Measuring Form and Radius of Spheres with Interferometry

The geometry of a nearly spherical surface, for example that of a precision optic, is completely determined by the radius-of-curvature at one point and the deviation from the perfect spherical form at all other points of the sphere. Measurements of radius and form error can now be made with interferometers to remarkable accuracy. We describe measurements of radius and form error of a precision silicon sphere, having a nominal radius of 46.8 mm, with the “extremely accurate CALIBration InterferometeR” (XCALIBIR) at the National Institute of Standards and Technology (NIST). For these measurements XCALIBIR is configured as a spherical Fizeau interferometer providing a field of view of 44°. To measure the radius, a variant of the well known interferometric radius bench method is used. Careful alignment of phase measuring and displacement measuring interferometers enables us to achieve a standard measurement uncertainty for the sphere radius of about 5 parts in 107. The measurement of the form error is complicated because the entire sphere surface cannot be imaged in one measurement. Instead, 138 overlapping areas of the sphere surface are measured. A “stitching” algorithm is then employed to assemble these measurements into a form error map for the entire surface. We show that form errors can lead to considerable uncertainty in the radius of a sphere obtained through a radius-of-curvature measurement with the radius bench method.