1 / 50

Chapter 13 Section 1 Spherical Mirrors – revision FYI

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.

zahina
Download Presentation

Chapter 13 Section 1 Spherical Mirrors – revision FYI

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Pages 13.1 – 13.12 Chapter 13 Section 1Spherical Mirrors – revision FYI

  2. Page 13.13 Chapter 13 Section 2

  3. Page 13.13 Measurement of Anterior Corneal:(1) Radius of Curvature (Keratometry)(2) Overall Topography (Keratoscopy)

  4. Burton (B & L Clone) Keratometer

  5. Nidek OPD-Scan “Topographer”

  6. Page 13.13 Measurement of Anterior Corneal:(2) Overall Topography (Keratoscopy) (1) Radius of Curvature (Keratometry)

  7. Page 13.13 Keratometry: mainly overviewModified objectives to follow

  8. 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

  9. 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.

  10. How Keratometry Works Page 13.14 Flat Cornea Steep Cornea

  11. 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

  12. 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

  13. Image size: distant object Page 13.14 Flatter r F f C h  h  f C F OBJ: r h  r

  14. 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:

  15. 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

  16. 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)

  17. 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

  18. Mirror h F C b The Keratometer Equation Page 13.14 h

  19. Mirror h F C Keratometer equation assumes that x = b used in keratometer b used in theory The Keratometer Equation Page 13.14 h

  20. 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

  21. Mirror h F C Assume virtual image here b Similar Triangles  Keratometer Equation h

  22. h F C = h  b b Similar Triangles  Keratometer Equation h Mirror

  23. Rearrange The Keratometer Equation From similar triangles:

  24. The Keratometer Equation Page 13.14 Rearrange the equation so we are solving for radius: OBJ

  25. 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:

  26. 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?

  27. 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

  28. 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

  29. 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

  30. 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

  31. Principle of Prismatic Doubling Single half-field prism creates two images with deviated image displaced laterally from original. Deviation calculated from: OBJ

  32. 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

  33. 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

  34. 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

  35. Topcon Keratometer What the Clinician Sees V 90 / H 180

  36. 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

  37. Corneal vertex h'60 h'150 B & L: Oriented to Measure r60 and r150

  38. 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

  39. 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

  40. 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

  41. 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

  42. 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

  43. 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

  44. 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

  45. 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

  46. 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)

  47. 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

  48. 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)

  49. 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

More Related