PePax

[P3D <LeRoyDDD@xxxxxxx>]

     Dave Worrell asked questions about 3-D using telephoto lenses, primarily
due to his interest in wildlife stereo. He had concerns about getting close
to dangerous subjects... also even the non-dangerous ones, if "wild", won't
often stay around as one sets up the stereo rig close enough to fill the
frame.

     The answer is the PePax or perspective/parallax ratio:
          With viewing conditions constant, as one increases the focal length
of the taking lenses, increase the lens separation by the same ratio. For
example, if you double the focal length, double the interlens separation.

     But wait! Not so fast, Stereoman!
     PePax only works for point objects.
     For a *point*, doubling the lens separation and focal length is
equivalent to moving half the distance to the point, but in real life one
can't move half the distance to *all* objects in the scene. Doubling the lens
separation doubles the depth parallax of *each* object in the scene; doubling
the focal length doubles *all* object image sizes.

     Imagine wanting to take a portrait of a football player on the 50 yard
line with the camera at the "zero" yard line.(Don't imagine to scale or the
field as regulation!) Put the goal post on the 100 yard line with a football
helment on one of the uprights; have the player cradling their helment in
front of them.
     Imagine the goal post of a size so that the image taken with 35mm lenses
show it twice as tall as the player. Since it's twice as far away, the
helment on the goal post is half the size of the one the player is holding
and has half the "depth."
     Since you think the player at 50 yards seems too small, you decide to
zoom to 70mm and double the lens spacing *instead* of moving half the
distance to the player and shooting from the 25 yard line.
     The player's image size is now on film as though at 25 yards with the
"depth" appropriate to that distance... but the goal post and helment are
also doubled in size and amount of depth, appropriate for a distance of 50
yards.
     If you had moved your normal camera setup to the 25 yard line, the
player would have gained size and depth for 25 yards and the goal
post/helment for their real distance of 75 yards... the player would have
doubled in each parameter, but the goal post/helment parameters would have
increased only by a factor of 1.5. (I think... math's not my strong suit!)
     This is an unavoidable "relative" distortion. How much it bothers the
spectator depends on the degree of distortion and how well the spectator is
willing to "read" the scene and disregard the distortion. In the above setup,
the distortion also is present between the helment about one foot closer than
the player's head and the head, but probably not very noticeable since the
distance ration is 1/150 instead of 1/2. We've learned to "read out"
perspective distortion in 2-D pictures and imagine the correct relationships
of objects... we can do the same with the PePax distortion.

     So you *can* use telephoto lenses and increased lens separation to
capture wildlife in 3-D. But it won't be really "natural."
     The least distortion is obtained when the "magnified and depthithied"
scene has few planes close together... the classic shot is birds in a nest on
a rockface... or maybe the football player and helment against the sky on the
top tier of the stadium.
     Actually, one should just get closer to the player.:=)

     It's possible that either more or less hyper-to-telephoto than the
one-to-one ratio of PePax might be read as more natural... in the same way
that we read the "stretch" of a longer viewing distance as natural to a
greater degree than we do "squash" resulting from being to close... or is
this just due to hardly ever seeing "squash" distortion?

     Since the part of my brain where stereoscopic thought resides is
beginning to overheat, I'm gonna' look at some slides in my new red button
viewer... some stretch, but none of 'em PePax! :=)

LeRoy Barco
LeRoyDDD@xxxxxxx


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