T3D Re: Phanto-cam Lens system

[Larry Berlin <lberlin@xxxxxxxxx>]

>Date: Thu, 29 Apr 1999
>From: Tom Hubin <thubin@xxxxxxxxx>
>.................
>A wide angle lens that does not distort would do it. So a fish eye is
>out. I've had a couple of thoughts that I am going to throw out.
>
>Thought #1
>
>Lenses for off axis viewing are usually called "pantoscopic". They are
>expensive but commercially available. They avoid the keystoning that
>occurs when you photograph a tall building from street level. They can
>sometimes be decentered different amounts to accomodate the preferred
>viewing angle.

*****  These are great comments!  Interesting name, quite close to
*Phantoscopic*! Do you know where to get more information on this type of
commercial lens? Catalog or URL?



>
>Thought #2
>.....................
>In thin lens theory, decentering a lens is equivalent to adding a prism.
>I wonder if there is a trick that can be used here. Something to be
>added to a standard camera.

****  Interesting thought. Decentering would be equivalent to adding a prism
to the on-axis view, but maybe not for off axis viewing. The purpose here is
to center the optics FOR the off axis view, which seems to imply the image
path would still center on the available optics to some extent.

Wouldn't adding a prism to a regualr camera be the same as aiming the camera
at a different angle? If so, this wouldn't work.


>
>Thought #3
>
>A single lens system has magnification and image distance that vary with
>distance to the object. An afocal lens system has a constant
>magnification. So keystoning does not occur as the object distance
>varies.
>
>It might be possible to use an on-axis telescope, binocular, or homebrew
>afocal system pointed at the center of the off-axis object. The image
>distance still varies with the object distance so the film is tilted.
>The film tilt must be calculated. The image of 2 points at opposite ends
>of the object will give you the film plane.
>
>There is also a formula for determining the film tilt. 
>
>tan(beta) = m * tan(alpha) or beta = atan( m * tan(alpha) )
>
>where:	alpha is the tilt of the object with respect to the optical
>system axis
>	beta is the tilt of the image with respect to the optical system axis
>	m is the lateral magnification of the optical system
>
>Zero tilt is the normal situation, perpendicular to the lens axis. The
>lateral magnification is the usual magnification. A 2 meter object
>photographed as an inverted 20 mm image has a lateral magnification of
>-20mm/2000mm = -0.01 .
> 
>Center of object is usually the angular center. That is, you would want
>the angle from near end to far end to be bisected to find the best lens
>axis. This minimizes off-axis aberrations. If your lens angle is wide
>enough then you can center wherever you want.
>
>Tom Hubin
>thubin@xxxxxxxxx
>

****  This last item is very interesting. I wonder if one could model an
afocal lens within a 3D program and use it for phanto-imaging? Is there
somewhere to find an approximate cross section for an afocal lens/system?

Thanks,
Larry Berlin

Email: lberlin@xxxxxxxxx
http://3dzine.simplenet.com/


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