Paper
20 November 2003 Defining the measurand in radius of curvature measurements
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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.
© (2003) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
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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Cited by 9 scholarly publications.
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KEYWORDS
Confocal microscopy

Eye

Error analysis

Motion measurement

Interferometers

Optical spheres

Optical benches

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