Description
Ideal spherical-surface sagittae with an explicit convex/concave thickness convention; negative edge thickness exposes inconsistent model dimensions.
Optical calculations distinguish lens power in diopters, prism notation, angular axes, geometric distances, and visual-acuity reporting scales. Sign conventions and length units are especially important when a formula combines power with decentration or vertex distance. A supplied model term is separate from a validated visual test or prescription.
Ideal spherical-surface sagittae with an explicit convex/concave thickness convention; negative edge thickness exposes inconsistent model dimensions.
When to use this tool
Use Lens Edge Center Thickness Geometry Term when you need this explicit optical, chart, frame, axis, or reference conversion with compatible supplied units.
How to use the tool and how it works
- Enter semiDiameter, frontRadius, backRadius, centerThickness, frontConvex, backConvex. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read frontSag, backSag, edgeThickness. Use the output convention below.
Require nonnegative semiDiameter and centerThickness and positive frontRadius and backRadius each at least semiDiameter. Compute each spherical sag with q=semiDiameter/r and sag=semiDiameter*q/(1+sqrt((1-q)*(1+q))). Return edgeThickness=centerThickness minus each sag if its convex flag is true, plus it otherwise.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| semiDiameter | Semi Diameter | Required. Finite number; minimum 0. |
| frontRadius | Positive front spherical-radius magnitude in the semiDiameter unit. | Required. Finite number; strictly above 0. |
| backRadius | Positive back spherical-radius magnitude in the semiDiameter unit. | Required. Finite number; strictly above 0. |
| centerThickness | Center Thickness | Required. Finite number; minimum 0. |
| frontConvex | Front Convex | Required. Boolean. |
| backConvex | Back Convex | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| frontSag | Front Sag | Required. Finite number. |
| backSag | Back Sag | Required. Finite number. |
| edgeThickness | Signed modeled thickness; negative outputs are retained. | Required. Finite number. |
{
"input": {
"semiDiameter": 3,
"frontRadius": 5,
"backRadius": 5,
"centerThickness": 3,
"frontConvex": true,
"backConvex": true
},
"output": {
"frontSag": 0.9999999999999999,
"backSag": 0.9999999999999999,
"edgeThickness": 1
}
}Limitations and assumptions
- All dimensions need one length unit and the radii are positive magnitudes with explicit face flags. Negative modeled edge thickness is retained; actual lens geometry, refractive power, material, manufacturing limits, and clinical fit are not verified.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use the appropriate complete optical or measurement model when a scalar term is insufficient. Verify power, axis, length, notation, and reference conventions before applying the result within a broader assessment.
References
Similar or alternative tools
- Aligner Bench Material Thickness Factor
Uniform sheet thickness from supplied area stretch and volume retention.
- Lens Thickness Optical Path Factor
Uniform-index slab optical path and excess over a supplied surrounding medium, not a full crystalline-lens model.