Uncertainties in interferometric measurements of radius of curvature

The radius of curvature of spherical surfaces may be determined using the well-known radius, or optical, bench. In this method, a figure measuring interferometer is employed to identify the null positions at the center of curvature (confocal) and surface (cat's eye) of the test optic. A linear slide provides motion between these positions and one or more displacement transducers is used to record the displacement between the cat's eye and confocal positions and, hence, the radius of curvature. Measurements of a polished Zerodur sphere have been completed on the X-ray Optics Calibration Interferometer (XCALIBIR) using both Twyman-Green and Fizeau configurations. Mechanical measurements of the spherical artifact have also been completed using a coordinate measuring machine (CMM). Recorded disagreement between the individual transmission sphere measurements and CMM measurements under well-controlled environmental conditions is larger than the limits predicted from a traditional uncertainty analysis based on a geometric measurement model. Additional uncertainty sources for the geometric model, as well as a physical optics model of the propagation of light, are therefore suggested. The expanded uncertainty analysis is described.