stereoacuity

[T3D Peter Abrahams <telscope@xxxxxxxxxx>]

>I thought the MMT and others of that ilk operated on a principle
>similar to interferometry. ..... Anyone know how
>images from different reflectors are combined?  Is that method
>applicable to eyeballs?  If so, it could help to explain why 
>vision with two eyes is sharper than vision with one.


The MMT (now being converted to a single mirror system) had different modes
of operation (for spectroscopy, the images were put in a line, according to
one source).  The primary optical arrangement was an incoherent array,
which took images from 6 mirrors and overlaid them at the image plane.
Although it was difficult to achieve, the basic schematic was not too
complex, just bouncing the images to a tertiary mirror that was faceted
and reflected the 6 images to a single point.  (BTW, an acquaintance who
worked there had the occasion to place his eye at the mutual focus.  He
said you would move your head around the spot, and get an impression of the
image.  When your eye was at the exact mutual focus, the image suddenly
exploded to become much brighter, more detailed, contrasty, etc.)
Peter Manly, _Unusual Telescopes_ (a good book, more descriptive than
analytical), p188, says that  the resolution of an array of telescopes is a
function of the size of each element  (the MMT, with 6, 1.8m mirrors, has a
resolution equal to the res of one 1.8m mirror, not equal to the potential
res of the 6.8m array).
Daniel Schroeder, _Astronomical Optics_, is a very authoritative volume on
that subject.  On p333, he says that the angular resolution of an array of
telescopes is essentially equal to the res of a single telescope of a
diameter equal to the distance spanned by the array.  He introduces some
complications, such as 'subsidiary peaks under the diffraction envelope'
from the distance between the mirrors.  Furthermore, this text is by no
means as easy to understand as Manly's.  I'll say, it seems clear to me,
with a less than total level of confidence.

If the resolution of two optical instruments whose images are combined, is
equal to the res of a single instrument of a diameter equal to the distance
spanning the two instruments, and the eye can fit this model, we are free
to speculate on some really fascinating aspects of binocular vision.  
Telescope users know that resolution increases dramatically as you increase
the diameter of your telescope.  A four inch refractor will show some
detail on Jupiter, a C8 will show a lot more, and a 20 inch Newtonian will
show the planet's surface in great detail.  The difference is dramatic, and
fits a mathematical model.  
However, resolution is limited by aperture (and by aberrations, eyesight,
the atmosphere, etc.), but only dependent on it at high magnification.  At
low powers, an instrument doesnt usually approach the potential resolution
of its aperture.  It is possible that this applies to stereoacuity (jumping
ahead here; see below.)

The entrance pupil of the eye ranges between about 2 to 7 mm, and the
interpupillary distance is 55 to 75 mm or so.  If binocular vision is
analogous to an incoherent array, stereo resolution could be partly
explained by this.  Of course, that is a big if.  In what way does the
nervous system resemble an image stacking optical system?
Howard & Rogers, _Binocular Vision and Stereopsis_, p150, elaborates on the
idea that stereoacuity is proportional to interpupillary distance.  This is
a mathematical formula, and it is difficult to tell if it is derived from
tests or from theory.  
Page 170, stereoacuity is reduced twice as much by lowering contrast in one
eye as by lowering contrast the same amount to both eyes.  If the image to
one eye is changed relative to the other, stereoacuity is reduced by more
than the monocular changes would indicate.  However, some depth perception
persists with large differences between the two images.  (Thus,
stereoacuity is an image processing function.)
Page 182, three types of stereo acuity were differentiated in tests.  They
resemble monocular acuity in that the different levels of acuity achieved
in the tests follow the order of the levels of the analogous monocular
tests.  Stereoacuity was measured in these tests at 3 arc seconds
(detecting a step of depth in a random dot stereogram), and 15 to 30 arc
seconds for another test.
Page 155, There is general agreement that, under the best conditions,
stereoacuity is in the range of 2 to 6 arcsec.  This is similar to the
limits of vernier acuity
MIL-HDBK-141 describes monocular acuity using different tests:  a cone in
the retina subtends about 1 arc minute, and optical resolution is limited
by this.  However, our image processors can considerably enhance this, to 4
arc seconds when viewing a break in a line (a vernier scale); or only one
half arc second (a line 1/2 arcsec wide against a blank background).  Thus,
monocular acuity, enhanced by the eye/brain system, can match stereoacuity.
MIL-HDBK-141 does not specify values for stereoacuity, but notes that
stereoscopic acuity is less when vision is less than 20/20, and does not
increase in persons with better vision than that.  Stereoacuity decreases
with lessened illumination, and markedly so when vision shifts from
photopic to scotopic.

So, now the question becomes, why isnt stereoacuity far better than
monocular acuity, since it has a vastly increased baseline?  Speculating
here, it is possibly because at the low magnification of our eyes, the
potential resolution is not used.

Binocular vision is definitely superior to monocular vision in rendering
contrast.  Using a telescope or microscope for long periods, in binocular
and monocular configurations, demonstrates this effectively.  This is
partly because each eye has a quantity of speck-like material in the
chambers, visible as floaters or invisible but detrimental to vision.  An
object could be blurred to one eye because of a floater, but the other eye
would see it, and binocular vision would use the combined image.  But tests
during WWII showed no substantial gain in resolving power when using
binoculars vs. using a telescope (this is not a test of stereoacuity).  

_______________________________________
Peter Abrahams   telscope@xxxxxxxxxx
the history of the telescope, the microscope,
    and the prism binocular


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