Visual Optics I

1
Visual Optics I

• Chapter 2
• Schematic Eyes

2
How do we handle the optics of something this
complex?
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Objectives

• Dealing with the eye as an optical system
• Reducing the complexity of real eyes to
  manageable schematic eyes
• Representing ametropia with schematic eyes

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Schematic Eyes
Page 2.1

• Simplified paraxial representations of the optics
  of real eyes

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Schematic Eyes
Page 2.1

• Simplified paraxial representation of the optics
  of real eyes
• Assume that all ocular surfaces are perfectly
  centered (single optic axis)

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Centered Optical System
Non-centered Optical System
Optic Axis
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Schematic Eyes
Page 2.1

• Simplified paraxial representation of the optics
  of real eyes
• Assume that all ocular surfaces are perfectly
  centered (single optic axis)

• To use paraxial optics, rays must be limited to
  the paraxial region
• Standard emmetropic schematic eyes are derived
  from the average constants of large numbers of
  real emmetropic eyes
• Simulate ametropia (myopia, hyperopia,
  astigmatism) by varying the constants of standard
  emmetropic schematic eyes
• Define three different schematic eyes, from
  complex to very simple
• Rule of thumb use the simplest schematic eye
  that will adequately represent the task/problem
  being considered

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Overview Optics of the Eye
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Define emmetropia

1. A healthy eye needing no correction for distance
   or near vision
2. A healthy eye needing no correction for distance
   vision
3. An eye needing no correction for distance or near
   vision
4. An eye needing no correction for distance vision

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Q1. Removal of which surface would make this eye
myopic (near-sighted)?

1. Anterior cornea
2. Posterior cornea
3. Anterior crystalline lens
4. Posterior crystalline lens

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Q1. Removal of which surface would make this eye
myopic (near-sighted)?

1. Anterior cornea
2. Posterior cornea
3. Anterior crystalline lens
4. Posterior crystalline lens

The posterior cornea is the only negative
refracting surface in the eye
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Q2. Flattening (to plane) of which surface would
make the eye extremely hyperopic (far-sighted)?

1. Anterior cornea
2. Posterior cornea
3. Anterior crystalline lens
4. Posterior crystalline lens

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Q2. Flattening (to plane) of which surface would
make the eye extremely hyperopic (far-sighted)?

1. Anterior cornea
2. Posterior cornea
3. Anterior crystalline lens
4. Posterior crystalline lens

The anterior cornea carries about 2/3 of total
ocular power
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Q3. If anterior chamber depth was decreased (all
other parameters unchanged) the emmetropic eye
would become hyperopic

1. True
2. False

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Q3. If anterior chamber depth was decreased (all
other parameters unchanged) the emmetropic eye
would become hyperopic

1. True
2. False

Treating the eye as a thick lens with the cornea
as F1 and crystalline lens as F2
Decreasing anterior chamber depth, decreases the
value subtracted from (Fcornea Fcr lens)
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Gullstrand 1 Exact Eye
Page 2.2
most complex
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Gullstrand 1 Exact Eye
Six refracting surfaces, 4 different refractive
indices,separate anterior and posterior corneal
surfaces,separate crystalline lens cortex and
nucleus
Page 2.2
Figure 2.1
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Exact Eye Thick Lens
1.00
1.336
1.336
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Exact Eye Equivalent Lens
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Exact Eye Thick Lens/Equivalent Lens
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Gullstrand 1 Exact Eye
Page 2.2
Figure 2.1
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Gullstrand 1 Exact Eye (Thick lens parameters)
Page 2.2
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Gullstrand 2 Simplified Schematic Eye
Page 2.3
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Gullstrand 2 Simplified Schematic Eye
Page 2.3
Three refracting surfaces, 2 different indices,
single corneal surface, single homogeneous
crystalline lens medium
Figure 2.2
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Gullstrand 2 Simplified Schematic Eye (Thick
lens parameters)
Page 2.2
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The Reduced Eye
Total ocular power reduced to a single
refracting surface
Page 2.5
Figure 2.3
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Reduced Eye Simplifications
Page 2.5
Figure 2.3

• Reduced surface represents the balance of power
  between cornea and crystalline lens (balance
  favors the cornea).
• Because the reduced surface represents a power
  balance, it sits about 1.67 mm behind the
  (anterior) corneal plane
• Pupil considered to coincide with the reduced
  surface (in reality, it is 2 mm behind the
  reduced surface)

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Reducing the Simplified Schematic Eye
Page 2.6
SS Eye
Reduced Eye
Figure 2.4
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Q4. In Visual Optics, three different schematic
eyes are used, varying in complexity from a
single refracting surface (reduced eye) to six
surfaces (exact eye). The reason for using three
schematic eyes instead of just one is

1. Accuracy. Some situations require more accurate
   representation of the optics of the eye than
   others
2. Necessity. Emmetropic eyes can be accurately
   represented by a single refracting surface, but
   ametropic eyes can only be accurately represented
   by multiple surfaces
3. Simplicity. It allows selection of the simplest
   schematic eye to accurately represent each
   situation
4. Complexity. Sometimes it is better to make an
   optics problem more complex than it needs to be

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Q5. Phakometry (the study of the crystalline
lens and accommodation) makes use of the small
fraction of incident light that reflects from
each ocular surface. Much of what we know today
about accommodation comes from early phakometry
studies. The most appropriate schematic eye to
use to measure size and brightness of the
reflected images in phakometry is

1. the Exact Eye
2. the Simplified Schematic Eye (SSE)
3. The Reduced Eye
4. None of the above

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Gullstrand 1 Exact Eye
Page 2.2
Figure 2.1
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Visual Optics

• The Human Eye Axes and Angles

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Why Define Axes and Angles?
1 Strabismus (ocular misalignment)
Which eye is deviating?
Which eye is deviating?
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Why Define Axes and Angles?
Where are the eyes looking? Where are the light
reflexes relative to the centers of the pupils?
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A note on Entrance and Exit Pupils
Significance?
When you look at someones eye, do you see their
actual pupil?
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Entrance and Exit Pupils
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Path of the Chief (Pupil) Ray through the Eye
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The Human Eye Axes (and angles) Near Vision
Page 2.7
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The Human Eye Axes (and angles) Near Vision
Page 2.7
Optic Axis a line through the optical centers of
the eyes refracting surfaces (ONN'O')
Figure 2.5
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The Human Eye Axes (and angles) Near Vision
Page 2.8
Figure 2.5
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The Human Eye Axes (and angles) Near Vision
Page 2.8
Figure 2.5
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The Human Eye Axes (and angles) Near Vision
Page 2.9
Figure 2.5
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Fixation Axis used in BV Eye Movements
Where is the eye looking as it rotates?
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The Human Eye Axes  Distance Vision
Page 2.8
The visual axis, PLS and fixation axis are all
parallel outside the eye in distance vision
(parallel incident ray paths from the distant
object of regard)
Figure 2.6
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The Human Eye Pupillary Axis
Page 2.9
Line traveling into object space through the
center of the pupil (EnP) normal to the cornea
Standing in front of a patient viewing normal
to their cornea at the center of the (entrance)
pupil, you are aligned with their pupillary axis
Figure 2.7
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The Human Eye Angles Near Vision
Page 2.8

• - angle between optic and visual axis (5?)
• - angle between optic and fixation axis
• - angle between pupillary axis and PLS
• ? - angle between pupillary and visual axis

Figure 2.5
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The Human Eye Axes  Distance Vision
Page 2.8
In distance vision, angle ? ? angle between
optic axis and PLS
Figure 2.6
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Page 2.11
Introduction to Ametropia
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Demographic question (no wrong answer) What is
your refractive error (ametropia)?

1. Hyperopia (far-sighted)
2. Emmetropia (no error)
3. Low myopia (lt ?5 D)
4. High myopia (gt ?5 D)

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Introduction to Ametropia

• Are you near-sighted or far-sighted?
• Near-sighted (myopic)
• high or low?
• high
• How do you know how myopic you are?
• Whats the difference between a 2 D myope and an
  8 D myope?
• Before we can quantify ametropia, we have to set
  a standard for emmetropia

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Standard Emmetropic Reduced Eye
Page 2.11
OBJ
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Emmetropia and Ametropia
Page 2.11
OBJ

• A longer eye needs lower power to be emmetropic

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Emmetropia and Ametropia
Page 2.11

• A longer eye needs lower power to be emmetropic

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Defining Ametropia
Page 2.12
Define ametropia in terms of the lens power that
will correct it
OBJ
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Correcting Ametropia - the Far Point
(A) In myopia, light from a distant object
focuses in front of the retina
Page 2.13
OBJ
(B) In myopia, light from the Far Point focuses
on the retina
OBJ
Figure 2.8
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Correcting Ametropia - the Far Point
Page 2.13

• The uncorrected myope readily identifies with the
  Far Point
• It is the furthest distance of clear vision
  (uncorrected)
• Objects beyond the Far Point appear blurred
• Objects at a range of distances inside the Far
  Point can be focused by accommodation

Figure 2.8 (B)
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Quantifying Ametropia
Page 2.15
e.g. Far Point 50 cm in front of the eye
Far Point vergence is equal and opposite to the
myopic eyes power excess We correct an ametropic
eye with a lens equal and opposite to its power
excess ? LMR A (Ametropia). Taking an eye with
the standard 22.22 mm axial length
The eye has standard axial length, so we could
define this as ?2.00 D refractive ametropia
(indicating that it differs from the SERE in
refractive power only)
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Quantifying Ametropia (cont.)
Page 2.15
Another eye with ?2.00 D myopia Fe 61 D
This eye has ?1.00 D refractive myopia and ?1.00
D axial myopia
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Spectacle Correction and the Far Point

• Provided light reaches the eye with Far Point
  vergence, a clear retinal image results
  (unaccommodated eye)
• It does not matter how Far Point vergence is
  produced
• by a real object at the Far Point
• by a spectacle lens that diverges light from a
  distant object so that incident vergence at the
  eye equals Far Point vergence
• by a contact lens that produces Far Point
  vergence fromlight

OBJ
Page 2.13
Figure 2.8 (B)
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Equivalence of Far Point Vergence Ametropia
Page 2.16
Optically, the eye sees no difference between a
real object in the Far Point Plane and incident
light diverged by a spectacle lens to produce Far
Point vergence at the eye (reduced surface)
Negative spectacle lens producing far point
vergence at the plane of the eye (reduced surface)
Light incident at the eye with far point vergence
focuses at the retina (unaccommodated)
Figure 2.9
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Equivalence of Far Point Vergence Ametropia
Page 2.17
Light waves demonstrate the equivalence
between(A) divergence of light to produce Far
Point vergence at the eye, and (B) divergence at
the eye from a real object at the Far Point
Figure 2.10
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Spectacle vs. Contact Lens vs. Ocular Correction
Page 2.17
Figure 2.10
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Spectacle vs. Contact Lens vs. Ocular Correction
Page 2.17
FS
FCL
FO
Figure 2.10
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Spectacle vs. Ocular Correction Examples
Page 2.17
FS
d
vertex distance
Figure 2.10
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Spectacle vs. Ocular Correction
Page 2.18
LOW MYOPIA EXAMPLE
??S
?MR
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Spectacle vs. Ocular Correction
Page 2.18
HIGH MYOPIA EXAMPLE
??S
?MR
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Hyperopia and the Far Point
Page 2.19
Figure 2.11 The uncorrected hyperopic eye has
too little power, so parallel incident light
focuses behind the retina (or would focus there
if it were not for the presence of the retina).
Convergent incident light is therefore needed to
move the image forward to the retina.
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Page 2.20
Far Point Vergence in Hyperopia
Underpowered hyperopic eye requires convergent
incident light at the reduced surface to focus
the image on the retina (unaccommodated)
Convergent incident light (in air) is traveling
toward a virtual Far Point (object) Plane
Figure 2.12
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Spectacle Correction in Hyperopia
Page 2.21
Positive spectacle lens power converges
incident light toward the Far Point Plane (in air)
Figure 2.13
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Spectacle vs. Ocular Correction Examples
Page 2.21
?MR
d
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Spectacle vs. Ocular Correction
Page 2.21
?MR
d
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Far Point, Eye Movements Spectacle Lenses
Page 2.23
As the myopic eye rotates, the Far Point traces
out a spherical surface, the Far Point Sphere
Figure 2.14
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Far Point, Eye Movements Spectacle Lenses
Page 2.24
In the spectacle-corrected patient, we want the
image produced by the spectacle lens (from
incident light) to fall on the Far Point Sphere
for all directions of gaze This is one of the
tenets of corrected curve ophthalmiclens
design
Figure 2.15
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Recap Key Objectives - Ametropia

• Ametropia is a mismatching of ocular power and
  axial length
• The Far Point of any (uncorrected) eye is
  conjugate to the retina for distance vision
• Ametropia is corrected by placing the second
  focus of the correcting lens at the Far Point