Measurement of Anterior Corneal: (1) Radius of Curvature (Keratometry) (2) Overall Topography (Keratoscopy)

1
Measurement of Anterior Corneal (1) Radius of
Curvature (Keratometry) (2) Overall Topography
(Keratoscopy)
Page 13.13
2
Burton (B L Clone) Keratometer
3
Page 13.13
Paraxial Theory of Keratometry

• Keratometer - instrument used in clinic to
  measure anterior corneal radius of curvature
• Main applications of rAC measurement
• contact lens practice (CL fitting, evaluation)
• corneal disease practice (e.g. keratoconus)
• IOL design (phakic and aphakic)
• pre-LASIK corneal evaluation

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Page 13.13
Paraxial Theory of Keratometry

• Which of these applications actually uses a
  keratometer?
• Main applications of rAC measurement
• contact lens practice (CL fitting, evaluation)
• corneal disease practice (e.g. keratoconus)
• IOL design (phakic and aphakic)
• pre-LASIK corneal evaluation

5
Paraxial Theory of Keratometry
Page 13.13

• Photokeratoscopes (corneal topographers) have all
  but replaced keratometers in specialty clinics
  and practices
• Principles of keratometry and keratoscopy are
  identical
• Both use the anterior corneal surface as a convex
  mirror.
• 4 of light incident at corneal surface
  reflected ? Purkinje Image I
• The virtual image formed by a convex mirror
  increases in height in direct proportion to
  mirror radius
• For a distant object h? ? r ? h? k ? r
• For a relatively distant object (30 to 50 cm) h?
  ? k ? r

OBJ
6
Convex Mirror Optics
Page 13.14
Mirror r 8 mm
F?
F
C
C
F
F?
Mirror r 4 mm
7
Sample Question 1
A patients right eye has anterior corneal radius
9.0 mm. When looking at a distant object, the
reflected image from the anterior cornea is 4.00
mm high. The left anterior cornea has anterior
radius 7.5 mm. For the same object, reflected
image height will be (A) 2.50 mm (B) 3.33
mm (B) 4.00 mm (C) 4.80 mm
?
8
Convex Mirror Optics
Fig 13.14Page 13.14

• Relatively distant object ? reflected (virtual)
  image close to mirror focus
• Keratometry assumes the image is at the mirror
  focus (even though it is not)

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The Keratometer Equation

• Paraxial equation derived for measuring anterior
  corneal radius.
• Based on the assumption that the reflected image
  is at the focus of the (anterior) corneal mirror

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The Keratometer Equation
Page 13.14
h?
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The Keratometer Equation
Page 13.14
h?
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The Keratometer Equation

• As object distance (?) increases
• the virtual image moves closer to the mirror
  focus
• the difference between x and b decreases
• Derive keratometer equation using similar
  triangles assuming the virtual corneal image is
  at the mirror focus (assume x b)

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Similar Triangles ? Keratometer Equation
h?
14
Similar Triangles ? Keratometer Equation
h?
Mirror
Accurate but impossible
Assumed so keratometry will work
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The Keratometer Equation
From similar triangles
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The Keratometer Equation
Page 13.14
Rearrange the equation so we are solving for
radius
OBJ
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The Keratometer Equation
From similar triangles
No radius yet - we want an equation for anterior
corneal radius. Use the lateral magnification
equation to rearrange
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Page 13.15
Using the Equation to Design a Keratometer

• Object distance (b) fixed in all keratometers
• Object height (h) is fixed in the keratometers
  that we will consider

• Direct proportionality means that if our
  instrument can measure h? ? simply calibrate to
  read out radius instead

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Sample Question 2
If anterior corneal radius is almost directly
proportional to reflected image height of the
mire (illuminated keratometer object), why not
just measure image height and convert to
radius? (A) no one ever thought of that (B) the
actual reflected image is too small to measure
accurately (C) even if a sufficiently accurate
scale could be devised, patient eye movements
would make an accurate measurement
impossible (D) accessibility the virtual
image is behind the cornea
?
?
?
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Solution to Direct Measurement Problem
Accessibility the virtual image is behind the
cornea A virtual image consists of divergent rays
reflecting back from the cornea. Capture and
focus those rays with an objective lens at a real
image plane inside the instrument The actual
reflected image is too small to measure
accurately Magnify the real image with the
eyepiece lens (about 5?) Even if a sufficiently
accurate scale could be devised, patient eye
movements would make an accurate measurement
impossible Split the real image inside the
keratometer into two images using a half-field
prism. Adjust the prism (power or position)
until the two images are touching end-to-end.
Required prism deviation for doubling (touching
end-to-end) ? image height

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Image Focusing and Magnification System
Fig.13.16Page 13.16
MIRE
OBJECTIVE
C
F
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Application of the Doubling Principle to
Keratometry
Add a Single Half-Field Prism (Base on-axis)
MIRE
IMAGE PLANE
CORNEA
½ h
h?
F
C
½ h
x
OBJECTIVE
OBJ understand effect of half-field prism on
image
Fig 13.17, Page 13.18
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Principle of Prismatic Doubling
Single half-field prism creates two images with
deviated image displaced laterally from original.
Deviation calculated from
OBJ
24
Moving prism toward image plane decreases image
displacement (x) Previously doubled images are
no longer doubled (now overlap) What new corneal
radius would this prism position suit?
What happens if we move the prism?
MIRE
PRISM (P?)
IMAGE PLANE
CORNEA
½ h
h?
F
C
½ h
?x
OBJECTIVE
Fig 13.17, Page 13.18
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B L Oriented to Measure r90 and r180
OBJ
Question 3 If most corneas are aspheric, what
is one drawback with a keratometer?
Answer only measuring radius at one location
(annulus) on cornea and it is NOT central radius
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B L Oriented to Measure r60 and r150
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B L Oriented to Measure r90 and r180
OBJ
Question 4 What does the above appearance
indicate?
Answer anterior corneal astigmatism. What
type? Against-the-rule
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Estimation of Total Corneal Power
Page 13.23

• Most keratometers read out both anterior radius
  and total corneal power. How is this possible?
• It is not!
• Keratometer gives only anterior corneal radius -
  it cannot measure posterior radius? total
  corneal power reading is an estimate
• Estimate usually reasonable because the anterior
  cornea carries so much of the total corneal power
  (big ?n)

OBJ
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Basis of Corneal Power Estimate

• To see how we could estimate total corneal power
  from Keratometry (anterior radius alone) ? modify
  the Exact Eye to simulate what the keratometer is
  measuring

• Effectively ? creating a new schematic eye with
  an anterior cornea only that gives the same total
  corneal power as the Exact Eye

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Basis of Corneal Power Estimate - Exact Eye
Page 13.23
r2 6.8 mm
Fe (cornea) 43.05 D
F1 48.83 D
F2 ?5.88 D
naqueous 1.336
nair 1.000
r1 7.7 mm
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Basis of Corneal Power Estimate - Modified Exact
Eye
Based on Keratometry ? want anterior surface only
naqueous 1.336
nair 1.000
r1 7.7 mm
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Basis of Corneal Power Estimate - Modified Exact
Eye
Based on Keratometry ? want anterior surface only
naqueous 1.336
nair 1.000
r1 7.7 mm
33
Basis of Corneal Power Estimate - Modified Exact
Eye
Keep true anterior corneal radius - this is what
keratometry measures
Why is new n? lt 1.336?
Want single surface cornea to give same 43.05 D
as the Exact Eye cornea
naqueous 1.336
nair 1.000
Using n? 1.3315, the 7.7 mm Exact Eye anterior
corneal radius yields correct total corneal power
43.05 D
r1 7.7 mm
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Page 13.24
Estimation of Total Corneal Power

• Calibration Refractive Index 1.3315 works for
  real corneas if
• anterior posterior corneal radii are in the
  same proportion as the SEEE cornea (7.7/6.8)
• central thickness of the cornea is 0.5 mm
• Usually a good estimate, but keratometer cannot
  verify either of these properties

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Calibration Refractive Indices - Real Keratometers

• Zeiss, Rodenstock 1.332
• B L, Haag-Streit (Javal-Schiötz) 1.3375
• American Optical 1.336
• BL and AO index based on corneal back vertex
  power estimate (using posterior cornea as
  reference plane)

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Page 13.24-25
Calibration Refractive Index - B L Keratometer

• Different keratometer calibration refractive
  indices will give different total power estimates

OBJ

• Contact lens practice ? corneal power estimate
  used to estimate total corneal astigmatism.
• Astigmatism rarely exceeds 10 of total corneal
  power( 43 D) ? 0.78 D discrepancy in total
  power estimate translates to ? 0.078 D
  discrepancy in corneal astigmatism
• Intraocular implant design formula uses total
  corneal power estimate from keratometry directly
  ? with 1.3375, the SEEE corneas in situ power is
  0.78 D higher

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Intraocular Implant Design

• Relies heavily on axial length and keratometer
  readings

OBJ when applying formula, the basis (ncal) of
the K value must be consistent with the A value
(design constant)
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Page 13.25
Corneal Power Estimate - Routine Applications

• Estimating total corneal astigmatism.
• Estimating total ocular astigmatism intraocular
  astigmatism averages 0.5 D atr ? for most
  patients with moderate to high astigmatism,
  corneal astigmatism is a good predictor of total
  ocular astigmatism
• Problem with estimates of total ocular
  astigmatism ? keratometry will not identify
  exceptions to the trend

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Page 13.26
Measurement of Anterior Corneal Astigmatism
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Measurement of Anterior Corneal Astigmatism

• Most keratometers have two prismatic doubling
  systems (one horizontal and one vertical)
• These keratometers can also be rotated around
  their optical axis to align with corneal
  principal meridian(s) at any pair of oblique
  orientations
• Astigmatism ? difference in radii (and estimated
  corneal power) between principal meridians

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Schematic View of the B L Optical System
ILLUMINATED MIRE
HORIZONTAL VERTICAL PRISMS
OBJECTIVE LENS
EYEPIECE
OBSERVER
PV
CORNEAL MIRE IMAGE
PH
APERTURE PLATE
OBJ
Fig 13.22, Page 13.27
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Topcon Keratometer Rotating to Align Patient
Corneal PMs
V 90 / H 180
Lab Handout
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Topcon Keratometer Not aligned with Corneal PMs
Fig 3.22 Page 3.45
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Topcon Rotating toward Alignment with PMs
OBJ
Lab Handout
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Burton B L Clone Keratometer
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B L and Topcon Keratometers
Both are One-position Keratometers Both variable
doubling instruments based on prism position ?
two orthogonal prism systems that move parallel
to keratometer OA as operator varies doubling
MIRE
PRISM (P?)
IMAGE PLANE
CORNEA
½ h
F
C
½ h
OBJECTIVE
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Relating Anterior Corneal Astigmatism to Total
Ocular Astigmatism
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Page 13.34
Relating Anterior Corneal to Total Ocular
Astigmatism
Estimate total corneal power from anterior
corneal radius using a calibration refractive
index 1.3315 (for Fe value) 1.3375 (for F?v
value) The total corneal astigmatism estimate
becomes the difference in estimated corneal power
between PMs of the astigmatic cornea
49
Example 3.13 - Estimating Total Corneal
Astigmatism
B L Readings 7.5 mm _at_ 30O 7.8 mm _at_
120O What is the estimate of total corneal
astigmatism?
Estimated corneal astigmatism F30 ? F120
1.73 D (using ncal 1.3315 ? estimate 1.70
D) Correct with ?1.73 DC axis ??
120
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Javals Rule Relating Corneal to Total Ocular
Astigmatism
Statistically derived relationship between
keratometer estimate of total corneal astigmatism
(using ncal 1.3375) and total ocular astigmatism
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Page 13.35
Javals Rule
OBJ

• AS cylinder power in spectacle correction
• e constant (effectivity correction and
  allowance for positive correlation between
  corneal and post- corneal astigmatism) 1.25
• A C corneal astigmatism (estimate using
  1.3375)
• AP physiological astigmatism (?0.50 DC axis
  90)

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Applying Javals Rule
OBJ

• Formula ? atr astigmatism arbitrarily negative
  (correction)
• (therefore express e.g. 0.75 D atr as needing a
  correction ?0.75 D ? 90, not 0.75 D ? 180)
• 0.75 D wtr needs e.g. 0.75 D ? 90, not ?0.75 D ?
  180
• ? always applying correcting cylinder axis 90
• Javals Rule only used for atr or wtr astigmatism
  (not for oblique astigmatism)

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Example 13.4 Applying Javals Rule
Page 3.52

• Ks for a patients cornea 44.75 D _at_ 180,
  44.00 D _at_ 90
• Determine spectacle cylinder according to Javals
  Rule

?0.75 DC ? 90 A C
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Example 13.4 Applying Javals Rule
Corneal correcting cylinder (A C) ?0.75 DC axis
90
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Page 3.54
Corneal Topography- Keratoscopy
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Keratoscopy
Page 3.54

• Keratometry measures anterior central radius at a
  specific annulus around the corneal vertex

• It tells us nothing about the rest of the cornea
  ? curvature variations farther out are not seen

• Most corneas are aspheric, flattening
  peripherally. Keratoscopy samples a large area
  of the corneal surface ? can assess asphericity
  and other surface variations

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Placido Disc-based Corneal Topographers
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Placido Disc the Original Corneal Topographer
Placido Disc observer views the pattern of
concentric white rings (mires) reflected from the
patients cornea through a central 4 D
lens. Very qualitative
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Placido Disc-based Topography Principle

• Shares same limitation as keratometry ? radius
  measurement uses a virtual image behind the
  cornea, not a specific reflection point on the
  cornea.
• In keratometry the actual reflection point is
  unimportant (other than decreasing accuracy for
  longer corneal radii)
• The actual reflection point becomes a limitation
  with keratoscopy ? trying to assess radius at
  specific distances (annuli) around corneal vertex

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Anterior Radius and Virtual Corneal Image
Corneal Mirror
C
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Corneal Surface Asphericity Reference Sphere
Method
Cornea
Fig 3.27 - Page 3.54
H
Optic axial point
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PDB Keratoscopy - Spherical Cornea
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PDB Keratoscopy - Spherical Cornea
F
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PDB Keratoscopy - Spherical Cornea
F
65
PDB Keratoscopy - Aspheric Cornea
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PDB Keratoscopy - Aspheric Cornea
67
PDB Keratoscopy - Aspheric Cornea
Aspheric Cornea
68
PDB Keratoscopy - Spherical vs. Aspheric Cornea
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Interpretation of PDB Corneal Topography
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Qualitative Assessment of Corneal Topography
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Qualitative Keratoscopy - Klein Keratoscope
Page 3.56
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Klein Keratoscope Patterns
Fig 3.30 - Page 3.57
With-the-rule Astigmatism
Superior Corneal Scarring
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Klein Keratoscope - Keratoconus
Fig 3.31 - Page 3.58
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Page 3.61
Corneal Topographers
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Typical Corneal Topographer Tomey TMS-1 EyeSys
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Haag-Streit Corneal Topographer
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Corneal Topographers

• Typical Topographer ? curved mire surface allows
  sampling larger area of corneal surface
• Video capture device acquires image
• Analysis software produces color-coded
• radius variation (asphericity) map
• power variation (estimated total corneal power)
  map
• corneal surface topography map (contour map)
• Built-in programs for many different types of
  analysis and interpretation of patients corneal
  topography

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Keratoconus

• Most common corneal degeneration
• Etiology not clearly understood - many theories
  (systemic disease, hormonal changes, rigid lens
  wear, UVB, mechanical effects - eye rubbing)
• More common in males (contradicts earlier
  studies)
• Detected in second or third decade of life
• Produces a cone-shaped corneal apex
• As cornea degenerates and stroma thins ? patient
  develops a high degree of irregular astigmatism
• Corneal graft often required in advanced cases

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Keratoconus
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Oval or Sagging Cone - Keratoconus
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Munsons Sign
Bulging of the corneal apex forms a V-shaped
protrusion of the lower lid in inferior gaze
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Corneal Topographers - Keratographs Analysis
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Normal (aspheric) cornea - Power Map
84
Normal Astigmatism - Bowtie Power Map (wtr or
atr?)
Page 3.65
85
With-the-Rule Astigmatism
86
Oblique (wtr) Astigmatism
87
Against-the-rule Astigmatism
88
Oblique Astigmatism
89
With-the-Rule Astigmatism
90
Oblique Astigmatism
91
Moderate Keratoconus OS
Page 3.62
14 yo male. Best corrected spectacle vision was
20/40 OU. OS image shows a slightly more
irregular central corneal curvature, and has a
slightly poorer best corrected spectacle acuity.
92
Moderate Keratoconus OD
93
Bilateral Keratoconus Bitemporal Symmetry
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Advanced Keratoconus
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Post-PRK Topographic Map
Significant decentration with a cone-like map
pattern
96
?????????????
97
Clue
98
Post-Penetrating Keratoplasty (full thickess
corneal transplant)
99
Left deep LASIK post-op topography Right
delayed corneal ectasia (9 months post-op)
100
Post RK - EyeSys topographic map OD
Appearance typical for a post-operative RK.
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Corneal Models and Detection of Keratoconus
Several research groups have derived analytical
models to predict keratoconus based on a series
of topographic attributes of the corneal
surface These are used as built-in automated
programs in some topographers
102
DSI Area-compensated greatest difference between
any two of eight sectors of the cornea.
Differential sector index
103
Keratoconus Prediction Index Components Klyce
OSI Maximum difference in area-corrected corneal
powers between any two opposites of eight corneal
sectors .
Opposite sector index
Differential sector index
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Keratoconus Prediction Index Components Klyce
Fig 3.34b - Page 3.63
CSI Area-compensated difference between the
central 3 mm of analyzed area and an annulus
surrounding the central area from an inner radius
of 1.5 mm to an outer radius of 3 mm.
Center-surround index
105
Keratoconus Prediction Index Components Klyce
Opposite sector index
Differential sector index
Center-surround index
106
Keratoconus Prediction Index Components Klyce
Other Parameters
Page 3.63

• IAI - Irregular Astigmatism Index an average of
  the inter-ring power variations along every
  meridian for the entire corneal surface analyzed.
  The IAI increases as local irregular astigmatism
  on corneal surface increases.

107
Irregular Astigmatism Index
3 5 2 1 6 .
108
Keratoconus Prediction Index Components Klyce
Other Parameters

• AA - Analyzed Area indicates the fraction of the
  the corneal area covered by the mires that is
  processed. AA is lower than normal in corneas
  with high irregular astigmatism ?mires break up.

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Rose K Keratoconus Contact Lens
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Contact Lens Fitting Software
111
Post RK - EyeSys videokeratograph OD
Right eye of a patient I yr after bilateral RK
with OZ's less than 2.0 mm.
112
Post RK - EyeSys videokeratographs OS
Left eye of same patient 1 yr after bilateral RK
(OZ's less than 2.0 mm).
113
S-shaped distortion to the far peripheral placido
rings nasally and temporally Distortion more
clearly visible at higher magnification ?
114
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