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Construction, specification, and mathematical description of aspheric surfaces
American Journal of Optometry and Physiological Optics
|March 1, 1983
Summary
This study details mathematical descriptions for rotationally symmetrical aspheric spectacle lens surfaces, enabling precise theoretical performance assessments of both zonal and continuous aspheric lens designs.
Area of Science:
- Optics
- Ophthalmology
- Materials Science
Background:
- Spectacle lenses utilize rotationally symmetrical aspheric surfaces, constructed as either zonal or continuous aspherics.
- Zonal aspherics feature annular zones with progressively lower surface power from the vertex.
- Aspheric surface power is often described by radial drop, but precise shape specification is needed for assessment.
Purpose of the Study:
- To provide precise mathematical descriptions for rotationally symmetrical aspheric lens surfaces.
- To enable theoretical assessment of spectacle lens performance based on surface shape.
- To unify the description of different aspheric lens constructions.
Main Methods:
- Development and manipulation of mathematical formulas for continuous aspheric surfaces.
- Formulation of descriptions applicable to all rotationally symmetrical aspheric surfaces.
- Analysis of surface power distribution from the lens center to the edge.
Main Results:
- Established precise mathematical frameworks for describing continuous aspheric lens surfaces.
- Provided methods for theoretical performance evaluation of aspheric spectacle lenses.
- Unified the description of zonal and continuous aspheric lens designs.
Conclusions:
- Precise mathematical descriptions are crucial for accurately assessing aspheric spectacle lens performance.
- The developed formulas enable comprehensive theoretical analysis of rotationally symmetrical aspheric surfaces.
- This work facilitates a deeper understanding and optimization of aspheric lens design.