Minimum Blank Size (MBS) Calculation: Frame Geometric Decentration, Effective Diameter & Lab Edging Mechanics

Under the standardized Optical Boxing System:

$$\begin{aligned} \mathbf{\text{Frame PD (FPD):}} & \quad FPD = A + DBL \\ \mathbf{A:} & \quad \text{Horizontal Lens Width (mm)} \\ \mathbf{DBL:} & \quad \text{Distance Between Lenses (Bridge Width, mm)} \\ \mathbf{ED:} & \quad \mathbf{\text{Effective Diameter}} \ (2\times \text{ longest radius from geometric center to furthest corner}) \end{aligned}$$

The total geometric decentration per eye ($dec$) is the distance from the frame's geometric center to the patient's visual axis (pupillary center):

$$dec = \frac{FPD - \text{Patient PD}}{2} \implies \mathbf{MBS = ED + 2 \cdot (dec) + 2.0\ \text{mm (Bevel Allowance)}}$$

Dispensing example:

• Frame dimensions: $A = 54\ \text{mm}$, $DBL = 18\ \text{mm}$, $ED = 58\ \text{mm}$.
• Patient's interpupillary distance ($PD$) = $62\ \text{mm}$.
• $FPD = 54 + 18 = \mathbf{72\ \text{mm}}$.
• $dec = \frac{72 - 62}{2} = \mathbf{5.0\ \text{mm decentration nasally}}$.
• $MBS = 58 + (2 \times 5.0) + 2.0 = 58 + 10.0 + 2.0 = \mathbf{70.0\ \text{mm}}$.
• The lab must order a $70\ \text{mm}$ blank. Ordering a $65\ \text{mm}$ blank will suffer catastrophic cut-out failure temporally!

In minus lenses, edge thickness increases with the square of distance from the optical center. Every millimeter of unnecessary decentration ($dec$) forces the temporal lens edge further outward, generating massive thick rims. Choosing a frame where $FPD \approx \text{Patient PD}$ (zero decentration) yields the thinnest, lightest possible eyewear.