The amount of light concentrated by the lens on each elementary area of the image determines its brightness or illumination. The ideal image would, of course, be equally bright over its whole area of good definition, and for lenses of narrow angle this is approximately true. But when it is desired to cover a wide angle the question of illumination becomes serious. The relationship between angle from the axis and illumination is that illumination is proportional to the fourth power of the cosine of the angle. This relationship is shown in the following table:


Image brightness

100 per cent.


94.1 per cent.


78.0 per cent.


56.2 per cent.


34.4 per cent.


17.1 per cent.

If the field of view is 60°, which corresponds to an 18X24 centimeter plate with a lens of 25 centimeter focus, the brightness is only 56 per cent., and the necessary exposure at the edge approximately 1.8 times that at the center. This effect is shown in Fig. 15. It is very noticeable if the exposure is so short as to place the outlying areas in the under-exposure period.

Barrel and pin cushion distortion.

Fig. 13. - Barrel and pin-cushion distortion.