P3D Re: Base Seperation Formulas

[Jonathan Gross <jonathan.gross@xxxxxxxxxxxx>]

Paul Talbot wrote:

> I was standing at a scenic overlook.  The ground fell away from my
> vantage point so it would not be a problem.  It fell down to a body
> of water, across which stood two volcanoes.  According to the signage,
> the two volcanoes were 52 and 54 miles from my vantage point.  I could
> set my SLR 70-210 zoom such that distant volcanoes filled the frame,
> with no foreground objects in the scene.  What should be the stereo
> base?

I think this is an interesting challenge, and I am exited to see the
range of answers.

That being said, my solution (based on the formulas in the book "Stereo
Photography" by Fritz G. Waack, DGPh AFIAP) makes the following
assumptions:

1) For the maximum stereoscopic effect, the stereo window (or, as Fritz
calls it, the near point distance) should be set just before the closest
point of the subject, or just shy of 52 miles (274,560 feet).  I would
like to point out that since there are "no foreground objects in the
scene," any base less than the calculated one will work, however, it may
not yield the desired stereoscopic effect.

2) The maximum parallax between the two 35mm film based images (delta)
is the (American ad hoc?) standard of 1.2mm (.04724") as reflected in
mounting gages available from a variety of commercial sources. 
Experienced viewers of stereographs are able to comfortably fuse images
with greater separations than this without difficulty, however, the
empirical value of 1.2mm is used.

3) The maximum focal length of the lens, 210mm, is used to fulfill the
requirement of "such that the distant volcanoes filled the frame." 
Depending on the height of the volcanoes and their horizontal separation
relative to the cameras' point of view, a smaller focal length might be
required.  Assuming that the problem is based in reality, however, the
likelihood that the height of, or that the separation between the two
volcanoes is a significant fraction of the 274,560 feet to the closest
volcano, then the greatest magnification will likely be employed to fill
the frame with their images.  As a point of comparison, I also provide
the calculation using the smallest focal length available (70mm).

With a 210mm focal length, the lens base which places the stereo window
at 52 miles is 1,569 feet.  This can more easily be calculated using the
1:175 base to nearpoint ratio associated with 210mm lenses when used
with 35mm cameras.

As promised for a point of comparison, the 70mm lenses would require a
base of 4,707 feet.  The base to nearpoint ratio for 70mm lenses is 1:58
when used on 35mm cameras.

I want to reiterate that lens bases less than these calculated distances
will "work", but that the greatest rate of change in parallax occurs
just behind the stereo window.  Therefore, the "Realist equivalent" of
filling the frame with subjects just beyond 6.5 feet is to place the
cameras farther apart in order to get the nearpoint just beyond the
stereo window.

Jon Gross


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