CS1-Lec.3- Keratomery

Keratometry: Fundamentals, Uses, and Relation to Refractive Error

  • Keratometry measures the anterior curvature of the cornea (including the tear film) to estimate the corneal dioptric power and its astigmatic orientation. It is part of objective refraction (alongside retinoscopy) and helps infer refractive error, anisometropia, and IOL power.

  • The cornea is the major refractive surface of the eye; the refractive power of the cornea is roughly the largest contributor to the eye’s total power (emmetropic eye ≈ 60 D total, with ~40 D from the cornea). The anterior surface is what keratometry samples.

  • Keratometry relies on the reflective properties of the cornea: the instrument projects mires onto the cornea and reflects images back, which are then measured to infer curvature.

  • Tear film quality and corneal surface quality affect the reflected image; poor tear film or corneal surface yields a poorer image and less reliable readings. Topography is more detailed for corneal surface assessment.

  • Keratometry has multiple clinical roles: objective curvature measurement, estimation of corneal astigmatism, monitoring corneal conditions (e.g., keratoconus, degenerative changes), aiding in ortho-k and post-refractive surgery assessments, screening for IOL power in cataract surgery, and evaluating contributing factors to anisometropia.

Keratometry: Key Concepts and Measurements

  • What keratometry measures:

    • The front (anterior) curvature of the cornea (and tear film) and its radius of curvature in the two principal meridians.

    • The dioptric power derived from that curvature in those meridians.

  • Two principal meridians: keratometry gives two readings at perpendicular meridians (usually ~90° apart). The steeper meridian is the power meridian; the flatter meridian is the axis meridian.

  • Typical corneal power: about 40–44 diopters in the cornea; the mean corneal power is around 43 diopters. The cornea’s power is the major refractive surface of the eye.

  • The keratometer uses a reflected image (mires) off the cornea. The measured image size relates to the curvature: smaller image implies steeper curvature, larger image implies flatter curvature.

  • Keratometry covers roughly the central 3 mm of the cornea; it samples the anterior surface and is an approximate method for corneal power.

  • It does not measure posterior corneal curvature; topography or newer instruments sample more of the cornea (anterior and posterior) and provide a fuller map.

Instrument and Core Components

  • Main components:

    • Illuminated Mires (MeAs) at the cornea (the reflected image you align).

    • Doubling prism: creates two additional mires so you can measure radius from multiple reflected images.

    • Aperture plate (also called Snyder’s disc): helps with focusing and creating a “ghosting” image to aid alignment.

  • How it looks inside:

    • The instrument shows three mires: one bottom-right that should be kept single (in focus); two others that must be aligned with the corresponding reference images by adjusting knobs.

    • Focusing changes the distance from the eye to the instrument so that the mire alignment goes from doubled (out of focus) to single (in focus).

  • Focusing and alignment cues:

    • You align the reflected mires so the pluses/overlaps line up; when in focus, the image is single and centered in the reticule.

    • The bottom-right mire is the one you keep single while aligning the others; when it’s doubled, you’re not in the right focus distance.

  • Typical keratometer layout and knobs:

    • Horizontal and vertical drums move the mires to measure horizontal and vertical components (radius in two meridians).

    • Axis knob rotates the instrument to align with the meridians of interest.

    • Locking knob secures the position once focused and aligned.

    • Forehead rest and chin rest position the patient; occluder blocks the non-tested eye.

  • Two main types of keratometer designs:

    • One-position keratometer: measures both meridians simultaneously.

    • Two-position keratometer (or Rotational): measure one meridian, rotate 90°, measure the other meridian separately (useful for irregular astigmatism).

  • Portable/autorefractor note:

    • Some modern automated instruments provide both meridians automatically; traditional slit-lamp-mounted keratometers require manual operation.

Keratometry Principle and Reading the Meridians

  • Principle: keratometry measures corneal curvature by analyzing the size of the reflected mires, which are determined by the curvature radius of the anterior cornea, then converts that radius to diopters.

  • Radius and diopters:

    • The reading process yields a radius value; a standard corneal radius corresponds to a dioptric power, e.g., a radius around 7.5 mm is reported as about 45 diopters in the example given.

    • The instrument uses a model where the image forms about 4 mm behind the cornea and is small, erect, and virtual.

  • Converting two meridian readings to a sphero-cylindrical prescription (minus cyl form):

    • Given two readings: P1 at angle θ and P2 at angle θ+90° (power in two principal meridians).

    • Sphere (S) and cylinder (C) are derived as:
      S = rac{P1 + P2}{2}, \ C = rac{P2 - P1}{2}

    • The axis of the cylinder is the meridian with the flatter power (the lesser diopter value). If P1 ≤ P2, axis = θ; if P1 > P2, axis = θ+90°.

    • The resulting minus-cylinder form is:
      Rx = S ext{ diopters at axis } A ext{ with cylinder } -C ext{ at axis } A

    • Example (simple, consistent): If P1 = 44.0 D at 180° and P2 = 46.0 D at 90°, then

    • S = (44 + 46)/2 = 45.0 D

    • C = (46 - 44)/2 = 1.0 D

    • Axis = 180° (flatter meridian)

    • Prescription: -1.00 ext{ @ } 180^ ext{o} and the power in the perpendicular meridian 45.0 + 1.0 = 46.0 D at 90°.

  • Recording formats:

    • Two meridians can be recorded as:

    • Power at the first meridian (P1) with axis θ, and power at the second meridian (P2) with axis θ+90°; or

    • Directly in minus-sil form: S, -C, axis A (where A is the flatter meridian).

    • Example in narrative form: P1 = 43.25 D at 167°, P2 = 42.50 D at 77° (two meridians 90° apart). Convert to minus cyl form:

    • Axis ≈ 85° (flatter meridian, 42.50 D)

    • Cylinder magnitude ≈ 0.75 D

    • Sphere ≈ 42.875 D

    • Prescription: about −0.75 @ 85 with the other meridian at 85° having 42.875 + 0.75 ≈ 43.625 D (these specific values are example-driven in the lecture; actual classroom numbers vary).

  • Important rounding and recording conventions:

    • Keratometry readings use eighth-diopter steps: 0.125, 0.375, 0.625, 0.875; recordings truncate (round down) to these steps.

    • If less than 1 D, prefix with a 0 (e.g., 0.125 D, 0.375 D, etc.).

    • When writing in minus-sil form, the axis is a three-digit value (e.g., 085, 170, 177). The axis is always the flatter meridian.

    • If the cornea is spherical (no cylindrical component), record sphere with an empty axis (no cyl) in minus-sil form.

Keratometry in Practice: Procedure and Common Scenarios

  • Setup and patient positioning:

    • Clean chin rest and forehead rest; place occluder on the non-tested eye.

    • Elevate or lower the instrument to align with the patient’s eye; use outer campus marks as rough alignment guidance.

    • The examiner focuses the eyepiece for themselves; if multiple users, refocus at each start.

  • Alignment and measurement steps:

    • Move the instrument laterally to locate the mires; look through the instrument and coax the reflected mires to align with the reticle.

    • The patient is asked to look down the tube; you should see three mires reflecting off the cornea; ensure the bottom-right mire is single (the others align by adjusting the knobs).

    • If the bottom-right mire is doubled or unclear, you’re not in the proper focus distance; adjust the focus knob and retry.

    • Once the mires line up (radial alignment), lock the instrument and read off the two meridians (horizontal and vertical drums).

  • Figures and interpretation reminders:

    • The horizontal drum moves the bottom-right mire horizontally; the vertical drum moves the upper-right mire vertically.

    • The axis knob rotates the instrument to align with the meridians; when the axis is correctly set, the mires line up in the corresponding circles.

    • The power meridian is the steeper meridian; the axis meridian is the flatter meridian.

  • Common errors and troubleshooting:

    • Occluder partially blocking a mire can hide a sign (pluses or minuses); adjust occluder.

    • If the horizontal/vertical mire do not overlap correctly, axis may be off; rotate the instrument to align axes, then adjust drums to overlap signs.

    • If the eye moves or the person has ocular pulsations, keep adjusting focus to maintain a single mire.

    • If there is irregular astigmatism, the two meridians may not be exactly 90° apart; the two-meridian measurement may still be used, or irregular astigmatism may require alternative assessment methods.

  • Measurement range and extension:

    • Bausch & Lomb keratometer range: roughly 36 D to 52 D.

    • To extend beyond this range, you can place a +1.25 D lens in front of the aperture to extend to ~61 D; conversely, placing a -1.00 D lens can extend lower toward ~30 D. An adjustment is required to account for the added lens in the reading; conversion tables are used to translate the extended reading back to keratometric power.

Accuracy, Calibration, and Sources of Error

  • Calibration issues:

    • Instruments can drift; calibration uses steel balls of known curvature/power mounted in the instrument. Measuring a known 45 D steel ball should yield 45 D; deviations indicate under- or over-reading (e.g., reading 44.87 D indicates an under-reading by 0.13 D). Adjustments may be needed.

  • Common sources of error:

    • Improper calibration or drift of the instrument.

    • Poor patient positioning or head movement; incorrect chin or forehead rest placement.

    • Poor fixation or misalignment of the mires due to eyelid, lid laxity, or ocular surface issues.

    • Tear film quality and corneal surface irregularities affecting mire clarity.

    • Incomplete alignment or failure to overlay the pluses and minuses properly, leading to miscalculation of radius and thus power.

    • Operator experience: first eye may take longer (≈40 minutes); second eye often faster (≈5 minutes) as familiarity increases.

  • Practical limitations:

    • Keratometry measures only the anterior corneal surface and near-center area; posterior corneal curvature and peripheral corneal variations are not captured.

    • For irregular astigmatism, keratometry may be less reliable; topography provides a better map in those cases.

Astigmatism: Regular vs Irregular and the With/Against Rule

  • Regular astigmatism: two principal meridians are perpendicular (≈90° apart) and mires read as two clear, perpendicular meridians. Common subtypes include:

    • With-the-rule (WTR): axis around 180° (±30°); the power meridian is around 90° (steeper at 90°). Example: axis ≈ 180°, power meridian near 90°.

    • Against-the-rule (ATR): axis around 90° (±30°); the power meridian is around 180°.

    • Oblique: axes between 31°–59° or 121°–149°; power meridians are not aligned at 90°; more challenging for some keratometer measurements.

  • Irregular astigmatism: principal meridians are not perpendicular; keratometry may not accurately capture the astigmatic pattern. Keratoconus is a common cause of irregular astigmatism.

  • Clinical note: Clinically, axis is more frequently discussed in optometry/ophthalmology, while power meridians are often referred to in optics. For regular astigmatism, axis and power meridians are 90° apart; oblique astigmatism has oblique axes.

  • Topography visualization: color maps show steeper (often red) vs flatter (blue) meridians; with-the-rule corneas show steep meridian near 90° (power) and axis near 180°, while against-the-rule shows the opposite pattern.

Jeval’s Rule (Geval’s Rule) and Modifications: Estimating Spectacle Plane from Corneal Astigmatism

  • Purpose: estimate the full spectacle cylinder and sphere from keratometry (corneal astigmatism) and known (lenticular) astigmatism to approximate the total refractive error at the spectacle plane.

  • Classic Geval’s rule (described in lecture):

    • Use an effectivity constant (k) of 1.25 and add approximately 0.5 diopter of lenticular cylinder to the corneal cylinder to estimate spectacle cylinder, with axis adjustments depending on the axis location (with-rule vs against-rule). If the axis is oblique, the rule is less reliable and may not be used.

    • This method yields a preliminary estimate of the spectacle cylinder and axis before refining with subjective refraction.

  • Modified Geval’s rule (Duval’s rule, simplified):

    • Removes the 1.25 multiplier (i.e., no effectivity constant). The corneal cylinder and lenticular cylinder are combined with a ±0.5 D adjustment depending on the rule (with-rule vs against-rule) to estimate the spectacle cylinder. The axis handling is similar (oblique axes often exclude the rule).

    • Intention: a simpler mental math approach that keeps adjustments in 0.5 D increments and avoids the multiplication by 1.25.

  • Practical notes:

    • If the axis is oblique, you typically do not apply Geval’s rule (or you apply it with caution or leave the corneal cylinder as a starting point and rely more on objective measurements and Rx refinement).

    • When applying the rules, you must determine whether the corneal cylinder is with-rule or against-rule in relation to how the lenticular component sits; the sign and axis adjustments depend on this relationship.

  • Example outline (as described in lecture):

    • Given corneal cylinder and lenticular cylinder, apply the rule to combine powers (with or without the 1.25 multiplier) and adjust axis by 90° if the signs require it; convert to minus cyl form for the final spectacle Rx, and note that the final Rx must be rounded to the nearest 0.25 D (quarter diopters) for sphere and 0.25 D (or 0.125 D increments for keratometry) for cylinder depending on the step used.

  • Important caveats:

    • Jeval’s/Geval’s rules provide estimates, not exact prescriptions. Refractive or pupillary testing (subjective refraction) is essential to confirm the final Rx.

    • Oblique axes require special handling; often these rules are not applied or are adapted.

    • In practice, many clinicians use alternative approaches (e.g., Duval’s, modified Duval’s, or the “modified Duval’s” method) depending on training and exam expectations.

Spherical Equivalent and Clinical Applications

  • Spherical equivalent (SE) definition:
    SE = S + rac{C}{2}
    where S is the spherical component and C is the cylindrical component.

  • Refractive vs corneal astigmatism:

    • Keratometry gives corneal astigmatism (measured on the cornea).

    • Refractive astigmatism (from autorefractors and subjective refraction) includes lenticular and spectacle-plane effects in addition to corneal curvature.

    • They may not match exactly because the lens (crystalline lens) and other factors contribute to refractive power.

  • Spherical equivalent uses acuity or metric tests to estimate the overall refractive error:

    • Eggers’ table (Eggers method): uses unaided distance acuity to estimate a spherical equivalent. Example guidance: 20/50 → around −1.25 D; 20/100 → around −2.00 D; hyperopes can be evaluated by adding +2.50 D during testing to relax accommodation (and then interpreting how much plus is needed to achieve acuity).

    • The “maximum plus to maximum visual acuity” (MPMA) method: a subjective refraction approach to push plus until acuity worsens, then reduce until the best line is found; often used in practice to estimate spherical equivalent when a full refraction isn’t possible.

    • Punctum remotem (far point) method: using the far point distance to determine refractive error; type of measurement:

    • If punctum remotem is at distance d (cm), the refractive error in diopters can be approximated by
      D \,=\, \frac{100}{d}
      where d is in centimeters. In meters, this simplifies to $D = 1/d$ with d in meters.

  • Punctum remotem and measurement in practice:

    • Punctum remotem helps estimate how uncorrected refractive error would affect vision in clinics where full refraction isn’t possible.

    • The relationship between spherical equivalent (SE) and punctum remotem allows clinicians to cross-check corneal-based estimates with acuity results.

  • Practical implications:

    • Spherical equivalent is used for planning and comparing Rx, particularly when cylinder corrections are refined across multiple steps (sphere and cylinder adjustments in quarter-diopter steps).

    • Understanding SE helps bridge keratometry (corneal power) with subjective refraction and IOL calculations.

Pupil, Punctum, and Puncta Remotem: Quick References

  • Punctum remotem (far point): distance where a myope sees best without accommodation; reflective relation to diopters via the distance to the far point.

  • Punctum proximal (near point): the near focal point; not typically used in keratometry/Rx estimation directly but referenced in optics discussions.

  • In exam practice, use Eggers’ table or punctum remotem methods as practical tools for estimating spherical equivalents and for validating keratometric-based estimates.

Putting It All Together: From Keratometry to a Tentative Spectacle Rx

  • Workflow outline:
    1) Obtain keratometry readings in two principal meridians (P1 at θ, P2 at θ+90°).
    2) Convert to minus cylinder form: determine S and C, axis as the flatter meridian.

    • S = \frac{P1 + P2}{2}, \quad C = \frac{P2 - P1}{2}

    • Axis = flatter meridian (the one with the smaller power).

    • Final: Rx = S \; @ \; Axis \; -C (in diopters).
      3) Consider corneal vs refractive astigmatism: keratometry gives corneal astigmatism; use subjective refraction to refine.
      4) Apply Jeval’s/Geval’s rules (and their modifications) to estimate spectacle cylinder and sphere, keeping in mind oblique axes may require direct keratometric values rather than the rule-based estimate.
      5) Use spherical equivalent formula to connect cylinder and sphere:
      SE = S + frac{C}{2}
      6) If possible, verify with Eggers’ table, punctum remotem, or modified Duval’s approach to refine the sphere, cylinder, and axis to a final Rx in quarter diopter steps (cylinder around 0.25 D steps; keratometry readings in 0.125 D steps).
      7) For IOL planning in cataract surgery, keratometry plus axial length informs IOL power selection; corneal curvature interacts with axial length to determine the needed IOL diopter.

  • Final considerations:

    • Keratometry is valuable for estimating corneal astigmatism and supporting early estimation of Rx, but it is not a substitute for subjective refraction and full refractive planning.

    • In exams and real life, expect to maneuver between Keratometry results, Geval’s/Duval’s rules (or modified variants), Eggers tables, and spherical equivalents to derive a coherent Rx; oblique axes require special handling and are more challenging.

Quick Concept Cheatsheet (Key Takeaways)

  • Keratometry measures anterior corneal curvature via reflected mires; two principal meridians; mean corneal power ~ 43 D; major contributor to total eye power.

  • Recording: denoted as minus-sil form when converting two meridians to S and C; axis equals the flatter meridian.

  • Instrument anatomy: illuminated mires, doubling prism, aperture/Snyder’s disc, horizontal and vertical drums, axis knob, lock, occluder, chin/forehead rests