T3D Re: Phanto-cam Lens system

[Tom Hubin <thubin@xxxxxxxxx>]

Hello Larry,

> Is such a lens merely a *wide angle* lens, or is there another way of
> increasing the field of view without the familiar distortions of a wide
> angle lens?

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.

Thought #2

As has been mentioned previously in this thread, the lens planes are
parallel to the film. The lenses or lens elements are usually
decentered. This makes the object distance constant and as a result the
magnification is constant. This avoids making rectangular objects image
as trapezoids (keystoning).

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.

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



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