The Loss of Illumination with Wide Angle Objectives 
by H. Kasper, Heerbrugg 
The question of the loss of illumination in the margin of wide angle photographs is 
often discussed in optical and photogrammetric literature, but frequently with er 
roneous conceptions and remarkable lack of clarity. It is usually accepted, or demon 
strated geometrically, that in objectives with small image deformation, the illumina 
tion varies with the fourth power of the cosine of the angle between the incident ray 
and the optical axis, disregarding the influence of vignetting of the lens margins. 
This law, representing “the limit which according to physical laws, cannot be ex 
ceeded”, is defined as the “natural loss of illumination” 1 . This hypothesis of illumina 
tion varying as the cosine fourth has led to a number of deductions which have 
retarded in many ways the development of photogrammetric wide angle objectives 
during the last decades. 
Instead of trying to develop new distortion free objectives with better light distri 
bution, at first attempts were made to compensate, or at least to reduce, the loss of 
light in existing objective types with special filters before or behind the lens 1 2 . 
These filters reduce the light in the center of the photograph so that the emulsion is 
exposed uniformly over the whole area. Because aero emulsions can accommodate a 
40 % difference in light intensity, the filter must only compensate for the remaining 
part of the loss of illumination. In spite of this fact, the disadvantage of the system is 
evident. When the illumination in the center is reduced by half, the effective aperture 
of the lens is reduced by the same amount. 
Secondly, it was thought that the angular coverage of objectives with small distortion 
must he limited to about 90°, as otherwise the light intensity in the image corners 
would be insufficient. 
Thirdly, the hypothesis of the “natural loss of illumination” varying with the cosine 
fourth led to the assumption that a better light distribution for lenses with coverage 
1 See, for example: C. A. Traenkle. Die Belichtungszeiten bei Luftbildaufnahmen. 
Z. f. Instrumentenkunde, 1938, p. 243. 
2 See, for example: M. Nagel. Ausgleich des Lichtabfalles in der Bildebene von Weitwinkel 
objektiven. Optik 1951, p. 24. Also see P. A. Tate. Illumination in the Focal Plane of Aerial 
Cameras, Photogrammetric Engineering, 1951, p. 19.