Re: PePax

[P3D John Bercovitz <bercov@xxxxxxxxxx>]

LeRoy "The Antichrist" Barco has raised the dreaded specter of 
PePax knowing full well that it is anathema to Orthoman and that 
it will send Orthoman into a tizzy!  As we know, making Orthoman 
dance amuses LeRoy.
 
PePax was an erroneous theory that actually started a long time 
ago and continued, even in scientific journals, into the 1950s.  
One manifestation was in theory of binoculars.  It was maintained 
that, if you for instance, had 8 power binoculars, you should make 
the objective spacing 8 times the normal human IPD.
 
Binoculars are very very similar to stereo photography systems.  
The oculars magnify images presented by their objectives.  Stereo 
viewers magnify the images created by stereo cameras.  So the 
aerial image of a binocular objective is the equivalent of the 
film.
 
The actual rules of image reconstruction are very simple and there 
are only two:
 
1) Changing the relative separation of the two camera perspectives 
has a linear scaling effect on all three dimensions of the 
reconstructed image.  If the separation is 130 mm, twice the 
separation of the eyes, the reconstructed image is scaled down by 
a factor of two.  This rescaling is of all three dimensions and 
this _includes_ the distance of the image from the person viewing.
 
2) Changing the relative focal lengths of camera and viewer has a 
linear scaling effect only on the third, or depth, dimension.  
This effect _also_affects_ the distance of the image from the 
person viewing.  If you shoot with an 80 mm lens and view with a 
40 mm lens, all objects will be brought in to half the actual 
distance from you but the other two (non-depth) _apparent_ 
dimensions will not have changed.  This is because, although the 
object now subtends twice the angle at the eye, it also appears 
only half as far away, creating the illusion that it has been 
brought closer but not made larger in the two non-depth dimensions.  
 
So what happens if you combine the two effects?  
 
0) The original scene:
 
               _______
              |       |
              |       |          <----- object
              |       |
              |_______|
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
            O           O           <----- eyes
 
 
 
1) Shooting with 2X normal stereobase.
   Consequence: Half size and half as far away:
 
                ___
               |   |          <----- reconstructed object
               |___|
 
 
 
 
 
 
           O           O           <----- eyes
 
 
 
2) Shooting with camera lens length 2X viewer lens length.
   Consequence: Full width but half as far away and half as deep.
 
               _______
              |       |          <----- reconstructed object
              |_______|
 
 
 
 
 
 
 
           O           O           <----- eyes
 
 
 
3) Combining 1) and 2) to create PePax error: 
   Shooting with 2X stereobase and 2X lens length.
   Consequence: Half width but 1/4 as far away and 1/4 as deep.
 
                ___
               |___|          <----- reconstructed object
 
 
 
           O           O           <----- eyes
 
 
 
Now you have to pay attention to the angles subtended at the eye 
(image subtension) and to the total amount of parallax.  That's 
where following PePax has the advantage even though it distorts 
reconstructed space, contrary to the PePax theory.  Me?  I'd still 
go for the armored remote-controlled Realist.  8-)
 
John B
 


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