P1252428576ZiduD

1
(No Transcript)
2
Chapter 13 Section 1Spherical Mirrors revision
FYI
Pages 13.1 13.12
3
Chapter 13 Section 2
Page 13.13
4
Measurement of Anterior Corneal (1) Radius of
Curvature (Keratometry) (2) Overall Topography
(Keratoscopy)
Page 13.13
5
Burton (B L Clone) Keratometer
6
Nidek OPD-Scan Topographer
7
Measurement of Anterior Corneal (2) Overall
Topography (Keratoscopy)
Page 13.13
(1) Radius of Curvature (Keratometry)
8
Keratometry mainly overviewModified objectives
to follow
Page 13.13
9
Page 13.13
Paraxial Theory of Keratometry

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

10
Paraxial Theory of Keratometry
Page 13.13

• (Most) corneal topographers are based on the same
  principle as keratometers
• Both use the anterior corneal surface as a convex
  mirror.

11
How Keratometry Works
Page 13.14
Flat Cornea
Steep Cornea
12
Q1 What is the optical basis of Keratometry?

1. height of the reflected image
2. height of the refracted image
3. position of the reflected image
4. position of the refracted image

13
How Keratometry Works
Page 13.14
Flatter
F?
F
C
C
Reality image not actually at focus for near
object (but its close)
F
F?
14
Image size distant object
Page 13.14
Flatter
r
F?
f ?
C
h?
?
h?
?
f ?
C
F?
OBJ
r
h? ? r
15
Paraxial Theory of Keratometry
Page 13.13

• (Most) corneal topographers are based on the same
  principle as keratometers
• 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 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
16
Q2 A patients right eye has anterior corneal
radius 8.0 mm. When looking at a distant object,
the reflected image from the anterior cornea is
4.00 mm high. The left cornea has anterior
radius 9.0 mm. For the same object, reflected
image height will be

1. 2.50 mm
2. 3.33 mm
3. 4.00 mm
4. 4.50 mm

17
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)

18
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

19
The Keratometer Equation
Page 13.14
h?
20
The Keratometer Equation
Page 13.14
h?
21
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)
• Negligible error in x b assumption in real
  keratometers

22
Similar Triangles ? Keratometer Equation
h?
23
Similar Triangles ? Keratometer Equation
h?
Mirror
24
The Keratometer Equation
From similar triangles
25
The Keratometer Equation
Page 13.14
Rearrange the equation so we are solving for
radius
OBJ
26
The Keratometer Equation
h and b fixed in contemporary keratometers
From similar triangles
?
?
No radius yet - we want an equation for anterior
corneal radius. Use the lateral magnification
equation to rearrange
27
Question 3
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?
28
Q3 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?

1. no one ever thought of that
2. the actual reflected image is too small to
   measure accurately
3. even if a sufficiently accurate scale could be
   devised, patient eye movements would make an
   accurate measurement impossible
4. accessibility the virtual image is behind the
   cornea

29
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

30
Image Focusing and Magnification System
Fig.13.16Page 13.16
MIRE
OBJECTIVE
C
F
31
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
32
Principle of Prismatic Doubling
Single half-field prism creates two images with
deviated image displaced laterally from original.
Deviation calculated from
OBJ
33
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
34
Q4 Based on the previous figure, how could the
keratometer prism be used to yield a measure of
anterior cornea radius?

1. for shorter corneal radii, the prism would be
   moved LEFT to double the images
2. for shorter corneal radii, the prism would be
   moved RIGHT to double the images
3. It could provide a qualitative comparison only
   between corneas based on separation or overlap of
   the images

35
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
36
Topcon Keratometer What the Clinician Sees
V 90 / H 180
37
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
38
B L Oriented to Measure r60 and r150
39
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
40
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
41
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

42
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
43
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
44
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
45
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
46
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

47
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)

48
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

49
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)
50
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