cosine to the fourth law

Definition: The brightness of the image away from the optical axis falls off at a rate proportional to the cosine to the fourth power of the angle the light makes to the perpendicular at the focal plane.
Darkness at the edge
In a super wide-angle lens, the fall-off can be more than two stops i.e. the periphery is darker than the centre by two stops -- unless corrected. This may take the form of optical tricks such as carefully introduced coma. Oddly, lenses with the widest of views -- fish-eye lenses -- are immune from this law and that precisely because of their curvilinear distortion.

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