Helen, don't you mean the exit pupil?

In some lenses vignetting is clearly intentional. I have two ~ 4 inch reversed tessar type macro lenses -- 90/6.3 CZJ "M" and 100/6.3 Reichert Neupolar -- with rather small rear elements located well behind the exit pupil. At fairly small angles off-axis the rear of the lens barrel obscures the exit pupil. As a result, both have small coverage at infinity but more than enough closeup. I really regret this property of the Neupolar, since over the field it covers -- wider near than far -- it does very well at all distances.

About cos^4 dropoff of illumination, Brian Caldwell has asserted repeatedly on usenet that he has designed short rectilinear lenses that are brighter at the edges than in the center. His trick, if I understand it correctly, is to design the lens so that on the image side of the lens the edge rays are nearly parallel to the central ray.

I'm not sure that Ludwig Bertele sold his soul to the devil, even though some of his designs smell a little of hot sulfur. I have in mind the 44/5.6 Super Aviogon I once got to hold. I held it out in front of me, and as I rotated it from "straight ahead" to "lens' axis 90 degrees off straight ahead" its beady little exit pupil wouldn't stop staring at me. Brrr!