accomodation and convergence

[T3D Peter Abrahams <telscope@xxxxxxxxxx>]

_Binocular Vision and Stereopsis_, Ian Howard & Brian Rogers (1995, 730pp,
$120) has quite a bit to say on this issue, including a 60 page chapter on
vergence.  Some of the most interesting aspects are not directly relevant
to mismatch.  The text is quite technical and odds are good for an error in
my post.
   An object at 25 cm distance requries the eyes to be converged to form an
angle of 14 degrees at the object.  Interpupillary distance is a component
of convergence.  Devices that change IPD, like the telestereoscope (4
mirrors, 2 in front of each eye and 2 to the side, at 45 degrees to the
line of sight) increase convergence without changing accomodation, and
degree of convergence is inversely related to distance to object; but with
prism eyeglasses convergence is added as a constant to all objects, again
without changing accomodation.
   In the dark, the eyes assume a position of tonic vergence, looking at
a point averaging 1 meter distant, and accompanied by myopia.  This is more
converged than the position the eyes usually take when covering one eye
(although this vergence or phoria can be inward or occasionally outward).
The difference could be due to the accommodation on an object by the
uncovered eye in phoria (tests for phoria use distant objects).  Dark
vergence is better correlated with phoria when viewing through .5 mm
pinholes, which eliminates accomodation from a test for vergence.  Neither
is a true resting position, seen in deep sleep, anesthesia, or death, which
is more divergent.
   Vergence adaptation is the response to long term changes, for example by
wearing prism eyeglasses, and is a form of the mismatch from the original
T3D post.  Up to 10 prism diopters (horizontal) of adaptation been
measured, and up to 3 diopters of vertical adaptation, see p392.  (Vertical
divergence was forced by 3 diopter prisms, oriented oppositely.  After
using 6 diopter prisms, some subjects could overcome vertical disparity
with the 3 diopter prisms.)  [Imposing 6 diopters of vertical disparity for
up to 10 minutes sounds like something done to a prisoner of war.  There is
no discussion in this section of headaches, etc.; and even the chapter on
pathology seems to have nothing on discomfort or headaches.  I am reminded
of an eye surgeon who prescribed my glasses, until my complaint of
headaches from glasses got the response that for headaches you see a
psychiatrist.]  Vertical divergence is preferred for some tests because it
is not affected by accomodation and not under voluntary control.  Tests
show that the minimum disparity that will cause vergence (vertical) is
about 1 arc minute, higher at the periphery of the retina.  The continual
tiny movements of the eye are much larger than that (7 arcmin in a monkey),
and alternate explanations of this are on p401.  Page 394 has a drawing
showing how vertical disparity occurs whenever the eyes view an object away
from directly in front, so we are naturally skilled at vertical vergence.
An object 33 cm distant, 24 degrees from the eyes axis both horizontally
and vertically, needs 3 diopters of vertical vergence to fixate.  On p400
are tests of vergence without accomodation, using Risley prism eyeglasses
to force increased vergence until fusion fails.  The horizontal range is 10
degrees, 3.5 of divergence and 6.5 of convergence (in both humans and
monkeys.)  A vertical range of 7.5 to 11 degrees (5.5 degrees in two
directions), was apparently permitted by a test pattern image over most of
the field.  
   There are many classes of vergence adaptation, apparently it is
well-studied.  Some subjects adapt to increased convergence, or divergence,
or dont adapt to one or either, to different degrees at different
distances and with the stimulus at the center or periphery, when introduced
gradually or suddenly, and as prism power is increased some show
accelerating degrees of disparity at different rates.  Dark vergence is
changed after prisms are removed, for a varying length of time.  Tests must
be delayed to avoid after effects.  Vergence adaptation in monkeys has been
shown.
   Fixation disparity changes with accomodation, shown when positive or
negative lenses are used.  These cause change in accomodation, which change
the tonic vergence.  
   These changes in vergence can also change with angle of gaze, with
prescription eyeglasses the edge of the lens acts as a prism & if the eyes
require unequal correction, they will adapt with one eye looking slightly
askew from the other, to varying degrees at different angles of view.  This
degree of adapted vergence will be applied to an area about 18 degrees wide.  
   Pages 393-8 cover accomodation and horizontal vergence.  They both cause
pupil diameter to change, constricting with near fix/focus to compensate
for smaller depth of field and increased spherical aberration, and dilating
with distant objects to reduce diffraction & increase illumination.
   Accomodation in diopters is the reciprocal of distance to object in
meters.  To correlate, vergence is measured in meter angles, 1 meter
angle of convergence is used to fix an object 1 meter away.
   An increase in accomodation causes convergence, and a decrease evokes
divergence, a response known as accomodative convergence (AC), active over
5 diopters of accomodation.  It does not use disparity, and images to one
eye can cause it.  Muller in 1843 learned that a subject can change
accomodation without affecting vergence.  AC is measured in a covered one
eye by placing lenses in front of the other, or by inducing accomodation
with lenses when the eyes are in vergence from prism eyeglasses.  These
tests and others can produce inconsistent results.  Interocular distance
must be figured into results.
   Disparity is a more efficient producer of convergence, accomodation is
used when convergence is almost complete.  Strabismus patients show
accomodative vergence in spite of their inability in binocular vision,
similar to a person with one eye closed.
   AC (distinct from CA), is convergence accomodation, the change in
accomodation evoked by change in horizontal vergence.  It is measured by
viewing objects at different distances through pinholes, to eliminate other
cues.  Lasers form a speckle pattern on the retina independent of
accomodation, and are also used to measure this.  Accomodation in diopters
is approximately equal to vergence in meter angles, with the gain of the
response less in older or presbyopic people.  Dimming illlumination to
scoptopic levels has little effect.  Accomodation does not vary with angle
of gaze.  Horizontal convergence increases the horizontal radius of
curvature of the cornea, probably from tension from the medial rectus muscle.
   CA and AC probably use concurrent, interacting neural commands.  But the
rectus muscles (skeletal) respond faster than the ciliary muscles
(autonomic), so vergence starts before accomodation.  However, they have
independent, possibly correlated, states at rest in the dark.
Steeper convergence can be attained when accompanied by near accomodation.
CA often causes excessive accomodation, evoked by high convergence.  H. W.
Hofstetter is cited for 1945 research showing dissociation of vergence and
accomodation by trained subjects.  
   After page 398, topics include proximal vergence, evoked by images
without disparity or accomodation cues, where the apparent distance changes
without actual change.  
   It takes about 1 second to complete a response to change in disparity,
and signals during the response guide the movement, p402.  Convergence has
a longer latency than divergence.  The much faster saccadic movements
contribute to some degree to vergence, p413.
   Horizontal vergence uses both medial extraocular muscles or both lateral
muscles, unique among eye movements and therefore requiring a special
neural circuit, found in monkeys, p425.
   Accomodation cues can conflict with vergence cues, and their linkage
makes it difficult to change one independent of the other, chapter 11,
p427.  In tests, apparent distance decreased linearly with increased
accomodation, overestimating objects closer than 31 cm and underestimating
distant objects, with important differences between subjects.  The apparent
distance to the object as seen by accomodation can be varied with
constant vergence distance, or vergence can be varied with accomodation
constant.  To vary vergence, a stereoscope with adjustable distance between
images is used, or prism eyeglasses, but unchanging accomodation and image
size detract from the test.  Viewing through pinholes eliminates
accomodation cues, and point source targets eliminate size cues.  Elaborate
tests along these lines are on p428.  Accomodation & vergence are used in
vision to estimate distance to a nearby object, with wide variation in
individual ability and much difficulty in testing.
   Atropine micropsia is produced when atropine disables the ciliary
muscles, and the eye tries to accomodate and induces convergence, causing
the brain to think that the object is nearer and therefore must be smaller.
 Vergence micropsia occurs when the eyes overconverge on a test pattern,
overlapping to the repeated image.  Vergence angle is that of a near
object, so the pattern seems nearer or smaller.
   Eserine causes contraction of the ciliary muscles, thus a lessening of
accomodative effort and macropsia, where objects seem farther and larger.
Vergence macropsia occurs when the eyes underconverge on a repeated pattern
and it appears further or larger.
   The limited resolution of the infant eye limits the use (and
measurement) of accomodation in babies.  Accomodative vergence was observed
but not measured in 2 month old babies.  Convergence and binocular fusion
was observed at 12 to 16 weeks.  Vergence movements were photographed at
one month, with improved precision at 3 months.  Vergence to correct for a
prism was not consistent until 6 months.  Dark vergence is at 35 cm at
several months, compared with 120 cm for adults.  (page 621).

There are 72 pages of references, available on-line at
http://www.hpl.ists.ca/bvs.html 
ftp://hpl.ists.ca/pub/stereo_vision/bv-s.txt



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


------------------------------

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