Transcript Physiological Optics III Dr. Prasert Padungkiatsakul

Physiological Optics III
Dr. Prasert Padungkiatsakul
Ocular Motility
Horopter
• Horopter
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is a spatial map of corresponding points across the retina,
appear to be @ the same distance from the observer as the
fixation point
= zero disparity, = an equidistant horopter
= representing how we perceive 3-D visual space
Theoretical point horopter = the locus of all points in
visual space that are imaged on corresponding points in
each eye w/n the eyes are converged to aim @ particular
fixation point.
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• Horopter
Extends both horizontal and vertical
 Longitudinal / horizontal horopter = a slice of
the horopter along the horizontal plane.
 The two fovea, each representing the
oculocentric primary visual direction are
corresponding points
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• Corresponding points
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A point w/c displacement by a degree off the
fovea in one eye and an equal displacement off
the fovea in the same direction in the other eye
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• Vieth-Müller circle
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The set of all possible pairs of corresponding
points would be stimulated by objects lying
anywhere on a circle that intersects the fixation
point and the nodal points of the two eyes. =
theoretical horopter circle, geometric horopter
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• Horopter
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Because we can’t stimulate the retinal points
directly, but we do know the corresponding points in
each eye by placing an object in physical space so
that its images in each eye are formed on
corresponding points.
With controlled condition, eye stationary,
convergence symmetrically, we can map the whole
corresponding retinal points = horopter
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• Facts about corresponding points
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are perceived as having identical visual
directions in the two eyes. can split the
images of an object into two independent
segregated images each presented to one eye,
and see where the object can be seen from
visual direction for each eye.
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• Facts about corresponding points
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Have no binocular disparity.
Horopter show us all the points in space that are
perceived as being @ the same distance from the eye
as the fixation points
horopter have zero disparity and be seen in a flat
plane equidistant to the fixation point
 no fusional eye movements needed
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• Facts about corresponding points
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If images displaced off the corresponding points, we get
crossed disparity or uncrossed disparity
horopter = the location in visual space of boundaries
between crossed and uncrossed disparities as we fixate a
particular point
 horopter will be the place in space where we are most
sensitive to changes in depth, change from crossed to
uncrossed, objects will appear to change from being closer
than fixation point to farther away
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• Facts about corresponding points
As locations in space deviate more from the
horopter, crossed or uncrossed disparity will be
introduced, and eventually diplopia will occur
as the limits of Panum’s areas are reached.
  horopter = the center of the range in w/c we
have single vision
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• Methods of Measuring the Horopter
(Horopter criteria)
Identical visual directions
 Equidistance / Stereoscopic depth matching
 Singleness / Haplopia
 Minimum stereoacuity threshold
 Zero vergence
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• Identical visual direction horopter
Measured by comparing two rods, one by both
eyes (Fixation point), other upper half be seen
by one eye and bottom half be seen by another
eye w/ polaroid filter
 The subject move the rod forward and
backward until both half-images of the rod
appear to line up perfectly
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• Identical visual direction horopter
The subject move the rod forward and
backward until both half-images of the rod
appear to line up perfectly
 Plot all the corresponding points = horopter
 Thick line, become thicker @ periphery because
the elevated spatial localization thresholds in
the peripheral retina
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• Identical visual direction horopter
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W/ fixation disparity, the horopter will be displace inward
for eso FD, outward for exo FD relative to where the
physical fixation rod line
Because the eyes are not really aiming @ the physical
fixation rod, they aimed @ a true fixation point slightly in
front of (eso FD) or behind it (exo FD)
The horopter is then simply shifted toward where the
visual axes of the two eyes crossing
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• Equidistance / Stereoscopic depth
matching horopter
Apparent frontoparallel plane (AFPP) method
 More precise method and easy to do w/
untrained subjects
 If an object produces monocular images that
have zero disparity, the visual direction of their
images must also be identical
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• Procedure
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The subject views a numbers of rods while fixating
the middle rod.
The subject then adjusts the distances of all of the
other rod until they all appear to be @ the same
distance away as the middle rod in a plane parallel
to the subject’s face
The horopter will be curved, but the percept of the
subject will be a flat plane
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• Equidistance / Stereoscopic depth
matching horopter
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The shape of the frontoparallel plane as perceived
by the subject will be the mirror images of the
horopter setting
Move the rod closer than fixation because the
horopter farther away from the fixation and they
are trying to compensate for this by moving the rod
inward to make their position appear in alignment
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• Equidistance / Stereoscopic depth
matching horopter
Advantage – the examiner can see the shape of
horopter directly from the subject’s placement
the rods
 Disadvantage – fails to reflect the effects of FD
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• Singleness / Haplopia horopter
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The horopter is related to the absolute
placement of the rods in space, the bias in the
rod setting, and stereoscopic threshold can be
obtained from the variance of those setting, or
our sensitivity @ detecting binocular disparities
between the images of the rods
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• Singleness / Haplopia horopter
Images on slightly noncorresponding points
may be fused into a single percept as long as
they lies w/in Panum’s fusional area
 Measures the extent of Panum’s fusional area
@ the fovea and @ eccentric location
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• Procedure
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The arrangement of the rods is similar to AFPP
Middle rod is always fixated, the 2nd test rod is
moved closer to the subject until diplopia is reached.
Repeated moving the rod farther away
Zone of singleness = space between these two limits
Measurement are made w/ test rods @ several
eccentricities on either side of the fixated rod
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• Singleness / Haplopia horopter
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The center of this zone of singleness is taken to be the
singleness horopter
The haplopia horopter indicates where corresponding
points lies
The width of the zone of singleness reflects Panum’s area
in w/c noncorresponding points are still seen as single
The present FD can bias the location of the horopter
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• Minimum stereoacuity threshold
(Maximum stereoacuity horopter)
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Measured by fixating on a central rod while
measuring stereoscopic threshold for a second
More eccentric rod, determining the smallest
stereoscopic disparity (change in depth) that can be
detected for that rod
Relies on the observation that we are most sensitive
to changes in disparity and less so from changes
relative to a nonzero
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• Procedure
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Start the test rods @ the same perceived distance as
the fixation point, move it in depth until the subject
just perceives it as being @ a different distance
Repeat this for different target distance.
The measurement is obtained by determining the
variance of the rod settings that are seen as lying @
the same distance
The problem w/ this technique is that it is extremely
time-consuming and difficult, is not practical use
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•Zero vergence
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The most difficult horopter to measure
Requires measurements of extremely small fusional
movements of the eyes using sensitive objective eye
movement recording equipment
The subject would view the fixation target, and a second
target would be flashed momentarily
If the test target fell on noncorresponding points in the two
eyes, the exposure of the test target elicits a motor fusional
response from the subject
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•Zero vergence
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If the test target has a binocular disparity
because it lies off the horopter, it would serve as
a stimulus to the vergence eye movement system
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•Important to note
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For all horopter criteria, horopter are typically
measured with the eyes fixating a target @ the
same vertical height, to ensure symmetric
convergence
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The shape of the empirical horopter
and its analysis
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The Vieth-Müller circle is defined by 3 points, the fixation
point and the entrance pupils of the eye.
For any point on the circle, the angle between the entrance
pupil, and fixation point for the left eye (angle 1) is equal
to same angle for the right eye (angle 2)
Angle 1 and 2 are called external longitudinal angle
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The shape of the empirical horopter
and its analysis
The Vieth-Müller circle is the loci of all
corresponding retinal points as influenced by
the optic of the eye
 R = the ratio of the tangent of the two external
longitudinal angles @ any point on the horopter
 R = the relative magnification of the retinal
images between two eyes
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R = 1, 1 = 2, the left and right eye magnification
are equal
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The shape of the empirical horopter
and its analysis
R  1 the physical targets are not actually lined
up in physical space, although they are
perceived as being lined up.
 R > 1 angle 2 > angle 1 in physical space, the
right eye’s image > the left eye’s
 R < 1 angle 1 > angle 2, the left eye’s images
> the right eye’s
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R > 1 2 > 1 in physical space, right > left
R < 1 1 > 2, left > right
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The shape of the empirical horopter
and its analysis
Plot the value of R for each data point on the
horopter as a function of the magnitude of the
angle w/ 2  analytical plot
 Interested in 2 values
• Slop H
• Y-intercept, R0
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The shape of the empirical horopter
and its analysis
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The analytical plot is simply the graph of the equation:
R = H(tan2) + R0
R0 = value of the tangent ratio R measured @ the fixation
point, the ratio of the magnification of the image size in
one eye relative to the fellow eye
This relative magnification results in a tilting of the
horopter relative to the frontal plane
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The shape of the empirical horopter
and its analysis
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R0 = 1, there is no skewing of the horopter, flat
slope @ the fixation point
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The shape of the empirical horopter
and its analysis
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R0  1, there is uniform relative magnification
(equal magnification @ every retinal location),
tilting the horopter
• R0 > 1, left image larger, horopter is rotated
toward that eye.
• R0 < 1, right image larger, horopter is rotated
toward that eye.
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The shape of the empirical horopter
and its analysis
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Empirical horopter does not coincide w/ the theoretical
Vieth-Müller circle
The horopter tends to be less sharply curved
The different between the horopter and the Vieth-Müller
circle is called Hering-Hillebrand horopter deviation, H
It tell us that our perception of space is warped a little
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The shape of the empirical horopter
and its analysis
H tell us the relative curvature of the horopter
 H = 0, horopter lies on Vieth-Müller circle
 H = +, horopter is less curved than ViethMüller circle
 H =  horopter is more curved than ViethMüller circle
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The shape of the empirical horopter
and its analysis
H is typically in the range of +0.1 to +0.2
 H is a measure of nonuniform relative
magnification across visual field
 Local sign are not laid out equiangularly, nasal
more packed > temporal
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The shape of the empirical horopter
and its analysis
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The precise shape of the empirical horopter is a function
of the fixation distance used when measure it.
W/ greater fixation distance, the horopter curves more and
more away from the observer, eventually becoming convex
Abathic distance = distance @ w/c the apparent and
objective frontal planes coincide, horopter is flat
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The shape of the empirical horopter
and its analysis
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H = 2a/b
• 2a = the interpupillary distance
• b = fixation distance
The bathic distance is typically about 6 m from the
observer
The curvature of the Vieth-Müller circle is also changing
proportionately w/ increased fixation distance
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Vertical horopter
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@ near point fixation distances, the theoretical vertical
horopter is a straight line parallel to the head and
intersecting the Vieth-Müller circle @ the fixation point.
Empirically, vertical horopter tilts away from true vertical
Vertical horopter actually inclines w/ its top farther away
from the observer than the bottom
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Vertical horopter
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Being less inclined relative to the visual axis w/ near
fixation and more inclined w/ distance fixation
This inclination increase until, @ distance, the
empirical vertical horopter tend to lie parallel to the
ground below eye level
The most natural horizontal surface @ distance are
below eye level
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The horopter in abnormal binocular
vision
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Aniseikonia = a different in magnification
between the two eyes, different size or shape
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Aniseikonia
About 2-3% of population
 Different retinal images size between 2 eyes
• Optical origin (Optical aniseikonia)
• Neural origin (Neural or essential
aniseikonia)
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• Optical aniseikonia
Axial aniseikonia (Axial anisometropia)
 Refractive aniseikonia (Refractive
anisometropia)
 Induced aniseikonia; caused by external optical
factors, an afocal magnifier called size lens.
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• Neural aniseikonia
A small magnitude nonoptical aniseikonia that
can occur even in emmetropes, two retinal
images are physically equal in size yet still
perceived to be different in size.
 Optical and Neural aniseikonia are independent
phenomena that can either have an additive
effect or cancel out one another.
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• Aniseikonia
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May have a substantial effect on binocular
visual perception, distorting our 3-D perception,
degrading stereopsis, large enough inducing
binocular suppression.
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• Size lens
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A thick lens w/ parallel front and back surfaces that
changes the magnification of an image w/o having
any dioptic power.
Spherical surface both front and back = overall
magnifier
Cylindrical surface both front and back induce
magnification in one meridian = a meridional size
lens, cause shape changes in viewed objects.
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• Size lens
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Magnifying effects
• Power factor
• Shape factor
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• Power factor
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h = vertex dist.
Fv = back vertex power of the lens
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• Shape factor
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t = lens thickness
n = index of refraction
F1 = front surface power
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• Size lens
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Magnifying effects
• In afocal magnifier, there is no refractive
power no power factor, only the shape
factor
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• Meridional magnifier
Place the magnifier axis 90 magnification
occur on horizontal meridian
 AFPP rotate about fixation point. Because the
difference in horizontal image sizes between two
eyes. R changes , horopter would be rotated
in the opposite direction as the AFPP
 Called geometric effect
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• Geometric effect
Can be explained easily by the geometry of the
horopter and of the magnified images.
 Horopter rotate toward the magnified eye,
observer perceives the world as rotated away
from the manified eye
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• Geometric effect
The degree rotation / tilting of the visual space
equation
tan  = [(M-1)/(M+1)][d/a]
 M= magnification of the size lens
 d = viewing distance
 a = ½ of PD
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• Geometric effect
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Stronger magnification, the greater rotation / tilting
Shorter the viewing distance, the greater rotation /
tilting
This condition is quite confusing to the patient
because the depth information
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Binocular cues, horizontal disparities
Monocular cues, overlap, texture gradients
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Leaf room
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Literally a room in w/c the wall, floor, ceiling are covered
w/ leaves to help obscure monocular cues to depth
The entire room look tilted and distorted w/n a magnifier
is place before one eye, geometric effect is that the wall,
floor, and ceiling all appear to slant
W/ an axis 90 afocal magnifier on the right eye, right wall
appear to be farther away than the left, except from the
tilting of the AFPP in the geometric effect
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Leaf room
The apparent size of leaves on the wall varies as
a function of the perceived distance of the walls,
 The floor slant downward to the right, ceiling
slant upward to the right
 the square leaves room no longer appears to
be square
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Leaf room
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The changes in the ceiling and floor (vertical position) is
not magnification effects, because the magnification
induces only horizontal binocular disparities
The changes in the apparent size and distance of the side
walls create a secondary illusion of slant in the floor and
ceiling
Only horizontal disparities produced a percept of depth,
vertical disparities does not
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Vertical magnification
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A small amount of vertical disparity leads to
diplopia because humans have limited vertical
fusional eye movement capabilities
an axis 180 meridional size lens would produce
no change in the apparent AFPP or horopter
But the world will seem tilted, similarly the effect
produced by an axis 90 magnifier placed in front of
the fellow eye.
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Vertical magnification
Nobody know why vertical magnification in one
eye looks like horizontal magnification in the
other eye
 Called induced effect because it cannot be
explained in terms of geometry
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Induced effect
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W/n uniformly magnified in the horizontal and vertical
meridians, both geometric and induced effects will be
generated, the strength of these two percepts is roughly
equal for small degrees of overall magnification but in the
opposite direction
If uniformly magnify an image in one eye by a small
amount, it will have little or no effect on the orientation of
the AFPP, the geometric and induced effects will simply
cancel each other out
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Aniseikonia
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Can be produced by asymmetric convergence, to
bifoveally fixate a nearpoint target that is not on the
vertical midline, the fixate target closer than the
other  different retinal image size.
Every diopter of refractive difference between two
eyes  1.4% relative magnification between two eyes
Magnification is equal in all meridians image no
tilting image
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Aniseikonia
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Induced effect break down w/ magnification greater
than 5%-7%
Relative magnification difference in aniseikonia >
7%  disruption of fusion  amblyopia if
present in an infant
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Oblique magnification
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Produces a different kind of tilted percept, cyclodisparity
Vertical lines tilted toward the meridian of magnification.
This tilt translates to horizontal binocular disparities that
in magnitude as you move vertically from the fovea, the
vertical disparities are opposite in sign for the upper and
lower visual field
= inclination / declination effect
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Inclination /declination effect
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A percept that the world is tilted about the
horizontal meridian, top of VF is tilted away
from you and the bottom toward to you or vice
versa
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Cyclovergence eye movements
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In oblique magnification, cyclorotary eye
movements act in a compensatory manner, lessen
the perceptual effects of the cyclodisparity
Patients may complain of the floor appearing to tilt
upward or downward
Oblique cylindrical lenses may also produce this
effect
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Knapp’s law
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Uncorrected refractive emmetropes has little effect
on image size relative to that of the emmetropic eye
Uncorrected axial ametropia produces an image size
much different from that of the emmetropic eye,
correction w/ spectacle lenses placed near the
anterior focal plane of the eye will produce an image
size that is the same as that of an emmetropic eye
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Aniseikonia
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Unilateral intraocular lens implants (IOLs) following
cataract extraction exhibit substantial aniseikonia,
especially IOL @ antr chamber, even some patients w/
bilateral IOLs
Monocular refractive surgery
High cylindrical lenses having unequal power in different
meridians  unequal magnification in these meridians 
the geometric and induced effects are unequal
ODH433/2547
Dr. Prasert Padungkiatsakul
98
Aniseikonia
The skewing of the horopter w/ spectacle
correction of high anisometropia and
astigmatism explains in part the complaint
distortions of environment around them
 Force the patient to make unequal amplitude
saccades and pursuit in each eye
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ODH433/2547
Dr. Prasert Padungkiatsakul
99
Brecher Maddox rod technique
Left eye views two penlights, w/ right eye
viewing them through a Maddox rod
 Right eye seen two red streaks of light
 Iseikonia = equal space between the penlights
and space between streaks of light
 Aniseikonia = the two spacings are unequal
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ODH433/2547
Dr. Prasert Padungkiatsakul
100
ODH433/2547
Dr. Prasert Padungkiatsakul
101
Space eikonometer
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A form of stereoscope w/ two vertical lines and an
oblique cross as target
A person w/ aniseikonia will see the cross as rotated
instead of in a flat plane parallel to the eyes and/or
one of the vertical lines closer to the observer
Iseikonic lens = the lens for correcting the
aniseikonia by modifying the front surface
curvature, thickness, and refractive index
ODH433/2547
Dr. Prasert Padungkiatsakul
102
ODH433/2547
Dr. Prasert Padungkiatsakul
103
Aniseikonia
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Changes the fixation distance, the geometric effect,
and induced effect distort our percept of space and
distorted horopter
All of these case show the R (uniform magnification)
has been altered not for H (nonuniform
magnification)
The value of H does not change even under a variety
of condition
ODH433/2547
Dr. Prasert Padungkiatsakul
104
Aniseikonia
The manipulations all reflect optical changes to
the horopter rather than neural changes
 W/ prism, there is a nonuniform magnification
across the prism, more magnification @ the
apex than @ the base
 Cause nonuniform distortions in the perception
of visual space and in the horopter
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ODH433/2547
Dr. Prasert Padungkiatsakul
105
Prism
Base-out  cause visual space to curve concave
toward the viewer
 Base-in  cause visual space to curve convex
toward the viewer
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ODH433/2547
Dr. Prasert Padungkiatsakul
106
ODH433/2547
Dr. Prasert Padungkiatsakul
107
Adaptation to Lens and Prism
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Prescribing lens and prism, the space perception
should not sacrificed in the attempt to obtain the
best VA, use caution if that lens induces aniseikonia
The visual system is capable of adaptation to
distortions of visual space, the adaptation is only
partial, still some remaining spatial distortion
W/ geometric effect being neutralized w/in 3-4 days
and induced effect 5-6 days
ODH433/2547
Dr. Prasert Padungkiatsakul
108
Adaptation to Lens and Prism
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Oblique magnification, the strength of this
adaptation is less.
The binocular visual system can tolerate small
amounts of aniseikonia w/o loss of function
40% of emmetropes have neural aniseikonia of at
least 0.8%  clinical symptoms (asthenopia) can
occur w/in 1-2% magnification differences, beyond
5% begins it influence stereoscopic thresholds
ODH433/2547
Dr. Prasert Padungkiatsakul
109
Adaptation to Lens and Prism



Oblique magnification, the strength of this
adaptation is less.
The binocular visual system can tolerate small
amounts of aniseikonia w/o loss of function
40% of emmetropes have neural aniseikonia of at
least 0.8%  clinical symptoms (asthenopia) can
occur w/in 1-2% magnification differences, beyond
5% begins it influence stereoscopic thresholds
ODH433/2547
Dr. Prasert Padungkiatsakul
110