Spherometry: description and error analysis of portable devices

Abstract

This work discusses four portable instruments that measure the radius of a concave or convex spherical surface. Some methods used on spherical measuring machines are first described, followed by the ‘geometrical method” which is easily adaptable to portable instruments. A brief description of the design of each device is given with the radius computing formula (according to geometric principle). The instruments measure directly the arc-depth (sagittal height) of a spherical sector at a specific diameter and the radius is calculated from these two parameters. The work then describes the various factors that can influence the accuracy of the final result. The final accuracy depends on the inaccuracy level of each factor and its weight in the computing formula. The error analysis facilitates a better comparison of the instruments' precision levels, in order to choose the most appropriate instrument. The differential analysis also indicates the relationship between the change in measured height and changes in the surface's radius.