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Publication Citation: Uncertainty Estimation for Multiposition Form Error Metrology

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Author(s): William T. Estler; Christopher J. Evans; Lianzhen Shao;
Title: Uncertainty Estimation for Multiposition Form Error Metrology
Published: September 01, 1997
Abstract: We analyze a general multiposition comparator measurement procedure that leads to partial removal of artifact error for a class of problems including roundness metrology, measurement of radial error motions of precision spindles, and figure error metrology of high-accuracy optical components. Using spindle radial error motion as an explicit example, we present a detailed analysis of a complete test with N orientation of a test ball with respect to the spindle. In particular, we show that (1) all components of the ball roundness error average to zero except those with frequencies of kN cycles/revolution, where k is a positive integer; and (2) the combined standard uncertainty of the measurement is proportional to 1/sqrt(N). We then show how a complete set of measurements for an N-position test can be synthesized from only two measurements, and we derive a general expression for the combined standard uncertainty as a function of the number of positions n (2 < n < N) actually measured in an N-position test. This uncertainty can serve as a useful guide to measurement design, involving trade-offs between multiple setup cost and complexity and required levels of angular harmonic resolution and combined standard measurement uncertainty.
Citation: Precision Engineering-Journal of the International Societies for Precision Engineering and Nanotechnology
Volume: 21(2-3)
Pages: pp. 72 - 82
Keywords: difference techniques,dimensional metrology,error separation,multistep methods,optical figure metrology,roundness,spindle errors
Research Areas: Metrology, Manufacturing