Coordinate Geometric Generalization of the Spherometer and Cylindrometer

TL;DR

This paper introduces a coordinate geometric approach to generalize the spherometer and cylindrometer, enabling measurement of aspherical surfaces beyond traditional spherical and cylindrical geometries.

Contribution

The paper develops a novel coordinate geometric framework that extends traditional instruments to measure aspherical surfaces, broadening their applicability.

Findings

Generalized instruments for aspherical surfaces

Enhanced measurement accuracy for complex geometries

Unified geometric approach for surface curvature measurement

Abstract

Spherometer is an instrument widely used for measuring the radius of curvature of a spherical surface. Cylindrometer is a modified spherometer, which can measure the radii of both spherical and cylindrical surfaces. Both of these instruments are based on a geometric relation unique to circles and spheres, from Euclidean geometry. A more general understanding is obtained using coordinate geometry. The coordinate geometric approach also enables a generalization of the spherometer and cylindrometer to devices, which can handle aspherical surfaces. Here, we present the newly developed coordinate geometric approach and its applications.