6. Retinal Disparity - Eye Movements & Binocular Vision Summer 2026

-βL = βR

-βL - βR = 0

How to find points with zero retinal disparity?

the circle including the fixation point and the two entrance pupils

What is the Vieth Muller Circle?

location in space where objects have equal oculocentric angles (βL = βR)

What does the Vieth Muller Circle show?

zero

Objects on the V-M circle have _____ retinal disparity

single

Objects on the V-M circle will be (single/double)

corresponding

When an object falls on the V-M circle, it will be imaged on _______ retinal points

crossed

An object inside the V-M circle will have (crossed/uncrossed) retinal disparity

positive

An object inside the V-M circle will have (positive/negative) retinal disparity

No

When an object is INSIDE the V-M circle, will the retinal disparity be 0?

No -- Will see double since retinal disparity is NOT 0

Will a patient see single if an object is INSIDE the V-M circle?

uncrossed

An object outside the V-M circle will have (crossed/uncrossed) retinal disparity

negative

An object outside the V-M circle will have (positive/negative) retinal disparity

no

When an object is OUTSIDE the V-M circle, will the retinal disparity be 0?

no -- the retinal disparity of the object will not be 0

Will a patient see single if an object is OUTSIDE the V-M circle?

no

When a patient has a R esotropia, is the object will be fixated by the deviating right eye?

uncrossed

When a patient has a R esotropia, they will have (crossed/uncrossed) diplopia

-D/t negative disparity for the object of regard

-Retinal disparity = βL - βR

Why does a R esotropia lead to uncrossed diplopia?

fixation

The V-M circle is defined by the _____ point

No

Is the V-M circle defined by the object in regard?

relative disparity

The difference in absolute (retinal) disparity between two objects (relative to another object)

-Relative disparity = φL - φR

What is the equation for relative disparity?

No

Is fixation point important when calculating relative disparity?

Relative disparity (again)

The difference in the angles of binocular parallax

η = PD Δd / d^2

Equation to Know for Relative Disparity when there are 2 real world targets Separated by a distance, d

a target is seen simultaneously by both eyes

What is dioptic stimulation?

separate targets presented one to each eye

What is dichoptic stimulation?

How a Stereogram Stimulates Depth (Pic)

How a Stereogram Stimulates Depth (Pic)

Relative disparity = (XL - XR) / d

Equation for Relative Disparity in a Stereogram

simulates a dot and a line target at different distances (Line behind the dot)

What does an anaglyphic stereogram simulate?

uncrossed -- negative disparity

**the line is OUTSIDE V-M circle

In this example (see pic), when the DOT is fixated, the line will have (uncrossed/crossed) disparity

crossed -- positive disparity

**the line is INSIDE V-M circle

In this example (see pic), when the LINE is fixated, the dot will have (uncrossed/crossed) disparity

double -- each of the targets will have retinal disparity

In this example (see pic), when the patient fixates on a point midway between the dot and the line, both line/dot will be seen as (single/double)

uncrossed -- negative

In this example (see pic), when the patient fixates on a point midway between the dot and the line, the LINE will have (crossed/uncrossed) disparity

crossed -- positive

In this example (see pic), when the patient fixates on a point midway between the dot and the line, the BALL will have (crossed/uncrossed) disparity

-physiological diplopia

-fusion

When you present disparate images to the two eyes, what is the result?

-motor

-sensory

What are the 2 forms of fusion that are BOTH needed in order to see an object single and clear?

movement that adjusts eye position so object of regard is imaged on both foveas

What is motor fusion?

Cortical mechanism in which images from two eyes are integrated into a single perceptual whole

What is sensory fusion?

suitably related to each other

Monocular sensations MUST BE ___________ otherwise will NOT have sensory fusion

rivalry will be present (alternate suppression)

If monocular sensations are not suitably related to each other, what is the consequence of this?

normal diplopia resulting from retinal disparity (object of regard is single)

What is the definition of physiological diplopia?

No

Do all small disparities cause diplopia?

A normal physiological process eliminates diplopia for small disparities

Why do all small disparities NOT cause diplopia?

the critical retinal disparity for double vision

What is the diplopia threshold?

an area in the retina of one eye, which when stimulated simultaneously with a point in the retina of the other eye provides single binocular vision

What is Panum's Area?

double

If an object is OUTSIDE Panum's Area, what will the patient see?

fusion of small disparities & allows single vision for all 3 circles on the Randot even though there is disparity present

What does Panum's area allow for?

the specific sensation of depth arising from relative disparity

What is the definition of stereopsis?

innate

Stereopsis is _____ and develops by 4 months of age

relative depth info

What does stereopsis provide?

lateral disparity

What is the stimulus for stereopsis?

No

Can stereopsis tell info about ABSOLUTE depth?

the minimum relative disparity required for stereoposis

What is the definition of stereothreshold?

PD Δd / d^2

What is the equation for stereothreshold?

stereoacuity

In clinic we use ______ instead of stereothreshold

-η = PD * Δd / d^2

-η = 0.06m (1m) / (7m)^2

-η = 0.00122 radians

-η = 0.00122 rad * 206,000

-η = 252"

-The tree has uncrossed disparity (negative) relative to the car and will be seen further away.

EXAMPLE RETINAL DISPARITY:

A car 6 m away is parked in front of a tree that is 7m away. What is the disparity of the tree relative to the car in seconds of arc? (PD = 6 cm)

-This is a dichoptic presentation

-η = (XL - XR) / d

-Distance to screen is 1m

-η = (0.001m) / 1m

-η = 0.001 radians

-η = 0.001 rad * 206,000

-η = 206"

-The image for the right eye is to the right = uncrossed disparity

-The line has uncrossed (negative) disparity relative to the circle

EXAMPLE RETINAL DISPARITY:

Circle and line targets are displayed on a synchronous shutter computer display at a distance of 1m. The right eyes image has a line 2mm to the left of the circle. The left eyes image has the line 3mm to the left of the circle. What is the disparity of the line relative to the circle?

-dioptic

-dichoptic

How are images presented to two eyes in clinic?

-standard VA charts

-near point cards

What are the dioptic ways in which images are presented to the 2 eyes in clinic?

-stereoscopes

-anaglyph (R/G)

-polaroid

-alternating shutters

What are the dichoptic ways in which images are presented to the 2 eyes in clinic?

a device that presents different images to the 2 eyes with mirrors and lenses

What is a stereoscope?

dichoptic targets on a white background

How a R/G Anaglyph Works

What is the stimulus that is presented?

the eye that is covered by the green lens

How a R/G Anaglyph Works

What eye will see the Red targets?

the eye that is covered by the red lens

How a R/G Anaglyph Works

What eye will see the green targets?

-Sherman Cards

-Coloring with R/G crayons

-R/G Tranaglyphs

How a R/G Anaglyph Works

What is a clinical example of a R/G Anaglyph that presents R/G targets on a white background?

to subjectively determine deviation of the eyes in multiple positions of gaze

What is Hess Lancaster Screen used for in clinic?

-White screen with patient wearing R/G glasses (red over right eye)

-Doctor shines red light in nine positions of gaze

-Patient overlays green light on top of the red light

Set-Up of Hess Lancaster Screen

Red

In the Hess-Lancaster Screen, the right eye, with the red filter, will see the (Red/green) light

Yes

Can a R/G Anaglyph use a black background instead of white?

HTS: Home Therapy System (Pic)

HTS: Home Therapy System (Pic)

alternating shutters/images to achieve dichoptic presentation

What is the function of a synchronous shutter stereoscope?

Only one eye sees an image at a time d/t the shutter function

With a synchronous shutter stereoscope, how many eyes see an image at a time?

in IMAX 3D movies or in VTS therapy

When are synchronous shutter stereoscopes used?

mirrors

The first stereoscopes used ______

Wheatstone Mirror Stereoscopes (Pic)

Wheatstone Mirror Stereoscopes (Pic)

Synoptophore (Pic)

Synoptophore (Pic)

can present targets at any vergence demand

What is important about the Synoptophore?

dichoptic presentation of images

How are images presented in Wheatstone Mirror Stereoscope?

η = - (XL - XR) / target distance from the eyes

What is the equation used to calculate relative disparity in a Wheatstone Mirror Stereoscope?

Original Brewster Stereoscope (Pic)

Original Brewster Stereoscope (Pic)

Common Brewster Stereoscope (Pic)

Common Brewster Stereoscope (Pic)

the lens (prism) stereoscope (see pic)

What is the optical principle of the Brewster Stereoscope?

η = (XL-XR) / target distance from the LENS

How to calculate relative disparity in Brewster Stereoscope?

no

Does the Brewster Stereoscope measure from the eye for the d measurement (entire optical system)?

No

Is stereothreshold a particular value of relative disparity?

a number of stimulus characteristics

What is stereothreshold dependent on?

poorer

Stereothreshold under the best conditions is slightly (better/poorer) than Vernier acuity threshold

2"

What is the threshold of Stereoacuity for thin vertical lines?

20"

What is the threshold of Stereoacuity for Snellen letters?

taller

(Shorter/taller) vertical lines will result in better stereoacuity

>30 minutes of arc

What length of vertical lines will result in the best stereoacuity?