Contact-lens optics, materials and tear lenses

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Optical Comparison: Spectacles versus Contact Lenses

Placing a corrective lens directly onto the pre-corneal tear film alters retinal image size, ocular field of view, prismatic aberrations, and vergence demands compared to spectacle wear.

Knapp's Rule & Anisometropia

Knapp's rule states that if a spectacle lens is placed at the anterior focal point of the eye (approximately $15.7\text{ mm}$ anterior to the cornea), the retinal image size in axial ametropia remains identical to that of an emmetropic eye. Conversely, in refractive ametropia (e.g., unilateral aphakia or keratoconus), contact lenses minimize aniseikonia and are the optical treatment of choice. In modern clinical practice, contact lenses are favored for both axial and refractive anisometropia because cortical sensory fusion, peripheral visual field continuity, and prismatic comfort outweigh theoretical spectacle magnification predictions.

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Contact Lens Materials & Oxygen Transmissibility

The corneal epithelium relies on atmospheric oxygen dissolved in the pre-corneal tear film ($P_{O2} \approx 155\text{ mmHg}$ open eye; $P_{O2} \approx 55\text{ mmHg}$ closed eye palpebral conjunctiva).

Material Categories

1. Rigid Gas-Permeable (RGP): Fluoro-silicone acrylate polymers. Deliver high intrinsic oxygen permeability ($Dk = 30 - 150+\text{ Barrers}$) through fluorine-silicone chains. Rigidity helps maintain the designed anterior optical surface, masking corneal astigmatism and ectasia.
2. Conventional hydrogels transport oxygen largely through their water component. Dk depends on formulation and water content; a single formula or 35–40 upper bound does not describe every material.
3. Silicone Hydrogels (SiHy): Crosslinked siloxane phases combined with hydrophilic hydrogel phases. Oxygen diffuses directly through silicone pathways independent of water content, delivering high oxygen permeability ($Dk = 100 - 175+\text{ Barrers}$). Higher modulus of elasticity makes lenses stiffer, occasionally provoking mechanical complications.

The Holden-Mertz & Harvitt-Bonnano Criteria

Oxygen transmissibility ($Dk/t$) measures oxygen flux through a lens of center thickness $t$ (in cm):

Oxygen transmissibility is permeability divided by lens thickness (Dk/t). Compare values using the same units and measurement conditions; central and local thickness, wear schedule and tear exchange affect physiology.

• Holden-Mertz Daily Wear Threshold (1984): Minimum $Dk/t \ge 24 \times 10^{-9}$ to avoid day-time corneal stromal oedema.
• Holden-Mertz Extended Wear Threshold (1984): Minimum $Dk/t \ge 87 \times 10^{-9}$ to limit nocturnal closed-eye stromal oedema to physiological levels ($\lt 4\%$, equivalent to overnight sleep without lenses).
• Harvitt-Bonnano Closed-Eye Threshold (1999): Updated human mathematical model requiring $Dk/t \ge 125 \times 10^{-9}$ to eliminate nocturnal hypoxia across the entire full-thickness cornea.

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Tear Lens (Lacrimal Lens) Optics & RGP Fitting Principles

When a rigid gas-permeable lens rests on the cornea, the fluid reservoir between the posterior lens surface and the anterior corneal surface forms a tear lens (lacrimal lens).

Astigmatic Neutralization Principle

The refractive index of human tears ($n_{\text{tear}} = 1.336$) is virtually identical to that of the corneal stroma ($n_{\text{cornea}} = 1.376$), differing sharply from air ($n = 1.000$). The tear lens neutralizes approximately $90\%$ of anterior corneal toricity, transforming the irregular or toroid cornea into a spherical optical interface. Residual astigmatism may reflect internal optics, incomplete masking, lens flexure or fitting effects, and should be measured by over-refraction.

The SAM-FAP Rule

The base curve (BC) of an RGP lens defines the anterior surface curvature of the tear lens, while the cornea's flat keratometry reading ($K_{\text{flat}}$) defines its posterior surface curvature:

• Fitting On-K ($BC = K_{\text{flat}}$): The anterior and posterior surfaces of the tear lens are parallel. Tear lens power is $0.00\text{ D}$ (plano).
• Fitting Steeper than K ($BC \gt K_{\text{flat}}$ in dioptric power, or shorter radius): The tear lens forms a positive meniscus, adding convergent plus power to the optical system. To compensate: SAM (Steeper Add Minus).
• Fitting Flatter than K ($BC \lt K_{\text{flat}}$ in dioptric power, or longer radius): The tear lens forms a negative meniscus, adding divergent minus power. To compensate: FAP (Flatter Add Plus).

$$\text{Power Adjustment} = 0.25\text{ D lens power compensation per } 0.05\text{ mm change in base curve } (\approx 0.25\text{ D})$$

Worked Tear Lens Calculation:

• Keratometry readings: $42.50\text{ D}$ in both principal meridians ($K_{\text{flat}} = 42.50\text{ D}$).
• Manifest spectacle refraction: $-4.00\text{ DS}$ ($d = 0\text{ mm}$).
• Selected base curve: $43.25\text{ D}$ ($0.75\text{ D}$ steeper than $K_{\text{flat}}$).

1. Calculate tear lens vergence: Because $BC$ is $0.75\text{ D}$ steeper than flat K, the tear lens power is $+0.75\text{ D}$.
2. Apply SAM: Add $-0.75\text{ D}$ to the spectacle refraction to neutralize the induced tear lens.
3. Contact lens power to order: $-4.00\text{ DS} - 0.75\text{ D} = -4.75\text{ DS}$.

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