On 7 Jul 1998 23:56:14 GMT, gbuchana@pc-24826.on.rogers.wave.ca (Gardner Buchanan) wrote:

>So, for fish-eye lenses, what does the focal length really mean,
>and how do they come up with it?

It is the minimum distance (at infinity-focus) between the film and
the optical center of the lens - which can be (and often is with
fisheyes) outside the actual structure of the lens.

>For "normal" lenses, FL can be used to (pretty well at least) work
>out the field of view, and from the diameter of the front element,
>the F-ratio.

Uh-uh - not the diameter of the front element, but the
diaphragm. In a 50mm f2 normal-type lens, the diaphragm
wide open is 25mm in diameter (50mm / f2 = 25mm...).
The front element may be the same size, but this will result
in poor corner illumination at wide stops (and perhaps
innaccurate f-stop markings at wide stops compared with
T-stops).

>I like think of the FL of a lens as the distance from
>the film plane to a pinhole which yields the same resulting
>magnification.

Yes. But in the exact center only. Different perspective
types (and also linear distortions) will result in different
angular coverage with the same FL lens on the same format.

>For fish-eyes though, this seems to fall to pieces. Consider some
>Nikon fish-eyes:
>
>- Where do you put a pin hole to achieve a 220 degree field of
> view like the Nikon 6mm F/2.8 has? Or even 180 degrees like the
> 18mm [16mm] F/2.8?

Nowhere, since the pinhole perspective is rigidly rectangular - but
the center magnification will be the same regardless of
perspective type.

>- Home come the Nikon 18mm [16mm] F/2.8 has a wider field of view at
> 180 degrees than the shorter focal length 13mm F/5.6 at 118
> degrees?

The magnification of a subject element is constant with rotation
away from center with a fisheye, but increases with a rectangular-perspective lens, decreasing the field covered within
the same format (frame). Or, it appears in a fisheye image that
things away from center get smaller, allowing more to fit within
the given frame...

>I know that some of these lenses produce different projections on
>the film plane than others. Still, a 180 degree field of view is
>180 degrees whether it is projected onto a circle or clipped off
>at the top and sides.

Yes - and all unobstructed lenses produce a circular image.
Normally a rectangular part of the image is cropped out of
the circle of coverage by the film frame. A circular image
can be made from any perspective-type lens, though, by
using a bigger frame.

>Clearly the F/ratio for lenses like these is not given by the width
>of the front element over the FL. The Nikon 6mm would wind up with
>a F/ratio of F/0.03 - one hell of a fast lens. What is being given
>here is obviously a T-stop.

No - see above...