Fisheye lens
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In photography, a fisheye lens is a wide-angle lens that projects deliberately distorted images.
All ultra-wide angle lenses suffer from some amount of distortion. While this can easily be corrected for moderately wide angles of view, rectilinear ultra-wide angle lenses with angles of view greater than 90 degrees are difficult to design. Fisheye lenses achieve extremely wide angles of view by foregoing a rectilinear image, opting instead for a special mapping (for example: equisolid angle), which gives images a characteristic convex appearance. A panorama by rotating lens or stitching images (cylindrical perspective) is not a fisheye photo.
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A special kind of fisheye lens, called circular fisheye lens, projects a circular image fully contained inside the frame, typically with an angle of view of 180 degrees.
The focal lengths of fisheye lenses depend on the film format. For the popular 35mm film format, typical focal lengths of fisheye lenses range from 6mm to 16mm.
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several mapping functions
The mapping of a sideways object leads to a picture position displacement from the (film-)picture-center. The manner of this conversion is the mapping function. "f" is the focal length of the optical system.
Normal (none-fisheye-) lens:
- gnomonical: <math>r = f * tan(a)<math>, works like the pinhole camera. Straight lines remain straight (distortion free). "a" has to be smaller than 90°. The aperture angle is gaged symmetrically to the optical axis and have to be smaller than 180°. Large aperture angles demand extreme effort and lead to very high prices.
Fisheyes can have many different mapping functions:
- linear scaled (equidistant): <math>r = f * (Pi / 180) * a<math> (a in °[DEGree]), practical for angle measurement (star maps). PanoTool assumes to that.
- orthographical: <math>r = f * sin(a)<math>, acts like an orb with the surroundings lying on it; max. 180° aperture angle.
- equal area (equisolid angle): <math>r = 2 * f * sin(a / 2)<math>, acts like a mirror image on a ball, best spacial effect (unsophisticated distances), suitable for area comparing (clouds grade detemination). This type won the recognition and also the photographers have to put up with it - because it compresses the marginal objects. The price of this lens are high, but not extreme.
- stereographic (conform): <math>r = 2 * f * tan(a / 2)<math>, would be perfect for photographers - because it doesn't compress marginal objects. No lens has been developed for this type by now, but this mapping is easy implemented by software.
All types of fisheye bend straight lines. Aperture angles of 180° and more are possible only by barrel distorsion.
[1] (http://www.fisheyelens.de) is deploying with this mapping (german language).