object from 
the same angles; thus the collimators materializing the principal rays passing through z must 
really have the considered inclinations of 15° and 30°. When on the contrary the object is placed 
at close range these angles change : the inclinations of 25° and 45° of collimators respectively 
correspond to the above said 15° and 30° ones. 
In other words, having the principal rays to pass always trough z, they may be conceived 
coming out from z, should it be a light point. Thus the geometrical constructions of the Fig. 15 
may be obtained conjugating z in z' through lens L. 
Then z sends a beam cone having a maximum aperture of 30° at the infinity, while for 
close range object, this aperture rises to 45°, Therefore lens L works under different conditions. 
Let us now suppose lens L is affected by a spherical aberration : a point z' does not 
correspond to z univocally but generally a caustic corresponds to z. 
Should we repeat the former constructions (see Figures 16 and 17), keeping into account 
that now z' is a variable function of the aperture according to the sketch as per the same figure, 
we note the principal rays cross the image plane in point different from those obtained when the 
lens L. was supposed having no aberration. 
e 4 Carrying these discrepancies according to the considered inclination, the distortion 
curves are obtained. The two distortion curves are different should the object is observed to 
infinity or to close-range under the same inclination. Just because lens L works under different 
conditions of aperture in comparison with pupil Z. 
Thus the distortion concept has been taken again to the spherical aberration concept of 
the pupil and the distance discrepancies have been transformed in aperture discrepancies. 
The above said theoretical and schematic idea is now explained by a practical example. 
Let us consider an usual '"six lenses' lens, quite symmetric, having a central shutter. 
The lens is formed by two outside doublets, slightly negative meniscus shaped, and by two inside 
positive meniscus. 
  
  
Fig. 16 - Infinity distortion 
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