1 November 1997 Rigorous decision of the excess fraction method in absolute distance interferometry
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Abstract
Absolute distance interferometry is a promising technology for comprehensive investigation of optical component parameters, including measurement of radii and thicknesses. In special interferometric schematics, it is applicable to measuring parameters of surfaces after grinding and can simplify null corrector design or eliminate its implementation for final testing aspherical surfaces. A universal method for precision length measurement, called 'excess fractions,' was proposed at the end of the last century to calibrate gauges. In this method, the interferometer compares an unknown distance with magnitudes of several wavelengths. The array which consists of the remainders of integer parts of the phase shift between the reference branch of the interferometer and the measuring distance, will be obtained. The proposed consideration of the 'excess fraction' method is based on the Chinese Remainder Theorem. It will be shown that the confidence interval of the obtained distance is equal to the confidence interval of the fractions. Consideration of the finite precision will make the method independent of which units will express, and provides the intervals of unambiguity of the method.
© (1997) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Il'ya P. Agurok, Il'ya P. Agurok, } "Rigorous decision of the excess fraction method in absolute distance interferometry", Proc. SPIE 3134, Optical Manufacturing and Testing II, (1 November 1997); doi: 10.1117/12.279134; https://doi.org/10.1117/12.279134
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