Aspheric vs. Atoric Digital Surfacing: Flattest Profile for High Cylinder Prescriptions

A standard aspheric lens alters its surface curvature from center to edge based on a single rotational conic constant ($Q$ or $p$-value):

$$z(r) = \frac{c r^2}{1 + \sqrt{1 - (1+Q)c^2 r^2}}$$

In pure spherical myopia (e.g., $-5.00\ \text{DS}$), this rotational conic curve works brilliantly. However, consider an astigmatic prescription of $-5.00\ \text{DS} / -3.00\ \text{DC} \times 180^\circ$:

• Along the 180° horizontal meridian, the optical power is $-5.00\ \text{D}$.
• Along the 90° vertical meridian, the optical power is $-8.00\ \text{D}$.

A single rotational asphere can optimize only one of these two curves! If optimized for $-5.00\ \text{D}$, the vertical $-8.00\ \text{D}$ meridian suffers massive peripheral marginal astigmatism and distortion.

An Atoric surface is non-rotationally symmetric. Freeform CNC diamond generators sculpt independent, unique conic curves along every single meridian ($0^\circ$ to $360^\circ$):

$$Q_{x} \ne Q_{y} \quad [\text{Independent Asphericities for Major and Minor Meridians}]$$

By independently flattening both the $-5.00\ \text{D}$ meridian and the $-8.00\ \text{D}$ meridian, edge thickness is minimized uniformly in all quadrants without inducing off-axis blur.

Compared to conventional toric lenses, ELLASUV Freeform Atoric Lenses deliver:

1. 30% Wider Clear Field of View: Elimination of marginal astigmatic blur enables natural side gaze without turning your head.
2. Flat Aesthetic Profile: Bulging edge thickness along the steep axis is reduced by 1.2 to 1.8 mm.
3. Zero 'Fishbowl' Warping: Straight architectural lines remain straight right up to the frame rim.