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Pages 13.1 – 13.12. Chapter 13 Section 1 Spherical Mirrors – revision FYI. Page 13.13. Chapter 13 Section 2. Page 13.13. Measurement of Anterior Corneal: (1) Radius of Curvature (Keratometry) (2) Overall Topography (Keratoscopy). Burton (B & L Clone) Keratometer.

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measurement of anterior corneal 1 radius of curvature keratometry 2 overall topography keratoscopy

Page 13.13

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

measurement of anterior corneal 2 overall topography keratoscopy

Page 13.13

Measurement of Anterior Corneal:(2) Overall Topography (Keratoscopy)

(1) Radius of Curvature (Keratometry)

slide9

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
slide10

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.
slide11

How Keratometry Works

Page 13.14

Flat Cornea

Steep Cornea

q1 what is the optical basis of keratometry
Q1: What is the optical basis of Keratometry?
  • height of the reflected image
  • height of the refracted image
  • position of the reflected image
  • position of the refracted image
slide13

How Keratometry Works

Page 13.14

Flatter

F

F

C

C

Reality: image not actually “at” focus for near object (but it’s close)

F

F

slide14

Image size: distant object

Page 13.14

Flatter

r

F

f

C

h

h

f

C

F

OBJ:

r

h  r

slide15

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:

slide16

Q2: A patient’s 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:

  • 2.50 mm
  • 3.33 mm
  • 4.00 mm
  • 4.50 mm
slide17

Mirror

h

h

F

C

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)
slide18

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
slide19

Mirror

h

F

C

b

The Keratometer Equation

Page 13.14

h

slide20

Mirror

h

F

C

Keratometer equation assumes that x = b

used in keratometer

b

used in theory

The Keratometer Equation

Page 13.14

h

slide21

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
slide22

Mirror

h

F

C

Assume virtual image here

b

Similar Triangles  Keratometer Equation

h

slide23

h

F

C

= h

b

b

Similar Triangles  Keratometer Equation

h

Mirror

slide24

Rearrange

The Keratometer Equation

From similar triangles:

slide25

The Keratometer Equation

Page 13.14

Rearrange the equation so we are solving for radius:

OBJ

slide26

h

Mirror

h

F

C

b

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:

question 3
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?

slide28

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?

  • no one ever thought of that
  • the actual reflected image is too small to measure accurately
  • even if a sufficiently accurate scale could be devised, patient eye movements would make an accurate measurement impossible
  • accessibility: the virtual image is “behind” the cornea
solution to direct measurement problem
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

slide30

b

KERATOMETER IMAGE PLANE (GRATICULE PLANE)

CORNEA

½ h

½ h

½ h

½ h

EYEPIECE (OCULAR)

Image Focusing and Magnification System

Fig.13.16Page 13.16

MIRE

OBJECTIVE

F

C

slide31

Application of the Doubling Principle to Keratometry

PRISM (P)

h

P

= h

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

slide32

Principle of Prismatic Doubling

Single half-field prism creates two images with deviated image displaced laterally from original. Deviation calculated from:

OBJ

slide33

h

P

< h

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

slide34
Q4: Based on the previous figure, how could the keratometer prism be used to yield a measure of anterior cornea radius?
  • for shorter corneal radii, the prism would be moved LEFT to double the images
  • for shorter corneal radii, the prism would be moved RIGHT to double the images
  • It could provide a qualitative comparison only between corneas based on separation or overlap of the images
slide35

GRATICULE PLANE

Two prisms means two deviated images

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

slide37

Corneal vertex

h'90

h'180

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

slide38

Corneal vertex

h'60

h'150

B & L: Oriented to Measure r60 and r150

slide39

Corneal vertex

h'90

h'180

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

slide40

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

slide41

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
slide42

ncornea 1.376

Basis of Corneal Power Estimate - Exact Eye

Page 13.23

Fe (cornea) +43.05 D

r2 = +6.8 mm

F1 = +48.83 D

F2 = 5.88 D

naqueous 1.336

nair 1.000

r1 = +7.7 mm

slide43

Fe (cornea) +43.05 D

r2 = +6.8 mm

F1 = +48.83 D

F2 = 5.88 D

ncornea 1.376

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

slide44

Fe (cornea) +43.05 D

r2 = +6.8 mm

F1 = +48.83 D

F2 = 5.88 D

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

slide45

Only option is to change naqueous

Basis of Corneal Power Estimate - Modified Exact Eye

Keep true anterior corneal radius - this is what keratometry measures

Why is new n < 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

slide46

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
slide47

Calibration Refractive Indices - Real Keratometers

    • Zeiss, Rodenstock 1.332
    • B & L, Haag-Streit (Javal-Schiötz) 1.3375
    • American Optical 1.336
  • B&L and AO index based on corneal back vertex power estimate (using posterior cornea as reference plane)
slide48

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 cornea’s in situ power is 0.78 D higher
intraocular implant design

IOL power for emmetropia

Constant based on IOL type

Axial length in mm

Average total corneal power based on keratometry

  • Relies heavily on axial length and keratometer readings:

Intraocular Implant Design

OBJ: when applying formula, the basis (ncal) of the K value must be consistent with the ‘A’ value (design constant)

slide50

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