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When more light reaches the centre of the negative than the periphery the result is an image that is bright in the centre but fades off towards the corners; a vignette. Vignetting is inherent to most lenses (especially lenses with a wide angle of view). It becomes most apparent when the aperture is wide open, but will disappear when it is a few stops down from maximum.
The effect of this “light fall-off” will largely go unnoticed but is most often visible when the subject being photographed has large areas of even colour and brightness.
The fall-off can be approximated using the cos4 or “cosine fourth” law; a formula indicating that the image brightness will fall off at a rate proportional to cos4 of the angle off the lens axis.
For example: A 45mm lens typical of one of our rangefinders has a 51.4º AOV, so the corners are 25.7º off-axis. Cos 25.7º = 0.9011, which to the fourth is 0.66. This means the corners get 66% of the amount of light that the centre gets, which is less than a full stop. A full stop less would be a 50% reduction of light (see Double & half).
In a very wide-angle lens, the fall-off can leave the periphery 2 stops darker than the centre. This can be corrected with a graduated neutral density filter which is clear at the edges and darker at the center, therefore leaving an even illumination on the film.
(The background image on this page was shot with the 48mm lens of the Konica Sii at maximum aperture f/2. Fall-off is evident in the top two corners as the sky was evenly lit.)
Lens - AOV - Fall-off
50mm - 46.8º - 71%
45mm - 51.4º - 66%
40mm - 56.8º - 59%
38mm - 59.3º - 57%