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Some lenses will produce distortion near a photo's edges (lines that should be straight begin to curve). Fisheye lenses definitely do this, and some ultra-wide lenses will do this too. I like wide lenses, but I'm not a fan of the distortion a fisheye lens produces.

What is the widest lens I can get before distortion is apparent? Lens length (mm) or capturable degrees would be the preferred answer format... but I won't be surprised if the answer is more complicated than that.

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It is much more complicated than that. There are 85mm prime lenses I'm aware of that exhibit some degree of barrel distortion, and barrel distortion is almost a given at the wide end of a zoom lens no matter how long that wide end is. On the other hand, at the "long" end of the Tokina 11-16mm f/2.8, you would have to be shooting brick walls to notice any barrel distortion, and even then it's only at the very edges of the frame (on a crop-sensor camera, of course). And the very same lens may exhibit different geometric distortions at the same focal length but at different focus distances. Modern lenses are a complex interplay between a lot of different lens elements that often change their spatial relationships as the lens is adjusted (focused or zoomed).

There are several prime lenses under 20mm that come close to being properly rectilinear. Sigma's 14mm lens was great in that regard, but a lousy lens otherwise, unfortunately (it was terminally soft anywhere but at the center of the image, had poor contrast, flare everywhere, etc.). Nikon and Canon both offer 14mm lenses that have slight and easily correctable barrel distortion (slight being relative in the extreme wide-angle world).

The good news is that geometric distortions are fairly easy to correct in post. (And recent Nikons will do it in-camera; I don't know about other brands.)

The bad news is that even if gross geometric distortions are corrected, that does nothing about the foreshortening distortion that makes spheres appear like ellipsoids and gives people at the edge of the frame funny-shaped heads.

That's not got anything to do with the rectilinearity (the absence of barrel and pincushion distortion) of the lens, but with perspective. In order for things to look right, your point of view (when looking at the picture) needs to be about the same as the camera's point of view was when the picture was taken. (Give it a try -- if you have a picture that has perspective distortion, just get your face really, really close to the print.)

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And yes, dammit, for the 842nd time, I am a human being! Though I'm pretty sure the average bot would have an easier time with a CAPTCHA term that involves partial differential symbols and lambdas than the average human being. (I know, it's the "graecum est" part, but that was the easiest of the four I had to go through to get a legible known part.) –  user2719 Apr 16 '11 at 6:41
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Stan, at your level of rep you shouldn't be getting the captcha page very often at all anymore. If you are, something to bring up on meta. –  mattdm Apr 16 '11 at 12:50
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Great answer. Only I would add something to address the 'fisheye' part of the question: Fisheye lenses are not simply very wide lenses, they use a different construction that turn straight lines into curves when not passing through the center of the frame. A perfect fisheye lens would still do that while a perfect rectilinear would not (although there is no such thing in any case). –  Itai Apr 16 '11 at 13:00
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+1 As always, a good, thoughtful, informed answer. I was surprised, though, that the role of sensor size was indicated only in passing. It would seem this is a critical factor: the "edge" of a lens depends fundamentally on that. E.g., a full format 35 mm lens may have a lot of distortion more than 20mm from the center but this will be irrelevant when mounted on a camera with a smaller sensor such as an APS-C. Also helpful would be some discussion of when distortion really becomes "apparent." The brick wall example suggests it depends on the subject but it must depend on the viewer, too. –  whuber Apr 16 '11 at 17:25
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@whuber: you are, of course, correct -- the only reason for the parenthetical reference in my answer was that the 11-16 is designed for (and thus corrected for) the APS-C-sized sensor. The subject, though, does have some importance (especially when the distortion is small) since we would be more likely to see slight geometric distortions in a subject that is essentially a bit of graph paper than in something a bit more organic in form. –  user2719 Apr 17 '11 at 0:32
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Barrel distortion is the result of lens design, regardless of focal length. The Canon 50mm f/1.4 has slight barrel distortion, that's only visible if you photograph a "straight line" at the very edges, and that is by no means a wide angle lens.

A fisheye lens is a special design created to enhance and underline barrel distortion. Canon and Nikon both make 14mm lenses that cover full frame and don't have the fish-eye effect. Do they have distortion at the edges? Yes, but it's not the barrel distortion of a fisheye lens, but distortion created by perspective, which is inherent in any wide-angle lens design, and is often both sought after and looks very natural.

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One way to answer your question is look at the distortion test results given by photozone.de.

For example here are two test results for representative wide angle zoom lenses:

Canon EF-S 10-22mm
Sigma AF 8-16mm

Run your cursor over the different focal lengths for the distortion diagram and you will see the results come up. I was surprised to see how relatively low the rectilinear distortion was (but that's just my opinion). You would need to do it yourself and make your own judgment call on this.

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All lenses show some degree of distorsion, but I suppose that you mean the difference between regular lenses and fish-eye lenses.

The widest non-fish-eye full-frame lens that I know of is the Sigma 12-24mm 1:4,5-5.6 DG HSM.

A focal length of 12mm on a 36mm sensor gives you an angle of view of 112,6°.

There are EF-S lenses with shorter focal length, but the angle of view is still smaller. An EF-S lens with a focal length of 8mm on a 22.2mm sensor gives an angle of view of 108,4°.

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