Artisan Lab Network
Optical Engineering Center
Optical calculation, estimation, reference, and tolerance-screening tools.
27 Calculators
Engineering Reference
Real-Time Results
Estimate Disclosures
Applied Optical Engineering
Calculation-first optical engineering.
Important Use Note
Calculations are provided for education and exploration only. Final production calculations are determined during manufacturing by the laboratory management system using proprietary and confidential mathematical algorithms developed by the LMS provider and/or lens designers. Results may differ from the traditional optical formulas shown below. A variance between these estimates and the manufactured product does not, by itself, constitute a production error.
Calculator Modules
Select Calculator
Prescription
Rx math
Lens Design
Thickness and curves
Prism & Binocular Vision
Prism analysis
Frame Geometry
Frame measurements
Quality Control
Tolerance checks
Optical Reference Library
Engineering Reference
Prentice Rule
Δ = cF
Prism from decentration in centimeters and power in diopters.
Equivalent Sphere
SE = S + C / 2
Quick average power for lens form and tolerance decisions.
Transposition
S′ = S + C
Convert plus and minus cylinder notation without changing power.
Vogel’s Rule — Plus / Plano
BC = SE + 6.00 D
SE = sphere + cylinder / 2. Use when SE is zero or plus; round the final suggestion to 0.25 D.
Vogel’s Rule — Minus
BC = SE / 2 + 6.00 D
SE = sphere + cylinder / 2. Use when SE is minus; round only the final suggestion to 0.25 D.
Vertex Compensation
F₂ = F₁ / (1 − (Δv/n)F₁)
F₁ = original signed power (D); F₂ = compensated signed power (D); Δv = original minus new vertex in meters (positive means closer); n = intervening-medium index (1.000 for air). Moving a plus lens farther reduces ordered plus; moving a minus lens farther increases minus magnitude. Transform both principal meridians.
Lens Clock
Mc × ((na − 1) / (nc − 1))
Converts measured curve to actual index.
Sagitta
s = r − √(r² − h²)
Curve depth from radius and half chord.
Power Vector
M, J0, J45
Useful for crossed cylinder math and prescription comparison.
ANSI Axis
Tolerance by cylinder
Axis tolerance tightens as cylinder power increases.
Artisan Lab Network
Optical Engineering Calculation Report
Transposition
Setup
Prescription: -2.50 D · -1.00 D × 180° · PD 62.00
Lens: Hi-Index 1.60 · BC 4.00 · CT 2.00 mm
Frame: Rectangle · A 52.00 / B 38.00 / DBL 18.00
Important Use Note
Calculations are provided for education and exploration only. Final production calculations are determined during manufacturing by the laboratory management system using proprietary and confidential mathematical algorithms developed by the LMS provider and/or lens designers. Results may differ from the traditional optical formulas shown below. A variance between these estimates and the manufactured product does not, by itself, constitute a production error.
Results
ALN Optical Engineering Center Calculator: Transposition Prescription: -2.50 D · -1.00 D × 180° · PD 62.00 Lens: Hi-Index 1.60 · BC 4.00 · CT 2.00 mm Frame: Rectangle · A 52.00 / B 38.00 / DBL 18.00 Sphere: -3.50 D Cylinder: +1.00 D Axis: 90°