This type of vignetting is caused by the physical dimensions of a multiple element lens. Rear elements are shaded by elements in front of them, which reduces the effective lens opening for off-axis incident light. The result is a gradual decrease in light intensity towards the image periphery. Optical vignetting is sensitive to the lens aperture and can often be cured by a reduction in aperture of 2–3 stops. (An increase in the F-number.) Light falls off with the inverse square of the distance form the source; a common pinhole camera that has a frame three times as wide as its focal length will have about two stops of falloff at the corners (that is, the corners receive 1/4 as much light as the center). The formula is falloff = ((d/ƒ)^2, where d is the distance from image center and ƒ is the focal length of the camera. I’ve made a nuke gizmo that attempts to model a basic vignette and works in reverse to remove vignettes from images.
Vignette for Nuke