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P3D Re: Re Stereo Base, Re Curious Deep Math Tale, Re 1/30 rule


  • From: abram klooswyk <abram.klooswyk@xxxxxx>
  • Subject: P3D Re: Re Stereo Base, Re Curious Deep Math Tale, Re 1/30 rule
  • Date: Sat, 15 Aug 1998 00:23:22 +0200

(continued)
What about depth of field scales? 
There is a lens having an aperture PQ and centre O. The point U is 
supposed to be sharply imaged on the film in point U*. 
A nearer point X will have its focus behind the film in X*, on the 
film it gives an blurred circle CC.
A farther away point Y is imaged before the film in Y*, it will give
another blurred dot on the film.

       |              |
       |              |                  ....---- X - - - U - - - - Y
       |              |         ...---'''     ..-'
       |           .. P ..---'''          .-''
       |  ...---'''   |                .-'
       C '            |             .-' 
  ..-' |         ---- O ----     .-'
X*     U*    Y*       |       .-'
  '-.  |              |    .-'
     ' C --..         | .-'
       |     ''-..    |'
       |          ''- Q 
       |              |         
       |              |         
       ^              ^              fig. 2
       film plane     lens plane    (C) Closearts

(This has to be my last ASCII try for some time. Again, higher
artists could add the lines UP, UQ, PU* and QU*, and similar lines 
joining Y with Y*.)
When the size of dot CC is equal to a predefined limit of definition, 
that means it is supposed to be indistinguishable from a real sharp 
point, XY is the depth of field. When you make the aperture smaller, 
leaving the points X, U, Y where they are, the dot CC on the film 
gets smaller. 

But suppose you keep the dot at the same seize and the lens aperture
too, but you change the focused distance by moving the lens farther
away from the film. 
Another Tiny Torch Virtual Experiment can illustrate this point. 
A string along the line X-U-Y is lit by back projection from a tiny
torch at CC. The part of string which is more or less sharply lit
will vary with the distance of the lens from the film. Again this is
easier to visualize when you think of the Angles involved. 
It is fun to do this experiment in reality with a small torch and a 
magnifying glass in a darkened room, directing the beam obliquely, 
a round cardboard aperture taped to the torch will help. 

Intuitively you will understand the relations between depth of field, 
stereo range, base estimation and torches.
You couldn't expect to get the Holy Grail without intuition?

So Standard Stereo Viewing Space dictates a standard angle between 
infinity and stereowindow, from that follows a deviation limit,
and from that constrains on stereo base and a stereo photography 
depth range limit. This limit is found back in depth of field 
ranges because all is governed by angles.

There is another analogy: stereo acuity and what I have called 
"photographic stereo acuity". Stereo acuity generally is measured
by devices or apparatus with determine the minimum range of depth
a person can discerne. This is not expressed as a length (minimum 
distance between the points) but as an angle. It turns out that this
angle is more or less independent of viewing distance, just what you
would expect from the Famous Torch Virtual Experiments. 
When you replace the Realist for a moment by eyes (some people hate 
to do this), stereo acuity angle resembles Angle "a" fig.1.

Several years ago you could find estimates of "stereo infinity"
in stereo photography literature. This meant the most far point 
which could be seen to be closer than infinity, in viewing stereo 
pictures. I omit details, but I have generalised that case to 
(photographic) stereo acuity at any distance. This again is an 
angle, which depends on several varying technical factors, but is 
supposed to be independent of the distances in Stereo Viewing Space.

Finally, I must say that I dislike all stereo base estimates 
or calculations that want you to fill up totally all available 
viewing space. Some day I'll give the reasons.
 
Abram Klooswyk


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