There seems to be a limit, around 0.33, on the fastest possible aperture. Is there a theoretical limit on how wide a non-fisheye lens can be? That is, what is the minimal possible focal lens for a given sensor size?

  • The theoretical limit with typical glass used for camera lenses for maximum aperture is f/0.5. If one had a diamond large enough and pure enough, one could cut a lens with a theoretical maximum aperture of f/0.235 because diamond has such a high index of refraction. That f/0.33 lens was a marketing gimmick that didn't actually work. – Michael C Apr 18 at 18:27
  • To clarify the question: You're looking for math to support what the shortest focal length of a lens you can get, for a given sensor/film size, before noticeable 'fisheye distortions' creep in? - You may need to define what level of acceptable distortions would be for a helpful and valid answer. – TheLuckless Apr 18 at 19:30
  • @TheLuckless, Yes, I'm asking about the shortest focal length. A ballpark info would be sufficient; forget about the non-fisheye clause. – Michael Apr 18 at 19:41
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    Well, 0mm is pretty much a hard limit for focal length. Probably not very useful, though. But, it does pretty much affirmatively answer "is there a theoretical limit ...". – twalberg Apr 19 at 2:39
  • @twalberg, :-) What about a positive limit? – Michael Apr 19 at 3:35

Regardless of any theoretical minimum focal length (with respect to sensor size), there is a useful limit.

On 35mm film and full frame sensors, the current widest-angle lens that is useful is 8mm. There are 4.5mm lenses that are meant for crop-sensor cameras, that could be mounted on full frame cameras, but there's no point in doing so. Why?

The 8mm lenses for full-frame cameras project a full-circle fisheye image that is just shy of 24mm in diameter, which corresponds to the narrow dimension of the sensor. That means the entire fisheye circle is imaged uncropped on the sensor. But that also means there is a lot of sensor area that is unused, outside of the image circle projected by the lens.

The 4.5mm lenses for crop sensor cameras project a similar full-circle fisheye image that is just shy of 15mm in diameter, which corresponds to the narrow dimension of Canon's APS-C sensor. So you could mount a Sigma 4.5mm lens onto a full frame Nikon or Canon, but the 15mm-diameter image wouldn't be taking advantage of the larger sensor size of the full frame camera.

Both the full frame 8mm lenses, and the crop frame 4.5mm lenses, have similar angles of view, over 180°. Actually, there is quite a bit of variability in the upper end of angle of view amongst all full-circle fisheye lenses. But that variability really doesn't matter, because the projected images from the extreme edges of the lens's view is compressed and distored into a rather thin ring near the circumference of the fisheye image circle. Even if you remap the projection at the edge of the circle in software, there's likely to be significant and severe distortion, color separation, vingetting, etc.

  • Thanks. This doesn't apply to non-fisheye lenses though: for rectilinear projection, reducing focal length always results in a wider view. Nevertheless, I don't see rectangular full frame lenses with focal length below 12 mm on the market. I wonder whether there's a physical reason for that. – Michael Apr 22 at 21:13
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    You're absolutely right, it doesn't apply for non-fisheye lenses. Part of the reason (I'm sure there's more) why you can't increase the angle of view arbitrarily close to 180° by shortening the focal length though it because at a certain point you're no longer talking about thin lenses (i.e., the thin lens approximation no longer holds). – scottbb Apr 23 at 0:26

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