SL3D per John B

[P3D john bercovitz <bercov@xxxxxxxxxxx>]

It is perhaps a conceit on my part, but I believe I am the one 
most associated on this list with an understanding of how SL3D 
works which does not agree with Bill's understanding but which 
does agree with most other people's understanding.  Paul Kline is 
probably the one most associated with a neutral stance and he has 
done more work with the hardware than most of us, so I think it 
would be good to hear from him too.  Either Bill Carter or Mark 
Lenhart could best represent their understanding of SL3D.
 
Does everyone know what a center of perspective is?  That's a 
point from which a scene is viewed.  In a pinhole camera, the 
center of perspective is the center of the disk or very short 
cylinder of air which is the pinhole.  All rays which are going to 
expose film must pass through that hole.  [Generally you want to 
view a photograph from its center of perspective; if you don't, it 
will be squashed or stretched (see any closeup portrait taken with 
a very short lens for an example of a stretched out nose).]
 
In a camera, the center of perspective is the entrance pupil of 
the lens*.  The entrance pupil of the lens is the aperture (iris) 
of the lens as seen from the object (scene) side of the lens.  So 
you could say the entrance pupil is the aperture as modified by 
any elements of the lens which lie in front of it.  Even though 
its position and size are modified by these elements, it still has 
a definite apparent diameter and position which can be measured 
remotely from the object side.
 
It is possible to put two apertures in a lens instead of one.  All 
you have to do is take out the iris assembly and substitute a thin 
black piece of sheet metal with two holes in it.  In fact, some 
makers of macro cameras do this very thing.  By installing two 
holes, you are creating two centers of perspective and that is the 
essence of stereo photography.  Of course now your big problem is 
how to separate or decode the two images; they will want to land 
practically on top of each other and will indeed land on top of 
each other for an in-focus object.
 
You can place these two apertures arbitrarily close to each other.  
You can make them touch each other; you can flatten the touching 
sides of each (make them D-shaped) so as to put them even closer 
together.  In fact, you can split the original aperture right down 
the middle and still get effective SL3D.  When you calculate the 
stereobase, D-shaped apertures act as if they were located at 
their centroids.
 
There are several ways to decode the signals.  One is to put 
mirrors behind the lens to direct the signals to different parts 
of the film.  Another is to put a red filter over one aperture and 
a blue filter over the other; this is the essence of the Songer 
patent.  Another is to put differently-oriented polarizing filters 
over the two apertures; this is the essence of Bill Carter's 
patent (if I understand its claims correctly).
 
The neat thing about split-aperture SL3D as done by Carter or 
Songer is that you can change the separation of the centers of 
perspective merely by changing the diameter of the opening of the 
camera's original iris.  If you stop all the way down, you still 
have two little D-shaped apertures which are very close to each 
other.  So as you get closer to an object, and so need more depth 
of field and hence a smaller aperture, you also reduce the 
separation of the viewpoints which is also necessary to keep from 
having too much on-film disparity in the stereo pair.
 
Bill (Mark?) has a formula which describes their understanding of 
how SL3D works but I do not understand its derivation.  Their 
formula predicts the same values the conventional theory does to a 
truly astounding degree of accuracy.  I don't believe you can 
devise a practical experiment which would distinguish the two.  
You can:
ftp bobcat.etsu.edu   cd pub/photo/photo-3d/SL3D
and pull down files which compare the two if you care to get into 
that much detail.
 
*You may think intuitively that the center of perspective is the 
primary principal point.  That's a good guess because any paraxial 
ray going into a lens through the primary principal point will 
leave the secondary principal point at the same angle to the optic 
axis that the ray entered the primary principal point at.  You can 
prove that the primary principal point is not the center of 
perspective rigorously but it takes some time so let's just look 
at a couple of intuitive arguments: 1) In a telephoto lens, the 
primary principal point is way out in front of the lens; this is 
what makes the lens so compact for its focal length.  Most rays 
going through the primary principal point would miss the entrance 
pupil and so would never land on the film.  2) Just as with the 
pinhole camera, the entrance pupil is the hole all rays must pass 
through and so it serves as the origin of a fan out of rays traced 
in reverse from the pupil to object points.  In a symmetrical lens 
(not telephoto or retrofocus), the entrance pupil and the primary 
principal point are coincident.
 
John B
 


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