(245) 
Let e be the ratio E a to the brightness in an axial direction E 0 . This will be: 
E« Q « 
e = 7, = 71— • cos 4 a 
E 0 Q„ 
e = q • cos 4 a 
In connection with this formula, a fourth power of the cosine “law” is 
often mentioned. Yet, this is totally wrong; for QT, too, is a function of a, 
and the decisive element in the brightness in each case (Q' a ‘ cos 4 «). 
Factor “q” is wrongly called a “vignetting” factor. Yet, the expression 
used not only contains the “vignetting”, but also the behavior of the principal 
ray through the lens. Unfortunately it is erroneously thought that q must 
needs be smaller than 1. 
The Wild Aviogon provides an example of a lens in which q can actually 
become larger than 1 at a suitable angle of incidence. The bundless of rays 
entering the lens laterally are refracted in the front part of the lens, so that 
their angle of incidence to the optical axis is reduced. Thus, they enter the dia 
phragm under this smaller angle of incidence. For this reason, the diaphragm 
allows a wider beam to pass than would be the case if the bundless of rays from 
the sides passed through the diaphragm under their initial angle of incidence «. 
Fig. 12 shows a number of original pictures of pupil size Q'« for various 
diaphragms, taken with the Wild Aviogon Prototype. The amazingly fast 
increase for Q'« can be seen particularly well for small diaphragms; these 
pictures show clearly that the distribution of illumination does by no means 
obey a so-called “cos 4 ” law. If this were true, all bundle cross-sections would be 
circular and of equal size. However, this is true only of lenses having a front 
diaphragm. The adumbration of the entrance pupil by the lens sleeve, thus the 
“vignetting” is noticeable for the greater angular openings where a 1 : 5.6 
diaphragm is used. 
For better comparison, q is entered in Fig. 13 as a function of the image 
radius, q = 1 = constant would correspond to a simple lens with a diaphragm 
in front of it, without any vignetting. Thus, Fig. 13 will permit to evaluate 
the gain in illumination power of the Aviogon, over a lens having a diaphragm 
in front of it. 
Fig. 14 shows the relative illumination power e = q • cos 4 a for various 
diaphragms. For the purpose of comparison, the value of cos 4 a is shown. This 
would be the illumination of a lens with q = 1, thus of a lens with a diaphragm 
in front of it. 
The q and e values for wide angle lenses of the types formerly used are 
given in Figures 15 and 16, in order to exemplify the high degree of improve 
ment achieved by the Wild Aviogon. The figures are self-explanatory. 
The test data given above show that theoretical expectations, based on the 
calculations, have been met in full. By this, we are able to judge the high quali 
ties and the extremely precise and uniform manufacture of the Wild Aviogon 
a fact which is particularly important to the practical photogrammetrist.