greater than 90° could only be obtained with a strong negative image displacement.
Disregarding the small importance of such lenses for cartographic purposes, develop
ment along these lines must lead to a dead end because it is based on a false assumption.
If instead of following the theoretical approach to the question of loss of illumination,
one determines the principles experimentally, he finds that the accepted views on
“natural loss of illumination” are inadequate. Certain justified doubts about the
cosine fourth law were recently expressed by E. Wandersleb 3 , without, however,
clarifying the problem.
He first accepts the validity of the purely geometric cos 4 a law for distortion free
objectives, but remarks that in many objectives with vignette free small diaphragms
more light is admitted at small angles than along the axis itself, and the illumination
only falls off at greater angles. The deviations given in the examples are very small,
but they lead him to an additional correction factor which depends upon the con
struction of the objective, and which in certain circumstances, may be greater than
one. He calls this correction the “Vignetting factor”. Wandersleb explains certain
observed anomalies by linking them up with vignetting, but the true solution remains
incomplete. Part of the phenomena covered by his correction factor have in reality
nothing to do with the conception of vignetting. They are only a function of the lens
combination because a true vignetting factor must never be more than one. Moreover,
his description does not show that it is possible to construct an objective which can
be advantageously freed from the cosine fourth law over the whole image area without
introducing negative image displacement 4 .
It is surprising that except for a few short remarks in Russian publications 5 theoretical
optics has not yet given a satisfactory explanation of the loss of illumination or a
concrete possibility for reducing it. This is in spite of the fact that 50 years ago
Steinheil designed a lens of small distortion in which the illumination loss was notice
ably less than that given by the cosine fourth law 6 .
Fig. 1 Steinheil objective — English
patent 21211 from year 1901.
3 E. Wandersleb. Tücken der Cosinuspotenzen und der Austrittspupille in der Lichtverteilung
über das Bildfeld des photographischen Objektives. Z. f. wissenschaftliche Photographie,
Bd. 46, Leipzig 1951.
4 In this connection the article by W. Uhl: Die natürliche Vignettierung von Photoobjektiven
bei beliebiger Blendenlage, Optik 1951, is worth reading.
5 G. Slussarejf. L’eclairement de l’image formée par les objectifs photographiques grand-angu
laires. Journ. Phys. USSR, 1941.
A. E Shersheni. Aerofotosjemka, Moskau 1949.
6 This objective is described in the English patent Nr. 21211 in the year 1901.
