title: Correcting for stage error motions in radius measurements.
abstract: Traceable radius of curvature measurements are critical for precision optics manufacturing. An optical bench measurement is repeatable and is the preferred method for low-uncertainty applications. With an optical bench, the displacement of the optic is measured as it is moved between the cat's eye and the confocal positions, each identified using a figure measuring interferometer. The translated distance is nominally the radius of curvature; however, errors in the motion of the stage add a bias to the measurement, even if the error motions are zero on average. Estimating the bias and resulting measurement uncertainty is challenging. We have developed a new mathematical definition of the radius measurand that intrinsically corrects for error motion biases and also provides a means of representing other terms such as figure error-correction, wave-front aberration biases, displacement gauge calibration and their uncertainties. With this formalism, it is no long necessary to design a high-quality radius bench to carry out a precision measurement; rather a lower quality is adequate, provided that error motions are repeatable and characterized and error motion measurement uncertainties are estimated.
authors.affiliation: Department of Physics and Optical Science, University of North Carolina at Charlotte, 9201 University City Boulevard, Charlotte, North Carolina 28223-001, USA. adavies@uncc.edu
authors.forename: Angela
authors.initials: A
authors.lastname: Davies
authors.forename: Tony L
authors.initials: TL
authors.lastname: Schmitz