Do strongly vignetted parts of a lens imaging circle gain depth of field?

Question

Usually, vignetting in a lens (when not caused by glass losses, intentional graded filters or sensor issues) is explained as being a consequence of the effective aperture being smaller in corner areas, due to more light hitting the lens barrel instead of the next element in line.

Does this lead to any practical gain in depth of field in corner areas? Does it add to field curvature in lens designs that already have focus shift from changing aperture? Is the unevenly shaped aperture (longer than it is wide) in the corners expected to cause any astigmatism-like effect (or actually explaining astigmatism)?

Answer 1

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).

Answer 2

Wider angle lenses tend to demonstrate more of all of the optical aberrations than narrower angle lenses do due to the need to have higher refractive power to provide a wider angle of view. All of the classic aberrations are caused by refraction, so it only makes sense that the more a lens must refract the light that strikes it, the more severe each of the aberrations will be and the more correction will be needed to control the higher amounts of those aberrations caused by that higher refractive power.

The causes of vignetting with wide angle lenses are at least two-fold and sometimes more:

• Light striking the front of the lens from the edges of the FoV are at wider angles than light from the center of the FoV. If the light from the edges of the scene is the same intensity as the light from the center of the scene, the angles with which the light from the edges of the FoV strike the front surface of the lens will spread that same intensity of light over a larger area of the front of the lens. It's the same principle that contributes to winter when the Sun is lower in the sky over the course of shorter days and the angles of the Sun's rays as they strike the Earth mean the same amounts of energy are absorbed over larger areas of the Earth's surface in the hemisphere where it is winter than in the hemisphere where it is summer and the Sun is higher overhead.
• More light from the edges of the FoV of wider angle lenses is lost than from narrower angle of view (longer focal length) lenses due to the higher refractive power such lens need to bend light for wider angles of view. Light from the edges of the FoV that passes through the lens' glass elements at a steeper angle must pass through more glass than light that strikes the front of the lens head on. The more glass the light striking the front of the lens passes through, the more of its energy is absorbed by the lens.
• In the case of unevenly shaped apertures, there is also either mechanical vignetting caused by something in front of the lens' front element or vignetting caused by the lens elements themselves not allowing the full entrance pupil to be seen from all parts of the lens' FoV. In the former case that something is usually a part of the lens' barrel. In the latter case it's usually a consequence of designing the front surface of the first element of the lens with a relatively flat surface instead of a highly bulbous one.

Does this lead to any practical gain in depth of field in corner areas?

Not really. The reason smaller apertures increase depth of field (DoF) is because they prevent less collimated edge rays striking all around the outside of the front element of the lens from passing through while allowing more collimated center rays to pass. In the case of vignetting, though, the light being reduced is not all edge rays - along with edge rays from the other side of the lens' front element, some of the light lost is closer to the center. The light allowed through the lens isn't all more collimated center rays, either. Much of the light allowed to pass through is light that strikes the nearer edges of the lens' front element, too.

Does it add to field curvature in lens designs that already have focus shift from changing aperture?

Quite the contrary. Focus shift is partially a consequence of uncorrected field curvature, not the other way around. Vignetting does not cause field curvature, either. Vignetting is a consequence of the same thing (a wider angle of view requires more refraction than a narrower angle of view) that also makes correcting field curvature, which is already there, harder to do in wider angle lenses.

Is the unevenly shaped aperture (longer than it is wide) in the corners expected to cause any astigmatism-like effect (or actually explaining astigmatism)?

Again, correlation does not mean causation. Astigmatism at the edges of wide angle lenses is a result of the first two things listed above that cause vignetting: higher refractive power and light from the edges of the FoV striking the front of the lens at wider angles than is the case with narrower angle lenses, as well as the different angles light from a singular point near the edge of the lens' FoV will strike different parts of the lens' front element.

Answer 3

The short answer to your question is "no"; there is no independent effect in corner areas.

The easiest way to understand it is to think of lens/aperture area as "exposure stacking"... each point on a lens contains all of the light required for a complete image, as seen from it's location. I.e. one image containing one portion of the total exposure at the sensor. And when you increase lens/aperture area you are increasing the number of images stacked on the sensor, thereby increasing the amount of light across the image as a whole.

Vignetting is caused when the edges of a lens sees a physical obstruction to the side (mechanical & optical vignetting). And that obstructed image is then spread across the image circle as one portion of the total exposure.

This is why stopping down removes vignetting and typically improves IQ across the image as a whole, because you are removing the images that originated from the edges of the lens; where optical errors are hardest to correct for and where vignetting originates.

If you are considering Depth Of Field as simply "sharpness," then it is almost always reduced at the periphery for the same reason... an imperfect lens and you can't stop down far enough to remove all of the errors.

But I don't think Depth of Field is really the right way to think of it... that is a perceptual factor dependent on how the output image is viewed. Depth of Focus; the placement of the point of focus relative to the image/sensor plane (front/at/behind), is a more relevant consideration. But since the issue is loss of light and optical errors; it is more a lack of focus/light, and affects all Depths of Focus equally.

The other possible cause of vignetting is that the projected image circle is marginally too small for the imaging area, similar to using a DX lens on an FX body... this is referred to as "natural vignetting," which is simply light falloff at the periphery due to the light's angle of incidence on the imaging plane. But again, this has no real effect on Depth of Focus/Depth of Field. And in this case you can't do anything about it (stopping down doesn't help).

Answer 4

Simply no, it’s a distortion due to the lower exposure in the outermost rings of the lenses without gains in anything else.

A theoretically perfect lenses could not have any vignetting at all, but in real life even when all lenses try to approach the theoretical perfection they can’t get quite there because physical limitations in manufacturing processes and available glass (or synthetic components).

No vignetting in a lenses is simply impossible, but vignetting almost invisible to the naked eye is possible but the lenses that can achieve that are extremely rare and very expensive.

So forget about avoiding it, learn what it’s for each of your lenese and take advantage of it when creatively and when composing your shoot.