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I have a camera module with a lens viewing angle of 185° and a focal length of 1.8.

But as far as I can tell, this camera module is not classified as a fish-eye lens.

The working distance is specified from 14cm->infinity. And while I understand that the horizontal FOV (mm) can be calculated from the lens viewing angle and desired working distance, I am confused at how this 184° viewing angle would effect the outputted image (would it be fish-eye? Is the working distance too small for the fish eye effect to be noticeable?)

Thanks for any clarification.

Gary
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Whether a lens is a "fisheye" or "rectilinear" lens is not determined solely on the basis of its focal length. The way a lens is designed also determines the type of projection it makes.

Your 1.8mm lens does have a very short focal length, but is also likely projecting a very small image onto a small sensor area. Such a lens can be made to project a rectilinear image (although it would probably still demonstrate some geometric distortion) or a fisheye image. The difference is in which things are (attempted) to be projected as straight: lines going from the center to the edge of the image like spokes in a wheel or parallel lines within the field of view. Another way of saying it is that fisheye lenses attempt to preserve angles at the expense of straight lines while rectilinear lenses attempt to preserve straight lines at the expense of angles.

There are both fisheye and rectilinear lenses designed for larger sensors (in the APS-C to FF range) that have overlapping focal length ranges. Canon makes a 14mm fisheye as well as a 14mm rectilinear prime. They also make an 8-15mm fisheye zoom lens and an 11-24mm rectilinear zoom lens. All of these are for full frame sized sensors. They also make a couple of rectilinear zoom lenses for APS-C sized sensor that are 10mm on the wide end. Other manufacturers offer similar lenses.

For more, please see these related questions:
Is the focus plane of a fisheye lens inherently curved?
Why don't smartphone cameras correct pincushion distortion automatically?
Does wide angle equivalent in crop sensor skew image?
Why doesn't the GoPro automatically correct for the fisheye distortion?
Why the faces in the corner tends to skew a bit in almost all smartphone cameras

Michael C
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  • 185° cannot be rectilinear. – Itai Sep 19 '17 at 21:07
  • Oops! I misread the question to say 165°. – Michael C Sep 19 '17 at 21:09
  • But why can't a lens with a 185° FoV be projected in a rectilinear fashion? Sure there would be "stretching" at the edges, but that is the case with all rectilinear lenses. It's just that with narrower angles of view it's not usually enough to be noticeable. – Michael C Sep 19 '17 at 21:14
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    It's not possible. As the angle-of-view approaches 180°, the rectilinear formula go towards infinity. It is undefined beyond that. This happens because you cannot project a 180° field-of-view onto a rectangle while preserving straight lines. – Itai Sep 19 '17 at 21:20