Corneal Asphericity (Q-Value), Conic Sections & Spherical Aberration: Optical Impact of Prolate vs Oblate Corneas

The sagittal elevation $z$ of the anterior corneal surface at radial distance $y$ is expressed by Baker's Conic Equation:

$$z(y) = \frac{y^2}{R_0 + \sqrt{R_0^2 - (1 + Q)y^2}} \quad \text{where } Q = -e^2$$

• $Q = 0$: Perfect Sphere (zero peripheral flattening; severe positive spherical aberration).
• $-1 < Q < 0$: Prolate Ellipsoid (natural human average: $\mathbf{Q \approx -0.26 \pm 0.18}$). Flat in periphery, steep at apex.
• $Q = -0.528$: Aplanatic Cornea (theoretically eliminates all fourth-order spherical aberration for infinite conjugates).
• $Q > 0$: Oblate Ellipsoid (flat at apex, steep in periphery). Typical post-myopic LASIK cornea.

Primary spherical aberration ($Z_4^0$) causes peripheral marginal rays to refract more strongly than paraxial central rays, focusing light ahead of the retina:

$$Z_4^0 \approx \frac{R_0^4}{8 \cdot (n-1)} \cdot \Delta Q \implies \text{Oblate Corneas } (Q > +0.50) \text{ Explode } Z_4^0 > +0.6\ \mu\text{m}$$

Under dilated pupil conditions ($>5.0\ \text{mm}$ at night), this aberration casts intense luminous halos and starbursts around oncoming headlights, causing severe night driving disability.

To correct post-LASIK oblate aberrations or naturally aberrated eyes, modern precision lenses incorporate negative spherical aberration profiles ($Z_4^0 = -0.20\text{ to } -0.27\ \mu\text{m}$), restoring aplanatic performance, crisp edge contrast, and expanded depth of focus.