Vergence
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§ Vergence is a consequence of horizontally displaced eyes.
§ equal size but opposite direction (disjunctive) eye movements
§ the slowest speed eye movement
§ most recent in evolution (primates only)
§ but latency still less than saccades...
§ Necessary stimulus: accommodation vs disparity

Reading
RHSC2 chapter 5, and vergence chapter 8 in Leigh & Zee.

Species differences
no vergence in cats
In chameleons the two eyes may be aimed independently.

DEMO: Prisms and accommodation
Juggling with prisms over both eyes, illusion of depth change.
UG Jude Cannon (1994). lateral deviation easier to overcome than versional deviation: studied by way of juggling performance.

The fragility of vergence
Vergence movements are rather small in amplitude, typically a few degrees for each eye. Maximum is about 30 deg?
disjunctive movements. Equal and opposite eye movements. (The movements do have to be equal size)
Recent in evolution. Cats normally can't make vergence eye movements. "Seeing double" is a sign of fatigue in the vergence system. "...disturbances of vergence [double vision...] are amongst the most frequent clinical ophthalmalogical symptoms; it is a common experience that it is these movements that are the first affected by fatigue, alcohol and other drugs."

Vergence eye movements are slowest to reach full development in infants and toddlers.
"Binocular alignment and vergence in early infancy," Hainline & Riddell, Vision Research 36: 3229-3236 (1995).

Exceptional humans who can diverge at will, like RHSC, Abraham Lincoln, Marty Feldman, (and maybe you) are uncommon individuals.

Parkinsonism can affect and even eliminate vergence eye movements (LZ2, p 280).

Vergence speed
Inspecting figures from RHSC2 chpt 5 it looks like once vergence get started it has a maximum speed of about 25 deg/sec.
Feel it yourself, how many hundred msec elapse looking from far to near, and vise versa.
Is there a "vergence saccade"? no, vergence appears not to be ballistic.
RHSC2, p118: "Convergence is considerably more rapid than divergence" ... 20 vs 10 deg/sec?

One idea to account for the slow speed of vergence: its speed may be limited by how quickly the lens can change shape and report on focus.

Latency: 160 msec or so

The stimuli for vergence
The near response: accommodation, vergence and pupil constriction.

Accommodative vergence
Image out of focus causes accommodation changes, and corresponding vergence movement. Accommodative vergence can be induced with one eye only, by a lens put in front of that eye.

Disparity vergence
Vergence only makes sense as a horizontal eye movement. Disparity is a measure of "error" in the horizontal alignment of the two eyes for a given target. See Fig 5.1 of RHSC2 for definition of diopter, for measuring disparity. 1 cm deviation 1 meter from 1 diopter prism.

With a 12D prism base out, flip in and out of visual pathway and experience disparity vergence, and the slow speed of the eye movement.

Challenge on page 105-06 of RHSC2: binocular fusion without fixation?

Fig. 5.4 of RHSC2: startlingly different pairs of images can induce vergence.

Is there such a thing as vergence smooth pursuit?

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Visual binocular cells driving vergence. From our study of the Pulfrich illusion we found that there are cells in the visual cortex that signal "nearness." Presumably these cells have some linkage to the vergence system.

Vergence plus saccade. Combining vergence with conjugate movements: saccades.
Saccades have long latency, so the first movement is a vergence. Can arrange (See Fig 5.5) that one eye doesn't have to move at all in a change of fixation, yet that eye will undergo both vergence and saccadic movement before the new fixation is found! Fig. 5.4B shows what happens when accommodation is the stimulus and the moving eye is occluded. Notice that (see L&Z Fig 3) the saccade needs to stop at precisely the place where a pure vergence movement will finish the change in fixation.


After the saccade the eyes are looking at point V2, from which an equal and opposite vergence movements lands both eyes on the new target. The left (lower) eye makes "unnecessary" vergence to the right, saccade to the left and more vergence to the right for both eyes to make equal movements.

Any vergence movement must be equal sized for both eyes: Scale the drawing from a line drawn through the nose to the target!

Models for vergence
Is vergence ballistic or guided?
They are slow, so it is not hard to do experiments that show vergence movements are guided: Try to interrupt a vergence eye movement and you will succeed!

Why is vergence so slow?
Suppose the pulse part of saccade pulse step were missing? Would that give us a vergence movement? Try it with your saccade stimulation: The eye movement is still too fast!

Here's another attempt: Model "guided step" with negative feedback, including the integrator we needed in the OMN "step". We let the integrator have unity gain. Here's the Laplace transform:

and

This is an overdamped system: basically a integral controller facing the plant. Because error is being integrated, error will be driven to zero.

§ Open loop studies & the neural integrator
See Fig. 5.13 and 5.14 for results. In the open loop pathway there must be an integrator! Notice the input is a square wave of disparity differences.

Vergence chapter 8 of Leigh & Zee 4th Ed, notes
Fusional vs accommodative vergence. The difference? fusional is driven by disparity.

A slowly accelerating eye movement, in the range of 5-20 deg per second, about 20 times slower than a saccade.

No motoneurons are devoted to vergence exclusively.

A step change in disparity results in a step change in motoneuron firing rate. No pulse involved! See L&Z Fig 2 for the "negative exponential" waveform.

It is not known how the disjunctive control is carried out, but some speculation has been made: the stimulus for convergence must activate both MR simultaneously, with step inputs. Somewhere in the visual system, binocular-driven neurons that respond to disparity differences project to the oculomotor centers.

Clinical problem: strabismus: defects of vergence
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The triad of the near reflex: As something approaches a human observer, the pupil constricts, the lens becomes rounder (parasympathetic responses) and the eyes converge. 2004: Type into Google "near reflex" eye Ohio University and click on the first (PDF) reference, course graphics from Patrick O'Conner, of Ohio University. The near reflex is in place by the 4th month of age.

The problem of computing the point at which to change from vergence to saccade.

Summary
§ A slow, recently evolved and easily disturbed eye movement system.
§ Stimulus: accommodation vs disparity
§ Neural substrate: a small step output that somehow is directed to both MR or both LR simultaneously.