As you known, the lens vignette (fall-off of the circle of good definition), is seen as a gradual dimming of an image from center to margins. The vignette has been with us always, as all lenses vignette to some degree. This is somewhat more of a problem today, as compared to the negative / negative film method employing an optical enlarger. Such a scheme somewhat negate the vignette as both lenses display fall-off and thus there is a cancelation. Conversely, a reversal print from a slide is worsened as the two vignettes are additive.

The vignette comes about from several sources. The mechanics or physical source is an obstructions such as narrowness of interior of the lens barrel due to poor design or improper diameter lens accessories that obstruct some marginal image forming rays.

Then there is optical vignetting caused when image forming rays from the boundaries of the scene traverse the aperture (iris). Imagine a view from the image plane looking back at the lens. If your viewpoint is on axis, you will see a circular iris. If your viewpoint is from one of the corners of the frame, you will see not a circle but an ellipse. This shape has less surface area thus image forming rays are abridged.

Then there is the fact that marginal image forming rays arrive obliquely. Circles of confusion that would image circular on axis now take on an elliptical shape also (cosine error) thus each will deliver less energy.

I never, till now, supposed that depth-of-field might be different center-to-margins. After thinking about it, I conclude that the circles of confusion at the margins are likely larger than on axis neighbors. Thus it’s more likely that depth-of-field will be abridged at the margins of the image (my belief anyway).