Physiological Optics III

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Physiological Optics III

• Dr. Prasert Padungkiatsakul

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Ocular Motility

• Horopter

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Horopter

• is a spatial map of corresponding points across
  the retina, appear to be _at_ 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 _at_ 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

• 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

• 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

• Because we cant 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

• 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

• Have no binocular disparity.
• Horopter show us all the points in space that are
  perceived as being _at_ 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

• 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 Panums 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 _at_ periphery because
  the elevated spatial localization thresholds in
  the peripheral retina

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Identical visual direction horopter

• 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 _at_ the
  physical fixation rod, they aimed _at_ 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

• 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 _at_ the
  same distance away as the middle rod in a plane
  parallel to the subjects 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

• 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 subjects placement
  the rods
• Disadvantage fails to reflect the effects of FD

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Singleness / Haplopia horopter

• 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 _at_ 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 Panums fusional area
• Measures the extent of Panums fusional area _at_
  the fovea and _at_ eccentric location

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Procedure

• 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 _at_ several
  eccentricities on either side of the fixated rod

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Singleness / Haplopia horopter

• 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
  Panums 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)

• 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

• Start the test rods _at_ the same perceived distance
  as the fixation point, move it in depth until the
  subject just perceives it as being _at_ 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 _at_ 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

• 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

• 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

• For all horopter criteria, horopter are typically
  measured with the eyes fixating a target _at_ the
  same vertical height, to ensure symmetric
  convergence

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The shape of the empirical horopter and its
analysis

• 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 _at_ 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 gt 1 angle ?2 gt angle ?1 in physical space, the
  right eyes image gt the left eyes
• R lt 1 angle ?1 gt angle ?2, the left eyes images
  gt the right eyes

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• R gt 1 ?2 gt ?1 in physical space, right gt left
• R lt 1 ?1 gt ?2, left gt 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

• The analytical plot is simply the graph of the
  equation
• R H(tan?2) R0
• R0 value of the tangent ratio R measured _at_ 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

• R0 1, there is no skewing of the horopter, flat
  slope _at_ the fixation point

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The shape of the empirical horopter and its
analysis

• R0 ? 1, there is uniform relative magnification
  (equal magnification _at_ every retinal location),
  tilting the horopter
• R0 gt 1, left image larger, horopter is rotated
  toward that eye.
• R0 lt 1, right image larger, horopter is rotated
  toward that eye.

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The shape of the empirical horopter and its
analysis

• 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 Vieth-Müller
  circle
• H ? horopter is more curved than Vieth-Müller
  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 gt temporal

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The shape of the empirical horopter and its
analysis

• 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 _at_ 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

• 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

• _at_ near point fixation distances, the theoretical
  vertical horopter is a straight line parallel to
  the head and intersecting the Vieth-Müller circle
  _at_ 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

• Being less inclined relative to the visual axis
  w/ near fixation and more inclined w/ distance
  fixation
• This inclination increase until, _at_ distance, the
  empirical vertical horopter tend to lie parallel
  to the ground below eye level
• The most natural horizontal surface _at_ distance
  are below eye level

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The horopter in abnormal binocular vision

• 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

• 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

• 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

• Magnifying effects
• Power factor
• Shape factor

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Power factor

• h vertex dist.
• Fv back vertex power of the lens

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Shape factor

• t lens thickness
• n? index of refraction
• F1 front surface power

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Size lens

• 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)/(M1)d/a
• M magnification of the size lens
• d viewing distance
• a ½ of PD

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Geometric effect

• 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
• Binocular cues, horizontal disparities
• Monocular cues, overlap, texture gradients

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Leaf room

• 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

• 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

• 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

• 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

• 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

• Induced effect break down w/ magnification
  greater than 5-7
• Relative magnification difference in aniseikonia
  gt 7 ? disruption of fusion ? amblyopia if
  present in an infant

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Oblique magnification

• 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

• 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

• 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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Knapps law

• 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

• Unilateral intraocular lens implants (IOLs)
  following cataract extraction exhibit substantial
  aniseikonia, especially IOL _at_ 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

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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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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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Space eikonometer

• 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

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Aniseikonia

• 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

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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 _at_ the apex
  than _at_ the base
• Cause nonuniform distortions in the perception of
  visual space and in the horopter

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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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Adaptation to Lens and Prism

• 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

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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

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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