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.
© 2005 Optical Society of America
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.3940) Instrumentation, measurement, and metrology : Metrology
(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure
(220.4840) Optical design and fabrication : Testing
Instrumentation, Measurement, and Metrology
Angela Davies and Tony L. Schmitz, "Correcting for stage error motions in radius measurements," Appl. Opt. 44, 5884-5893 (2005)