P3D Re: Stereo base formula

[abram klooswyk <abram.klooswyk@xxxxxx>]

(Please! Quiet! We can only discuss stereo base here for a short time
if we don't make much noise and admit that it _should_ be on T3D.)

Dogbreath wrote (P3D Digest 3245, 15 Mar 1999):
> (...) please refresh my memory on the formula (...)
> (...)the simple 1/30th rule, but that doesn't seem to take the focal 
> length of the lens into account (or, if it does, it's based on the 
> 35mm lens of the Realist and other 5 perf cameras) (...)

Tony Alderson wrote (P3D Digest 3246, 15 Mar 1999):
> (...) correct. The 1/30th rule assumes a 35mm lens and a far plane 
>at infinity. And it assumes the near point will be at the stereo window. 

No, the 1/30th rule is not only for 35 mm. It also holds for a Medium
Format system or for _any_ system which uses a "normal" focal length for
that format _and_ assumes "a far plane at infinity", _and_ assumes "the 
near point will be at the stereo window".

Why is this so?
Stereo is for viewing. Start from viewing, continue with viewing, and
then go to viewing. Viewing prevails.
>From there, go back to projection and viewers, then back to mounting, 
then back to photography, then finally to stereo base estimation.

Looking at infinity your visual axes are parallel, making a zero angle.
Looking back at some 2 meter (7 feet) distance they swing some angle.
Angles mostly are measured in degrees, minutes, seconds.
More convenient in these discussions is the unit Radian, one radian
is subtended by a circle arch (segment) of a length equal to the radius
of
that circle, it is about 57.5 degrees, so one degree is a little over
1/60 radian (and a one-foot ruler seen at 60 feet subtends one degree).

With 65 mm interpupillary distance, in looking at 2000 mm distance your
visual axes make an angle of 65/2000, about 1/30 radian.
Now looking at some projected stereo slide, when again the far point
is at infinity and the near point at about 2 meter (7 feet), the same 
angular swing applies, 1/30 radian. 

It seems to be more or less accepted that the depth range from 7 feet to
infinity is a useful range in stereo projection. So you can speak of a
STANDARD STEREO VIEWING SPACE which extends from 7 feet (2 meter) to 
infinity, a change of the visual angle (or swing) of 1/30 radian. 
This is where the 1/30 rule comes from, it is a viewability constraint,
originally it has nothing to do with lenses, and indeed it would apply 
to pinhole stereo photography.

How to get this amount of swing in projection?
It depends on the system you use. The 5P system (Stereo Realist family)
uses standard mounts for standard pictures, automatically giving the
right swing, based on the standard Deviation acquired in the 
photography with these camera's. The on-film deviation for 5P is 1.2 mm,
for a focal length of 35 mm, so again the swing angle is 
1.2/35 or 1/30 radian.
  
When you use Medium Format, nominally 6x6 (cm) you can use a similar 
standard, with a proportionally larger deviation, but the ratio
deviation/camera focal length must stay 1/30, when you accept the
mentioned standard stereo viewing space.

Now what about 24x36 formats, longer focal lenses and macro?
The question is: how are you going to view them?  _Viewing prevails_.

Do you use 200-mm camera lenses and keep the slides only for yourself,
to view them in a stereoscope with 200 mm lenses? Just use the 
1/30th rule and don't bother about 7 mm deviations.
 
But if you mix your slides in one show, one projector, one club, one 
competition, with 5P slides, then make sure not to surpass 1.2 mm 
deviation all the time (allowing double depth a few times).

As 50 mm is 50/35 times the Realist focal length, your deviation will
get
proportionally larger. As 140 mm is 2x the Realist base, your deviation
will be doubled using that base. In a macro shot 1:1 with a 50 mm lens
you will have an "working" focal length of 100 mm (2x extension).
So 50/35 x 100/50 will enlarge your deviation 3 times with respect to
5P.
You could use (1/3 x 1/30)= 1/90 of the distance of nearest point as
base, 
but as your depth range will not extend to infinity, a 2 or 4 times
larger
value will be OK, and some stretch is acceptable.
 
Tony Alderson:
>we are not very familiar with the shape of tiny things anyway.

Indeed, with the exception of circular shapes. I have seen many oval 
daisies and the like produced by the Macro Realist :-)

Abram Klooswyk


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