Measuring Fisheye Projection Curves

[Thomas Sharpless]

If you are a serious panographer, you know that after focal length, the most important property of a lens is its projection curve, that relates angle of incidence to radial distance in the image. You also know that while all ‘normal’ lenses are designed to the same rectilinear curve, ‘fisheye’ lenses have many different projection curves; and that to get the best out of a given fisheye you must respect its curve. But did you know that since version 11, PTGui can measure that curve for you?

Back in the 1980s a NASA engineer named Donald Gennery figured out that a single number could describe all realistic lens curves, via a simple combination of the sine and tangent functions. Gennery’s parameter ranges from -1 to 1 and relates to the various ideal curves as follows:

-1: sine (mirror ball)

-0.5: equal-area spherical (most modern fisheyes)

0: equal-angle spherical (classic Nikon & Canon FEs)

0.5: stereographic (some Samyang FEs)

1: rectilinear (all ‘normal’ lenses)

It covers everything between these ideal lens types too.

The ‘fisheye factor’ in the new PTGi lens model is Gennery’s parameter. PTGui can optimize it but normally just sets it to a nominal value and relies on the correction polynomial to fit the curve. To measure a fisheye, first set the correction coefficients a,b,c to zero in the lens tab. Then in optimizer tab, enable fisheye factor, this disables a,b,c. Optimize; go back to lens tab to see the fitted value of Gennery’s parameter.

Reporting G values estimated this way might help us better understand the fine points of using fisheyes.

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