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F-Theta

F-Theta lenses are a class of Fisheye lenses

F-Theta lenses are also called “equidistant“, “linear scaled“, “äquidistant” or “angular
F-Theta lenses use an image mapping function of type
r = f \theta
Non distortion 180° F-Theta lenses have an image circle or \pi * FocalLength mm
A non distortion F-Theta lens of 1.37mm focal length has an image circle of d = \pi 1.37 mm = 4.30 mm
Therefor a f=3.17mm F-Theata lens with an image diameter for 180° of 4.15mm has a distortion of (4.15/4.3)-1 = 0.965-1 = -3.5%

maintains angular distances

F-Theta angles
weak medium strong max
115 159 217 360 and more

full360[1]

see
Fisheye Types