P3D Curious Deep Math Tale

[Michael Georgoff <Michael_Georgoff@xxxxxxxxxxxxxx>]

Regarding the issue of math and stereo base...  Let me start by saying I
am NOT a "math-as-base" zealot.  I understand the position that Andrea
and Bruce take, and I see the point of bracketing, and rule-less
creative options and freedom, and the need for quick and simple
in-the-field, on-the-spot rules.  I like how Bob Aldrige put it "Yes,
the separation is calculated on the fly rather like the exposure."  Life
in not lived in a lab filled with metrics, life is out there where you
JUST DO IT and shoot.

But, I do have a stereo base math tale to tell from a strange, murky
landscape of formulas...

A while back (pre-recent exchanges), I decided to jump into the math, as
deep as I was capable of doing.  Being a simple man, I wondered about
simple issues.   What if that dog is 4 feet away and I have either a
slide bar or variable-base twin rig, what should my base be?

The General Solution calls for distance to subject, near point and far
point.  Being a simple man, I dunno from near and far, I just want a
stereo picture of that dog.  So, I use standard depth-of-field formulas
to derive Near and Far per my knowing the dog is 4 feet away and the sun
is out, hence f/16.

I start a spreadsheet which evolves into a combination of Depth of Field
and The General Solution.  I input distance to subject and f-stop, as
well as my focal length and favorite circle of confusion figure, and Mr.
Spreadsheet works our Near and Far.  Then, Near and Far feed into the
General Solution, which is also hungry for an on-film-deviation figure.
Ah, yes, that'll do it, this will solve it all.  I build it for f-stops
from 2.8 to 16.  I build it for distances ranging from 3 to 25 feet.
I'll just print this out, keep in my back pocket, grab the camera and
off I go.  I am sure that Bob is, in fact, my uncle.  BUT...

... it gets curiouser and curiouser.  It appears that stereo base is
dependent on f-stop.  That is all.  Over a range of distances, base is
the same per each f-stop.  All f/2.8's call out the same base.  All
f/5.6's the same.  I figure I'm an idiot, I have no idea what I'm doing,
I'm in it over my head, and, being the aforementioned simple man, I go
back to doing something simple, like nailing lime Jello Jigglers to the
kitchen ceiling while writing bad cowboy poetry... 

Then, I start it all over again a few months later, getting it done
again last night.  I'm thinking all along that I must have made a
spreadsheet error on my original efforts, so I start a brand new
spreadsheet, rebuild it from the ground up.  Hmmm.   Same results.  I
fool with it some more and realize a constant exists between f-stop and
base:

IF Depth of Field formulas are used to feed The General Solution,
(Given a 50 mm lens, C of C of .025mm, OFD of 1.2 mm)
THEN these are both true:
 Stereo base in inches = 47.244/f-stop.
 Stereo base in mm = 1200/f-stop.
(NOTE: These constants change per focal length, C of C, and OFD figures,
but they remain constant)

WANTED: Deep Math Guys who I can email my spreadsheet to, so as they can
figure out what I'm doing wrong, or confirm this a curious, but true,
artifact.  Also wanted: Reasonable explanations about the apparent
curious constant.

THEORY: The premise is that there would be objects at precisely Near and
Far in-focus points per the outer limits of DOF, and that these same
near and far object are those which are used in an on-film deviation
calculation.  Even if does prove true, how often are your DOF points and
your near/far the same?  So what, is this usable?  Would this suggest a
constant can be calculated (based on focal length, C of C, and OFD
figures) so that base = x/f-stop?

Anyone want to have a look?  Email georgoff@xxxxxxxxxxxxxx for a copy of
the spreadsheet.  As for me, I'm going to the mall to find a red
polyester suit (like TomCat) and a new rhyming dictionary, and then a
55-gallon drum of Jello powder from Costco.


Michael Georgoff
San Jose, CA


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