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Master Optical Engineering Suite v2.0 | Yamout Optical Center

Yamout Optical Center

Since 1978 Lebanon

Master Optical Engineering Suite Version 2.0 Single-File • Turbify-Ready

Interactive Master Optical Engineering Reference & Lab Report

Calculators + live examples + lab-ready geometry diagrams: Sagitta, Decentration, MBS, Edge Thickness, plus v2.0 extensions for aspheric/atoric concepts, free-form lens notes, and wrap/tilt compensation. Built for clinical use, staff training, and lab communication.

Modules

Pick a section. Everything updates live and diagrams follow your inputs.

Geometry

Centration & MBS

Prism

Vertex & Tilt/Wrap

Materials

v2.0 Aspheric/Atoric & Free-Form

1) Physical Geometry

Radius of curvature + sagitta (exact/approx). Use mm inputs; power in diopters.

Spherical surface model

Refractive Index (n)

Surface Power (F, D)

Semi-Diameter (y, mm)

Use |F| for radius?

Radius of Curvature r (mm)

—

Exact Sagitta s (mm)

—

Approx Sagitta s≈ (mm)

—

Notes

—

Formulas

r = 1000 (n − 1) / F

s = r − √(r² − y²)

s ≈ (y² · F) / (2000 (n − 1))

Tip: In labs, we often use the magnitude |F| for geometric depth comparisons. Signed power matters for optics; geometry is depth magnitude.

Diagram: Sagitta Geometry

Chord = 2y. Sagitta = curve depth. Updates live from your inputs.

SVG

The arc represents the lens surface. The straight line is the chord. The vertical drop at mid-chord is the sagitta.

Edge Thickness (Minus Lens)

Quick engineering estimate: ET = s_back − s_front + CT. Use magnitudes for s.

Thickness model

Index (n)

Semi-Diameter y (mm)

Center Thickness CT (mm)

Sag method

Front Surface Power F_front (D)

Back Surface Power F_back (D)

Sag Front (mm)

—

Sag Back (mm)

—

Edge Thickness ET (mm)

—

Interpretation

—

Lab Notes

This model is a **geometry estimate** (spherical surfaces, no bevel, no roll/polish allowances). Real lab edge thickness also depends on: bevel placement, frame groove depth, safety bevel, lens design (aspheric/atoric), and actual base curve selection.

Diagram: Edge Thickness Cross-Section

Shows front/back sagitta and resulting edge thickness. Updates live from ET inputs.

SVG

Not to scale. Intended for staff training and patient-friendly explanation (why frame size + index change thickness).

2) Centration & Minimum Blank Size

Decentration + MBS (ED + 2·Dec + 2mm safety). Great for ordering blanks and avoiding cut-out.

Fit & stocking

Frame Eyesize A (mm)

Bridge DBL (mm)

Patient IPD (mm)

ED (mm)

Total Decentration Dec (mm)

—

Minimum Blank Size MBS (mm)

—

Effective Radius y_eff = (ED/2)+Dec (mm)

—

Blank Stock Check

—

Formulas

Dec = ((A + DBL) − IPD) / 2

MBS = ED + 2·Dec + 2 mm

y_eff = (ED/2) + Dec

Diagram: Decentration & MBS Geometry

Visualizes ED circle + decentration shift and the resulting minimum blank size.

SVG

The ED circle is centered on the lens shape. Decentration shifts the OC relative to the blank. MBS ensures full cut-out plus safety allowance.

3) Prentice’s Rule (Induced Prism)

P = (F · c) / 10 where c is mm from OC. Useful for troubleshooting discomfort and verifying centration tolerances.

Dispensing check

Lens Power F (D)

Decentration c (mm)

Direction (label only)

Induced Prism P (Δ)

—

Quick Note

—

Formula

P = (F · c) / 10

Live Example

Try: F = −6.00D and c = 2.0mm → P = 1.20Δ (approx). Even “small” decentrations can matter with high power.

Training

Clinical interpretation

If a patient reports headaches, pull, or “image swim,” verify: PD measurement, frame alignment, monocular PDs, and whether the OC was set correctly. In high minus prescriptions, induced prism rises quickly with even a few mm of error.

4) Vertex Compensation

Fc = F / (1 − d·F), with d in meters (change in vertex distance). Common for strong Rx when moving lens closer/farther.

Strong Rx

Rx Power F (D)

Vertex Change d (mm)

Lens moved…

Compensated Power Fc (D)

—

Practical Note

—

Formula

d(m) = d(mm) / 1000

Fc = F / (1 − d · F)

Tilt / Wrap Induced Astigmatism

Engineering approximation: C_induced ≈ F · tan²(θ). Useful for “why does wrap feel weird?” education.

Approx model

Lens Power F (D)

Tilt / Wrap θ (degrees)

Context

C_induced (D)

—

Note

—

Engineering Reminder

This is a **simplified demonstration** used for staff training. True compensated prescriptions depend on lens form, index, position-of-wear, and design (often handled via surfacing software / free-form optimization).

Power at Any Meridian

Meridian power model for sph/cyl/axis: Fθ = Sphere + (Cylinder · sin²(θ − Axis)). Use to teach “where max power lives”.

Meridian scan

Sphere (D)

Cylinder (D)

Axis (°)

Meridian θ (°)

Fθ (D)

—

Max / Min Meridians

—

Material Selection Matrix

Select a material to load n / Abbe / density. Use it to compare thickness and optical clarity tradeoffs.

Lab + dispensing

Material

Index (n)

Abbe (V)

Density (ρ)

Typical Use

Chromatic risk hint

Clarity Flag

—

Staff Message

—

Quick rules

Abbe low (≈30) → higher chromatic aberration risk (edge “rainbows”).
Higher index → thinner, but not always best clarity-to-cost.
Density influences weight and comfort, especially in large frames.

Thickness Comparison Helper

Use the same geometry estimate across different indices to show the patient / staff what changes (and what doesn’t).

Demo tool

Semi-Diameter y (mm)

CT (mm)

Ffront (D)

Fback (D)

ET @ 1.60 (mm)

—

ET @ 1.67 (mm)

—

ET @ 1.74 (mm)

—

Difference (1.67 → 1.74)

—

Note: This uses the same spherical-sag thickness model as the ET module for a consistent “engineering comparison.”

Version 2.0 Extensions

Aspheric / Atoric concept demo + free-form overview + wrap compensation notes (staff training layer).

Advanced module

Aspheric sag (concept)

A true aspheric surface is not a perfect sphere. One common sag model (concept) uses a conic constant k:\n

z(y) = (y² / r) / (1 + √(1 − (1 + k)·(y² / r²)))

Interpretation: changing k changes how quickly the surface “flattens” in the periphery, helping reduce rings and improve cosmetics.

Atoric (concept)

Atoric surfaces extend the aspheric idea by using different curvature behavior across meridians (useful in astigmatic prescriptions). In practice, modern atoric designs are typically handled via design libraries and optimization software rather than manual calculations.

Free-form lenses (overview)

Free-form surfacing uses CNC-generated surfaces to match position-of-wear, corridor behavior (PAL), and wearer-specific parameters. Key inputs: vertex distance, pantoscopic tilt, wrap angle, PD/height, fitting point, and frame dimensions.

Aspheric “k” Demo

This is a *concept demo* to show how periphery sag changes when k changes (not a substitute for real design files).

SVG + math

Base Radius r (mm)

Semi-Diameter y (mm)

Conic Constant k

Compare vs sphere

Aspheric sag z(y) (mm)

—

Sphere sag s(y) (mm)

—

Difference (Asph − Sphere)

—

The curve is exaggerated for visualization. In real lens design, “small” sag differences can meaningfully change thickness, rings, and optics.

Yamout Optical Center • Lab & Engineering Notes

This suite is designed for staff training, quoting, and lab communication. For production orders, use your lab’s design library and position-of-wear workflow.

Since 1978

Tip: If you want, I can replace the simple YOC mark with your exact gold-emboss style logo SVG (still single-file), and add a PDF-ready cover page section.