[photo-3d] Brewster and Wheatstone on the stereo base 5/5

[Abram Klooswyk <abram.klooswyk@xxxxxx>]

That toe-in stereopictures can be viewed perfectly, when only 
viewing convergence is matched to them, has been demonstrated 
again for 35 mm stereophotography in more recent years. 
J. E. Gould wrote on what he called "Near Point Stereoscopy" 
in the Stereoscopic Society Bulletin No. 37, March 1972 (pp 
3704-3706). He used convergence angles of 12 to 20 degrees 
for close-ups, mounted them in cardboard mounts, which were 
bent backwards in a flattened V form and then viewed in a 
special designed stereoscope with toeing-in lenses.

Wheatstone continued his 1852 reading by giving a table of 
"inclination of the optic axes" matched to distance, it runs 
from 2 degrees - 71.5 inches to 30 degrees - 4.6 inches. 
(For the latter distance you have to be very young or myopic - 
Wheatstone was indeed shortsighted.) This all assuming the 
same convergence in _viewing_, in a later paragraph confirmed 
by: "(...) the projections (...) correspond exactly with the 
inclination (...) under which they are viewed."
 
Interestingly the table does _not_ assume that the "distance 
of the camera from the object may be taken arbitrarily", 
Wheatstone gives the formula upon which the table is based: 
               distance = a/2 * cotang theta/2
where a is the distance between the two eyes and theta "the 
inclination of the optic axes".

A very funny fact is that this formula is _the very same_ 
as Brewster would give 4 years later (see 3/5), only with 
different symbols and a little reshuffled!

So what is the quarrel about?
Main cause seems that Wheatstone's phrasing is a little 
confusing. To the formula and the table he says: 
"... it shows the angular positions of the camera required 
to obtain binocular pictures which shall appear at a given 
distance in the stereoscope in their true relief." 

True relief is what Brewster wants all the time. 
But Wheatstone is also interested in "miniature 
representations" and what we now call stretch and squeeze. 
"Under the usual circumstances (...)", so in natural vision, 
convergence, distance and retinal projections are coupled. 
"but, by means of the stereoscope, we have it within our power 
to associate these circumstances abnormally, and to cause any 
degree of inclination of the axes to coexist with any 
dissimilarity of the pictures." "(...) M. Claudet prepared for 
me a number of Daguerreotypes of the same bust, taken at a 
variety of different angles, so that I was enabled to place in 
the stereoscope two pictures taken at any angular distance 
from 2° to 18° (...)".
Then Wheatstone describes the "undue elongation", "features 
... exaggerated in depth", and on the other hand "undue 
shortening". "The apparent dimensions in breath and height 
remain in both cases the same." These effects of course didn't
loose there significance after one and a half century.

Apparently Brewster was so annoyed about the suggestion to 
take pictures in which nature was violated that he missed the 
point of the visual experiments. 

But near the end of the chapter on "rules for binocular 
pictures" Brewster considers "under what circumstances the 
photographer may place the lenses of his binocular camera at a 
greater angle than that which we have fixed." 
1. "family portraits" - "angle of 2° for 6 feet" 
   (so _no_ greater angle) 
2. "any object whatever, when we wish to see them exactly as 
    we do with our two eyes" - "the same method" 
    (so again _no_ greater angle) 
3. "a portrait to assist a sculptor" - "a greater angle may be 
adopted in order to show more of the head."  (!)

And: "if we wish to have a greater degree of relief (...) in 
viewing colossal statues, or buildings, or landscapes (...) we 
must increase (...)." 
"We must (...) suppose the statue to be reduced n times, and 
place the semi-lenses at n X 2.5 inches." A today well-known
hyperstereo rule, but not the 1-in-30 rule.

But Sir David Brewster concludes with the famous words: 
"To add an artificial relief is but a trick which may startle 
the vulgar, but cannot gratify the lover of what is true in 
nature and in art." 

So it turns out that Wheatstone's opinions on the conditions 
under which "true relief" is reproduced do not essentially 
differ from Brewster's, he only used a wider variety of 
viewing angles, especially for experimental purposes. 
As ever since, the viewing method is the clue to the technique 
of stereo picture taking.

However, Brewster nor Wheatstone gives a rule which can be 
seen as a precursor of the one-in-thirty rule.
The essential feature of that rule is that it imposes a limit 
on permissible depth _range_. It says that, _when the scene 
extends to infinity_ , the base should not be larger than
1/30th of the nearpoint distance.
Limitation of the depth range is not advised by Brewster or 
Wheatstone. That became an issue only after some more decades, 
and probably first in France. 
But that's another story.

Abram Klooswyk