1.1 Placido-Based Corneal Topography: Axial, Tangential & Elevation Maps

1.1 Placido-Based Corneal Topography: Axial, Tangential & Elevation Maps

Placido corneal topography is a common method for mapping the anterior tear-surface reflection. For the Advanced Contact Lens Technician (NCLE-AC), interpreting topographic maps helps the technician recognize patterns that require clinical diagnosis and supports the fitting of custom corneal, intralimbal, and scleral gas permeable contact lenses.

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Principles of Placido Disc Reflection

Placido-based corneal topographers project a series of alternating black and white concentric illuminated rings (mires) onto the anterior ocular surface. The anterior pre-corneal tear film acts as a convex specular mirror, reflecting these mires as virtual images known optically as the first Purkinje-Sanson image.

A calibrated high-resolution charge-coupled device (CCD) video camera, mounted coaxially in the center of the Placido cone, captures this reflected pattern. Dedicated image-processing algorithms analyze thousands of individual data points along the ring edges to compute the spatial coordinates, slope, and local radius of curvature across the cornea.

Mire Spacing and Distortion Diagnostics

• Compressed (Narrow) Mires: When mires reflect off a steep corneal zone, the reflected rings appear compressed and crowded together. A shorter radius of curvature ($r$) produces high dioptric optical power ($D = \frac{n - 1}{r}$).
• Expanded (Widely Spaced) Mires: When mires reflect off a flat corneal zone, the reflected rings spread farther apart, indicating a longer radius of curvature and lower dioptric power.
• Mire Ovality: Regular astigmatism compresses mires along the steep meridian while widening them along the orthogonal flat meridian, yielding an elliptical ring pattern.
• Mire Undulation, Skewing, or Breakup: Localized distortion, pinch patterns, or ring breaks highlight irregular astigmatism, localized corneal ectasia (such as keratoconus), superficial scars, epithelial basement membrane dystrophy (EBMD), or pre-corneal tear film desiccation.

Inherent Technical Limitations of Placido Systems

1. Tear Film Dependency: Because Placido systems image the air-tear interface, any focal dry spot or rapid tear break-up creates severe pseudo-steepening or data dropouts.
2. Anterior Surface Exclusivity: Placido reflection captures only the anterior tear surface. It provides zero information regarding posterior corneal curvature, corneal depth, or full-thickness stromal architecture.
3. Central Aperture Blind Spot: The central camera aperture creates a blind spot of approximately 0.5 mm to 1.0 mm at the corneal vertex where no mires are projected, requiring mathematical interpolation across the central line of sight.
4. Peripheral Limbal Drop-off: Beyond 8.0 mm to 9.0 mm, steep peripheral curvature, high angle of incidence, and obstruction by the nose or brow limit peripheral limbal coverage.

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Axial (Sagittal) Curvature Maps

Axial power maps (also referred to historically as sagittal maps) display global corneal curvature trends. In an axial algorithm, the radius of curvature ($r_{\text{axial}}$) for any given point on the corneal surface is mathematically defined as the distance along the surface normal from the corneal surface to the point where it intersects the central optical axis of the topographer.

$\text{Power}_{\text{axial}} (D) = \frac{n_{\text{keratometric}} - 1}{r_{\text{axial}}} = \frac{1.3375 - 1}{r_{\text{axial}}}$

Algorithmic Assumptions and Inherent Biases

Because the axial algorithm constrains all surface normal vectors to terminate on a single, shared central reference axis, it enforces a spherically based assumption. This creates a pronounced mathematical smoothing effect across the entire color map:

• Smoothing of Local Contour: The dioptric power displayed at any paracentral point is an averaged composite of the local slope and its geometric relationship to the central axis.
• Overestimation of Cone Area: In keratoconus, axial maps artificially smear steep dioptric colors into surrounding flatter zones. This causes axial displays to can broaden the apparent footprint of localized ectatic steepening.
• Underestimation of Peripheral Flattening: Axial maps fail to show how rapidly a normal or ectatic cornea flattens toward the limbus, showing a gradual, falsely elevated dioptric curve in the periphery.

Exam Key Point: Axial maps are ideal for evaluating global refractive trends (such as regular with-the-rule vs. against-the-rule astigmatism, refractive cylinder axis alignment, and baseline spherical power), but they should not be used alone to locate the precise apex of an ectatic cone or to select rigid lens landing zones.

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Tangential (Instantaneous / Local) Curvature Maps

Tangential power maps (also termed instantaneous or local curvature maps) calculate the true local radius of curvature ($r_{\text{tangential}}$) at each specific point along the local tangent plane. Crucially, the center of curvature is not constrained to the central instrument axis; instead, it floats independently on the local surface normal.

Why Tangential Maps Excel in Irregular Corneas

Because tangential maps calculate each point independently without central axis averaging:

1. Precise Cone Apex Localization: The point of maximum curvature ($K_{\text{max}}$) is rendered at its exact anatomical coordinates without being pulled artificially toward the central optical axis.
2. High Spatial Resolution of Margins: Tangential maps clearly demarcate the transition zones between steep ectatic tissue and adjacent normal flat stroma. This is vital when identifying the steep superior shoulder of a keratoconic cone or the abrupt inferior thinning zone in Pellucid Marginal Degeneration (PMD).
3. Accurate Peripheral Rate of Flattening: The true, rapid rate of peripheral corneal flattening (asphericity) is rendered faithfully, allowing contact lens specialists to evaluate the landing zone geometry for intralimbal and scleral lens haptics.

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Elevation Maps: Reference Surfaces and Micron Profiling

While axial and tangential maps express optical bending power in diopters ($D$), elevation maps describe the physical three-dimensional topography of the corneal surface in microns (µm) relative to a standardized mathematical reference surface.

Reference Geometries

• Best-Fit Sphere (BFS): A spherical reference body whose radius of curvature and center of rotation are calculated mathematically (via least-squares regression) to match the average elevation profile of the patient's cornea. An 8.0 mm or 9.0 mm calculation diameter is standard.
• Best-Fit Toric Ellipsoid (BFTE): An ellipsoidal, astigmatic reference surface utilized to neutralize regular corneal toricity, allowing isolated asymmetric ectasias to stand out clearly.
• Fixed vs. Float Reference Modes: In fixed reference mode, the vertex and radius are locked to specific baseline values. In float reference mode, the reference body is permitted to translate along the X, Y, and Z axes to achieve the lowest possible root-mean-square (RMS) deviation across the sampled surface, maximizing elevation sensitivity.

Elevation Color Scale Conventions

• Warm Colors (Red, Orange, Yellow): Indicate positive elevation (+) where corneal tissue sits above (protrudes anterior to) the reference surface. In keratoconus, the cone apex presents as a warm positive elevation island.
• Cool Colors (Blue, Violet, Indigo): Indicate negative elevation (-) where corneal tissue dips below (posterior to) the reference surface. Depressions, troughs, and peripheral flattening appear as cool zones.
• Green Bands: Represent the zero elevation line, where the corneal tissue precisely intersects the reference surface.

$\text{Elevation } (\mu\text{m}) = \text{Corneal Surface Height} - \text{Reference Surface Height}$

Application to Specialty Contact Lens Fitting

In specialty rigid contact lens design, dioptric curvature maps do not provide the physical depth required to clear an irregular cornea. A positive elevation value means the measured surface lies above the selected reference body at that location. It does not equal the clearance required beneath a contact lens: reference-zone diameter, alignment, lens geometry, decentration, settling, and tissue response all affect the final on-eye relationship. Use elevation to guide initial design, then verify bearing and clearance with an actual diagnostic lens or validated impression/free-form workflow.

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Clinical Comparison: Axial vs. Tangential vs. Elevation Maps

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Worked Clinical Scenario: Keratoconic Cone Localization

A 26-year-old male with progressive keratoconus in the right eye undergoes diagnostic topography. The practitioner evaluates all three maps prior to trial lens selection:

• Axial Map Findings: Demonstrates a broad, diffuse zone of inferior steepening measuring 6.2 mm in diameter. Simulated Keratometry (SimK) reads 47.50 @ 105 / 52.25 @ 015 ($\Delta K = 4.75\ D$). If relying strictly on this map, the practitioner would assume a massive oval cone and consider a large 10.5 mm intralimbal lens.
• Tangential Map Findings: Resolves a compact, round, highly circumscribed steep zone measuring only 3.2 mm in diameter, centered 1.8 mm inferotemporal to the line of sight. The true peak power ($K_{\text{max}}$) is 54.50 D, with an immediate, rapid dioptric fall-off to 42.00 D in the mid-periphery.
• Elevation Map Findings (8.0 mm BFS Float): Identifies a localized positive elevation peak of +68 µm corresponding exactly to the 3.2 mm tangential apex, surrounded by a broad -35 µm depressed zone.

Clinical Management Decision

The tangential and elevation maps prove that this patient does not have a broad oval ectasia, but rather a compact nipple cone. Designing a large-diameter lens based on the axial map would cause massive mid-peripheral clearance starvation and lens seal-off. Instead, the practitioner selects a small-diameter (8.8 mm) multi-curve corneal RGP with a steep base curve aligned to the +68 µm apex and a rapid peripheral clearance curve, providing optimal centration and healthy tear exchange.

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Common Exam Traps

1. The Dioptric Peak vs. Elevation Peak Discrepancy: Candidates often assume that the point of highest dioptric power on a curvature map is the highest point on an elevation map. Curvature measures the rate of change of slope, not absolute height. The physical elevation peak and the maximum dioptric power point frequently diverge by 0.5 mm to 1.0 mm.
2. Confusing Axial Smoothing for Pathologic Cone Size: Selecting a rigid lens diameter based on the apparent cone size on an axial map is an exam failure. Axial smoothing can broaden the apparent footprint of localized steepening.
3. Overlooking the Placido Tear Film Artefact: High dioptric red spots on a Placido map caused by a localized tear film breakup (dry spot) are frequently misdiagnosed as early keratoconus. Inspect raw mire quality and repeat scans after blinking; interpret persistent patterns alongside tomography and the clinical examination because tear breakup and surface disease can create artifacts.