Knife-Edge Optimization & Base Curve Selection for High Hyperopia Plus Lenses

In a plus lens, the front convex surface curve ($F_1$) is steeper than the back concave curve ($F_2$). The center thickness ($t_c$) is determined by edge thickness ($t_e$) plus the difference in sagittal depths:

$$t_c = t_e + (s_1 - s_2) \approx t_e + \frac{y^2 \times F}{2000(n - 1)}$$

In standard stock plus lenses, manufacturers leave a thick edge ($t_e \approx 2.0\text{--}2.5\ \text{mm}$) to ensure the lens doesn't crack during generic framing. In a $+5.00\ \text{D}$ CR-39 lens across a 65mm blank, this results in an enormous $7.5\ \text{mm}$ center thickness!

In bespoke optical labs like ELLASUV, lenses are never cut from generic pre-molded stock blanks. Instead, the edger digitally traces the patient's exact frame aperture and decentration:

• The surfacing generator calculates the precise minimum edge thickness ($t_e = 0.8\text{--}1.0\ \text{mm}$) needed only at the single furthest temporal or nasal corner of that specific frame.
• By shaving the minimum edge thickness down to this exact 1.0 mm safety margin, the center thickness ($t_c$) collapses from $7.5\ \text{mm}$ down to $4.2\ \text{mm}$—slashing lens weight by almost 50%!

Spectacle Magnification ($SM$) is governed by the combination of Power Factor and Shape Factor:

$$SM = \underbrace{\left( \frac{1}{1 - t_c \cdot \frac{F_1}{n}} \right)}_{\text{Shape Factor}} \times \underbrace{\left( \frac{1}{1 - d \cdot F_v'} \right)}_{\text{Power Factor}}$$

Notice that a thick center ($t_c$) combined with a steep front base curve ($F_1$) dramatically inflates the Shape Factor, magnifying the eyes into grotesque proportions. By using 1.60 or 1.67 Aspheric profiles with flatter base curves and thin knife-edge centers, the 'bug-eye' effect is neutralized, restoring a completely natural facial appearance.