[tech-3d] David's "Complete Formula" for Stereo Base

["Michael K. Davis" <zilch0@xxxxxxxxxxxx>]

Hi David,

I just finished pouring over your terrific article at:

http://www.berezin.com/3d/Tech/lens_separation_in_stereo_photog.htm

I am truly amazed at how closely your "Complete Formula" mirrors the
geometrically "correct" formula known as the "General Solution" (used by
Bercovitz, Spicer and others.)  You've added a correction for viewer focal
length mismatch, which I strongly suspect Bercovitz would do also, without
hesitation, but what surprises me the most is how LEAN your formula is -
much easier to look at and work with!  And your explanation of the factors
is terrific, not to mention the tips you add near the bottom, like tossing
a rock into the air and waiting for it to hit the ground - as a visual aid
for syncing shutters when two people are firing them at several feet apart!
 Excellent!
  
I really enjoyed reading the whole article and consider it one of the best
written, most practical pieces I've seen for those doing stereography with
variable base equipment.  I ran my favorite set of Near and Far distances
to see how your "Complete Formula" performs alongside the "General
Solution" and the often inadequate 1/30 and 1/15 rules.  Again, I have to
tell you I'm amazed...

Have a look at this table of base values contrasting the General Solution
at 100% MAOFD against the 1/30 and 1/15 Rules (1/15 is often used for
Near:Far ratios of 1:2 and lower) and the "Complete Formula."

This table was calculated for a 65mm lens and matching viewer and 1/30 was
chosen as the "Depth Factor" for use in your formula, with the "Far Point
Factor" fixed at a value of 2 once the Near:Far Ratio falls below 1:2 (per
paragraph 3 in your discussion of this factor.)  By the way, your
explanation of why you do this is great - I abandon the General Solution at
this Near:Far ratio also.  By fixing the "Far Point Factor" at 2, you're
essentially going to the 1/15th rule (assuming your "Depth Factor" is 1/30)
while still accounting for any mismatch in Viewer FL mismatch to Camera FL.
 The article I posted recently, "Stereo Base Calculation with a $20.00
Handheld", discussed how I abandon the General Solution at Near:Far ratios
of 1:2 or less.  This freezes the base separation , which essentially
forces the on-film deviation to automatically shrink as the Near:Far ratio
goes from 1:2 toward 1:1 - thus avoiding the "wierd" stretch you discussed
when subject depth is shallow and one tries to maintain the same "Depth
Factor" or "% of MAOFD" that is used to good effect at higher Near:Far ratios.

Anyway, have a look at how closely the "Complete Formula" hugs the "General
Solution" at a deviation of 100% MAOFD, when a depth factor of 1/30 is
chosen and note, too, how your formula perfectly equates to using the 1/15
rule once the Near:Far ratio falls to 1:2 (again, these calculations were
done with matching 65mm viewer and camera lenses):


Near      Far      N:F Ratio   100% MAOFD     1/30     1/15    "Complete
Formula"

15ft    25,000ft    1:1667       151mm       152mm              153mm

15ft    1500ft      1:100        153mm       152mm              154mm

15ft    750ft       1:50         154mm       152mm              156mm

15ft    375ft       1:25         158mm       152mm              159mm

15ft    150ft       1:10         168mm       152mm              169mm

15ft    75ft        1:5          189mm       152mm              191mm

15ft    52ft        1:3.5        212mm       152mm              214mm

15ft    37.5ft      1:2.5        252mm       152mm              254mm

15ft    31.5ft      1:2.1        288mm       152mm              291mm

15ft    30ft        1:2          302mm                 305mm    305mm

15ft    20ft        1:1.33       602mm                 305mm    305mm


Conclusion:   Your formula gives us nearly the same numbers had with the
"General Solution", with a lot less brain strain and it has nifty features
thrown in like the "Lens Factor" for accomodating viewer focal length
mismatch.   Where Bercovitz and others encourage users of the "General
Solution" to use a DESIRABLE deviation - i.e. something LESS than MAOFD if
that's your preference, you offer a test methodology for tuning the "Depth
Factor" to a desirable value.  The same testing could be done to select a
percentage of MAOFD, of course, for use with the "General Solution."

Still, I have studied the General Solution at length and know it to fit the
geometry perfectly, so I'm compelled to declare it perfectly accurate where
your equation is nearly perfect - so close though, that I would surely use
it if simplifying the math was imperative for getting it programmed into a
spreadsheet or a calculator.  You can just look at it and readily see how
the factors impact each other. It's so easily "digested"!  

As a newbie to stereography, I'm just a tiny grain of sand amongst
boulders, but I can't resist saying that I recommend your formula (and the
article) heartily!

Thanks for sharing your methods!  

Mike Davis


>Date: Sat, 18 Nov 2000 18:58:51 -0800
>From: "David Lee" <koganlee@xxxxxxxxxxxxx>
>Subject: Re: Stereo Base
>
>
>
>> Is there some way you could condense the formula for those of us new at
>Stereo, and are satisfied >taking a spread sheet into the field. I would
>want to put the formula in an Excel spread sheet. also >would results be
>skewed to much if a guy used a constant for the far point? Please respond to
>me >direct if you choose.
>>
>
>In my presentation on camera separation at the last convention I tried to
>simplify the formulas into simple concepts which can easily be used in the
>field. All the math in the world is useless if it is too combersome to use.
>Steve Berezin copied my article onto his website.
>http://www.berezin.com/3d/Tech/lens_separation_in_stereo_photog.htm
>
>By the way, there is still time to sign up to receive a free copy of the
>first card of my new stereo card series. The series will be exclusively
>landscape images using 2 cameras. I plan to include supplementary notes that
>explain all my techniques, including what goes into my decisions in choosing
>camera separation.
>
>David Lee
>koganlee@xxxxxxxxxxxxx
>
>
>


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