PanoTools mailing list archive

Sender:Helmut Dersch
Date/Time:Tue, 24 Apr 2001 20:37:30 +0200
Subject:Re: FoV versus focal length formula for fisheye lenses?


uwai schrieb:
> > >
> > > w = f * fov (fov in radian) for equidistant projection.
> > >
> > > w = 2 * f * sin(fov/2)      for equal area projection.
> > >
> > > Almost all fisheyes are designed as one of the two projections.

The "fisheye"-mapping used in PanoTools is the first formula
(equidistant), both for full-frame and circular fisheye lenses.
The second formula (equal area) happens to be identical to the
mapping of spherical mirrors, which is available as an option
in the "remap" tool.

> I think nikon 8mm F2.8, 6mm F2.8, 6mm F5.6, FC-E8 + E900 master lens are
> designed as equidistant, while olympus 8mm F2.8, sigma 8mm F4(MF) are as
> equal area.

I can confirm this from my own data for the Olympus 8mm, Sigma 8mm, and
Nikon 6mm. The Nikon 8mm F2.8, however, seems to be of the equal area
type as well as the Sigma 15mm and several 35mm lenses for MF-cameras. 

The two formulas are similar with some slight differences in the
outer regions of the image circle. It is possible to use the
equidistant projection formula for any fisheye lens and treat the slight
mismatch using suitable radial correction parameters a/b/c.


Helmut Dersch

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