UNCERTAINTY ESTIMATION FOR MULTIPOSITION FORM ERROR METROLOGY

We analyze a general multiposition comparator measurement procedure th at 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 optica l components. Using spindle radial error motion as an explicit example , we present a detailed analysis of a complete test with N orientation s of a test ball with respect to the spindle. In particular, we show t hat (1) all components of the ball roundness error average to zero exc ept those with frequencies of kN cycles/revolution, where k is a posit ive integer; and (2) the combined standard uncertainty of the measurem ent is proportional to 1/root N. We then show how a complete set of me asurements for an N-position test can be synthesized from only two mea surements, and we derive a general expression for the combined standar d uncertainty as a function of the number of positions n (2 less than or equal to n less than or equal to N) actually measured in an N-posit ion test. This uncertainty can serve as a useful guide to measurement design, involving trade-offs between multiple setup cost and complexit y and required levels of angular harmonic resolution and combined stan dard measurement uncertainty. Published by Elsevier Science Inc.