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Uncertainties in Interferometric Measurements of Radius of Curvature



Tony L. Schmitz, Angela Davies, Christopher J. Evans


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 best fit spherical surface (cat''s eye) and center of curvature (confocal 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 the Twyman-Green and Fizeau configuarations.  Mechanical measurements of the spherical artifact have also been completed using the NIST Moore-48 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.
Conference Dates
July 29-31, 2001
Conference Location
San Diego, CA
Conference Title
International Society for Optical Engineering


diffraction, interferometry, radius of curvature, uncertainty analysis


Schmitz, T. , Davies, A. and Evans, C. (2001), Uncertainties in Interferometric Measurements of Radius of Curvature, International Society for Optical Engineering, San Diego, CA (Accessed April 19, 2024)
Created January 1, 2001, Updated February 19, 2017