A spherometer is an indispensible instrument that makes it possible to accurately estimate the radius of curvature of a spherical surface.
It is very advantageous to be able to quickly estimate the radius of curvature of a spherical surface without having to set the subject lens or mirror up in a separate stand to do testing. This is particularly true during the rough grinding stages when the surface reflectivity is typically quite poor. A good spherometer fills this role nicely.
The spherometer makes use of the simple relationship between a circle (sphere) and the sag of that circle between points separated by a known distance as shown here. A simple application of the Pythagorean Theorem makes it possible to write the mirror sag as
The spherometer design described in the accompanying paper (5.5 MB) uses spherical feet as shown below. This makes the mathematics somewhat more involved, but it affords some desirable benefits as well.