While most lenses are designed to avoid any distortions, Fisheye lenses are ultra wide-angle lenses (with a focal length usually smaller than 28mm, depending on the crop-factor) to create distortions. While “normal” wide-angle lenses can only display a maximum degree of 90° within the picture, fisheye-lenses can go far beyond that point. Depending on the type of lens, you get different views (e.g a typical fisheye-lens = 180° )

If you want a detailed article (as i don’t want to go into math here) see the wikipedia "Fisheye_Lens" Article

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