I am in complete agreement with John on distinguishing vignetting from cos^4 - and not because I also have a Tucson background. The two forms of falloff are completely different mechanisms.
But the main thing to keep in mind for this thread - it has nothing to do with what the OP is asking about.
As for Rudolf, here is a line from Lens Design Fundamentals:
"Vignetting is one of the reasons why the illumination on the film in a camera falls off at increasing transverse distances from the lens axis. Other reasons are (a) cos^4 law, (b) distortion of the pupil..."
So there are many reasons illumination may drop off - and it won't strictly obey cos^4 in a real system anyway. So it is important to keep vignetting separate from the other causes for drop off.
Hi, Frank; sure, semantics, no problem there. But, keep in mind... Rudolf, with his Kodak hat, was working for a company that, above and beyond else, made cash-cow film and cameras. And the camera specialists called it "cos fourth vignetting". e.g. >>>
"Cos4 vignetting describes the natural light falloff caused by light rays reaching the sensor at an angle. The light falloff is described by the cos^4(θ) function, where θ is the angle of incoming light with respect to the optical axis in image space. The drop in intensity is more significant at wide incidence angles, causing the image to appear brighter at the center and darker at the edges."
And the word vignette originated in the most general pre-optics context of artwork, where the edge of a (typically circularly-formatted portrait) image is intentionally-feathered / darkened. Later, the camera and optics guys gleaned the word and eventually claimed exclusivity.
So, I'm just preferring a term that the artists and photographers used and use... no one right or wrong, just different contexts. And appending the cos4 to the term makes it overtly unambiguous. As Alan Wertheimer was wont to say, out in the lab, "We seem to be is a state of violent agreement!"
I did a lot more than just lens design, much "non-image-forming geometrical optics", lots of that lighting design for GE, ITT, Volkswagen, smalls... So that same illumination falloff (trying to uniformly illuminate the road or desktops from above) had cosNs in there, and the targeted inverse correcting function we called "batwing". Semantics tends to be parochial to ones background, like local dialects. Diversity is good! Tom