Measuring Form and Radius of Spheres With Interferometry
Quandou (. Wang, Johannes A. Soons, Ulf Griesmann
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 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 the precision silicion 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 accurate measurements XCALIBIR is configured as a spherical Fizeau interferometer providing a field of view of 44 degrees. 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 10^7. The measurement of the form error is complicated because it is impossible to image the entire sphere surface in one measurement. Instead, 138 overlapping areas of the sphere surface are measured. A stitching algorithm is then employed to assemble these measurements to derive a form error map for the entire surface.