D
Doug Kerr
Guest
In a photographic system, for a given object luminance (brightness), the image illuminance on the film or equivalent declines as we move outward from the center of the image as a result of the geometric optics involved. The result is a relative darkening of the image toward its borders. If we consider a lens having certain ideal properties, it can be shown that the decline in relative illuminance goes very nearly as the fourth power of the cosine of the angle by which the object point is off the camera axis (measured in "object space" at the center of the entrance pupil of the lens).
I have just released to my technical information site, The Pumpkin, an updated version of my tutorial article, "Derivation of the "Cosine Fourth" Law for Falloff of Illuminance Across a Camera Image", available here:
http://doug.kerr.home.att.net/pumpkin/index.htm#CosFourth
This article derives the "cosine fourth" relationship from fundamental optical and photometric principles.
In this new version, the presentation has (hopefully) been improved and some collateral matter, not really needed, has been removed. I have also expanded my discussion of a major "alternate" result presented by some other authors.
I have also expanded the discussion of a related phenomenon that makes the effect of falloff worse in digital cameras.
I have just released to my technical information site, The Pumpkin, an updated version of my tutorial article, "Derivation of the "Cosine Fourth" Law for Falloff of Illuminance Across a Camera Image", available here:
http://doug.kerr.home.att.net/pumpkin/index.htm#CosFourth
This article derives the "cosine fourth" relationship from fundamental optical and photometric principles.
In this new version, the presentation has (hopefully) been improved and some collateral matter, not really needed, has been removed. I have also expanded my discussion of a major "alternate" result presented by some other authors.
I have also expanded the discussion of a related phenomenon that makes the effect of falloff worse in digital cameras.