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Fish-Eye Lenses

Fish-Eye lenses offer a field of view which may be as much as 180° or more.  Straight lines in a scene are mapped to a curved surface:



These lenses have very short focal lengths compared with the image sensor diagonal.  The principle is similar to looking through a telescope from the end opposite the eyepiece. A fairly large number of optical elements is needed to correct for chromatic aberration and flare:



Laiken (1995).

They were originally introduced in optical astronomy for wide field star survey, but from the mid-1960's they were also manufactured commercially for 35 mm cameras (Miyamoto 1964).  Various designs have been compared by Kummler and Bauer and nearly all have similar performance. A few designs have been adapted for high-end digital cameras which have image sensors that are smaller than a full 24 x 36 mm film frame.

In Radcor, load the image first. Then, to transform the Fish-Eye image to a flat surface, click on the Fish-Eye Radio button:



and click or drag the Field Of View trackbar to modify curved image lines so that they are straight:



It may be helpful to check the Grid box so that guide lines are available.



You can rotate the result to see the left and right portions of the flattened image if a lens designed for a full 35mm frame is used with a smaller sensor that clips the top and bottom sections of the otherwise circular image:



Drag on the lower trackbar for this purpose.



Click on the Apply button to transform the full image, then open the File menu and save it to a new file. In Radcor, interpolation is used automatically to prevent the jagged edges on sharp lines, so there is no need to set this option manually.

Method:

The FOV (Field Of View) algorithm of Devernay and Faugeras used in Radcor compares favorably with other algorithms analyzed by Claus and Fitgibbon



It differs from that used in PTLens and other programmes, since it is based upon the optical design of many common fish-eye lenses rather than on an general mapping function.

Bibliography:

D. Claus, A. W. Fitzgibbon, A rational function lens distortion model for general cameras. Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - 2005, Volume 1 213 - 219 
F. Devernay, O. Faugeras. Straight lines have to be straight. Machine Vision and Applications  13, Springer Verlag, 2001 14-24

J. Kumler, M. Bauer, Fish-Eye lens designs and their relative performance, SPIE Proceedings-Current Developments in Lens Design and Optical Systems Engineering,  2000,  360-369

M. Laikin, Lens Design, Second Edition,  Marcel Dekker, New York 1995,  95-96.

K. Miyamoto, Fish Eye Lens, Journal of the Optical Society of America, 54, 1964, 1060 

A Google-Scholar or CiteSeer search brings up a vast literature concerning non-linear lenses including Fish-Eye and Catadioptric designs. The latter use curved mirrors of various shapes to reflect 360° panoramas recorded by cameras with normal lenses, usually for security purposes. Images from these can not be treated in Radcor.

Acknowledgement:

Jean-Pierre Scherrer of Geneva, Switzerland http://www.pbase.com/scherrer/ called the problem of Fish-Eye lens correction to the author's attention and supplied the test image above as well as many more, all made with a Byelo-Russian Peleng 8mm lens mounted on a Nikon D200 camera body.