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A fisheye lens is an extremely wide-angle lens that is purposely designed to have extreme barrel distortion.

Is there such a thing as a lens purposely designed to have pincushion distortion? What would that look like?

(Yeah, you can do it in software, but you already get better results from doing these things optically if you can.)

  • Anamorphic lens from the film industry seems a candidate... – Jindra Lacko Apr 22 '17 at 16:45
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    @JindraLacko I thought anamorphic lenses are still rectilinear, just with different magnification on each axis...(?) – MathematicalOrchid Apr 22 '17 at 16:49
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    A fisheye's distortion is a necessary product of it's wide angle of view (usually 180 degrees, sometimes more- 220 degrees for one Nikon lens), not an end in itself. – BobT Apr 22 '17 at 17:16
  • @BobT - except at the ultimate extreme fisheye distortion isn't a necessary product if you're willing to throw money at the problem. I've got a 7mm rectilinear lens, which is rather wider than many lenses that allow themselves the fisheye distortion. – Chris Wuestefeld Apr 25 '17 at 18:27
  • Interesting... What film/sensor format is your 7mm rectilinear lens designed for? – BobT Apr 26 '17 at 13:45
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The opposite of a fisheye is a rectilinear lens.

You probably did not find one because your definition is wrong. Distortion of a fisheye lenses is not barrel distortion, it is that a different projection or mapping is obtained by design. Angles are usually preserved but not straight lines, unless they pass through the center of the frame.

A rectilinear lens on the other hand is designed to preserve straight lines, regardless of where they occur in the frame. This makes it impossible to map an angle of view close to 180 into a flat image.

Wikipedia has interesting diagrams showing the difference and even various types of fisheye lens projects.

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    Fisheye and rectilinear lenses are not really opposites -- there are many mapping functions a lens could adhere to. – Brandon Dube Apr 24 '17 at 2:53
  • They are, however, the two most common counterparts at wide angles of view. – Michael C Jun 4 '17 at 2:38
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A fisheye lens isn't designed to have extreme barrel distortion -- the distortion is the result of trying to map a sphere onto a plane.

A regular lens follows the equation image height = focal length * tan(half angle of view).

Tangent blows up near 90 degrees, so you cannot map a 180 degree field of view onto a plane.

Near this, equal changes in angle map to larger and larger changes in location on the image. This is what stretches the corners out in an ultra wide angle rectilinear lens.

Another mapping function is image height = focal length * half angle of view. This maps the same change in angle into the same change in space anywhere on the sensor. It is also often the function used by ultra wide angle lenses, to avoid the difficulty of a low distortion design and difficulty putting a huge FoV onto an image of finite size.

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Answering the title question, one opposite of a fish eye lens, regarding the focal length (which is a small one, therefore an ultra wide lens) is a Super telephoto lens.

As Itai responded, the objective is not the distortion, that is an effect due the projection. You have similar distortions on panoramas for example, after stitching several images together. The difference is that you do not notice them because of the framing.

So the opposite to a barrel distortion is no distortion.

A pincushion distortion could be made during photography using a defective mirror.

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