P3D The Third Deformation of 3D, Convergence changes (3 of 6)

[abram klooswyk <abram.klooswyk@xxxxxx>]

Using George Themelis' letter symbols, but adding C for
Convergence, photographic convergence C depends on Stereo
Base B and the distance of the subject from the camera I,
the angle of convergence in radian is roughly B divided by I
(C = B/I).
(With small angles only. A radian is about 57.3 degrees,
 so one degree is about 1/60 radian, which is one inch at
 60 inches, or one cm at 60 cm distance).

The third condition for orthodox Orthostereoscopy is:
C = Cv, or in words: the convergence of the axes of the
eyes in looking at an object in stereoscopic viewing space
should be equal to the angle of the camera lenses' "viewing
lines" in the photography of the object in real space.
(In this discussion I suppose the term convergence  to
include other effects which scale stereopsis, see P3d 3575)

If viewing convergence is a variable, how is it influenced?
This is seen most directly in stereo projection.
Operating the horizontal control of the projector lenses
moves the images on the screen in or out.
For orthostereoscopy a left "infinity" point should be about
6.5 cm to the left of the right one on the screen, then the
angle of viewing convergence is zero.
It is easy with the controls to make the screen infinity
separation larger or smaller. Superimposing the infinity
points makes the separation zero, then viewing convergence
from a seat at 7 feet is 2 degrees.
Moving the right infinity point even further to the left, it
comes to the *left* of the left one (resembling so called
crossed disparity). Then the convergence angle to the
infinity points is more than 2 degrees, and even more to near
points of the stereoscene, which then is seen floating in
front of the screen. (Similar effects occur in changing
viewer lens separation, if it is adjustable).

It is often forgotten that viewing convergence is influenced
in mounting too. But the well known Stereo Realist mounting
system, with its distant, medium and close-up masks, is based
on the principle of correcting viewing convergences to a
standard. The standard is: convergence between infinity and
a stereo window at 7 feet, which means convergence from zero
to 2 degrees.

This is automatically achieved when a "distant" mask is
used and the nearest photographed object was at (not closer
than) 7 feet. In this case (the distant or normal shot) the
separation of infinity points on the developed *uncut*
film is 70 mm (equal to lens separation), and the near point
separation is 71.2 mm. The difference of 1.2 mm is by
definition the near point *deviation*.

After cutting, transposing and mounting in a distant mask,
the near point separation is equal to the mask aperture
separation, 62.2 mm. Infinity separation becomes 63.4 mm.

But when you have a close-up shot with a nearest point of
30 inches (2.5 feet, 76 cm) the near point separation on the
*uncut* film becomes about 73.2 mm. So the difference with
the infinity separation (70 mm) is no less than 3.2 mm
(again, this is by definition the deviation of that near
 point).
Therefore you have restricted the far point in your scene to
about 4 feet (120 cm), so the far point separation on your
uncut film is 72.0 mm (1.2 mm less than the near point
separation, as in the distant shots). So you have restricted
the *deviation difference* to 1.2 mm.

In mounting this close-up shot in a close-up mask, the near
point separation becomes 62.2 mm, equal to the near point
separation of the distant shot mounted in the distant mask.
The far point separation again becomes 63.4, equal to the
far point (or infinity) separation of the distant shot in
the distant mask.
This is the very core of the Realist mounting system.

Now, what happens with the viewing convergence?
(To be continued)

Abram Klooswyk