Defining the measurand in radius of curvature measurements

Angela Davies; Tony L. Schmitz

doi:10.1117/12.504884

20 November 2003 Defining the measurand in radius of curvature measurements

Angela Davies, Tony L. Schmitz

Proceedings Volume 5190, Recent Developments in Traceable Dimensional Measurements II; (2003) https://doi.org/10.1117/12.504884
Event: Optical Science and Technology, SPIE's 48th Annual Meeting, 2003, San Diego, California, United States

Abstract

Traceable radius of curvature measurements are critical for precision optics manufacture. An optical bench measurement of radius is very repeatable and is the preferred method for low-uncertainty applications. On an optical bench, the displacement of the optic is measured as it is moved between the cat's eye and confocal positions, each identified using a figure measuring interferometer. Traceability requires connection to a basic unit (the meter, here) in addition to a defensible uncertainty analysis, and the identification and proper propagation of all uncertainty sources in this measurement is challenging. Recent work has focused on identifying all uncertainty contributions; measurement biases have been approximately taken into account and uncertainties combined in an RSS sense for a final measurement estimate and uncertainty. In this paper we report on a new mathematical definition of the radius measurand, which is a single function that depends on all uncertainty sources, such as error motions, alignment uncertainty, displacement gauge uncertainty, etc. The method is based on a homogeneous transformation matrix (HTM) formalism, and intrinsically defines an unbiased estimate for radius, providing a single mathematical expression for uncertainty propagation through a Taylor-series expansion.

Citation Download Citation

Angela Davies and Tony L. Schmitz "Defining the measurand in radius of curvature measurements", Proc. SPIE 5190, Recent Developments in Traceable Dimensional Measurements II, (20 November 2003); https://doi.org/10.1117/12.504884

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