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Phase-shifting algorithms for the interferometric measurement of form error, diameter variation and refractive index inhomogeneity of fused silica spheres

Published

Author(s)

Chu-Shik Kang, Ulf Griesmann, Johannes A. Soons

Abstract

High-precision spheres have many applications in precision engineering and metrology, such as the calibration of transmission spheres for interferometry, density standards for mass metrology, and spherical gyroscope rotors. For these applications it is important to know the form error of the sphere. Optical interferometry can be applied to measure the form errors of opaque spheres with high spatial point density. Interferometric measurements of transparent spheres, however, are difficult due to the interference of light reflected by the "back surface" of the sphere. Fourier transform phase-shifting interferometry using wavelength tuning can, in principle, separate the fringe patterns originating from the multiple cavities. However, commercially available interferometers require a specific ratio of cavity lengths, which is difficult to realize for sphere measurements. In this paper we propose the application of phase-shifting algorithms (PSAs) based on characteristic polynomial (CP) theory to measure form error, diameter variation and refractive index inhomogeneity of transparent spheres in a four-surface interference configuration. Computer simulations were used to calculate the intensity variation at a pixel when shifting the frequency of the laser in equal steps. CP theory was used to optimize algorithms to estimate phase maps of three cavities: the full cavity, the cavity formed by the surfaces of the fused silica sphere, and the empty cavity. The phase maps were then combined to obtain the diameter variation of the sphere and its refractive index inhomogeneity. The performance of the algorithms was evaluated by a computer simulation.
Proceedings Title
Proceedings of the 12th International Conference of the European Society for Precision Engineering and Nanotechnology
Conference Dates
June 4-8, 2012
Conference Location
Stockholm, SE
Conference Title
12th International Conference of the European Society for Precision Engineering and Nanotechnology

Keywords

Interferometry, Sphericity, Refractive index

Citation

Kang, C. , Griesmann, U. and Soons, J. (2012), Phase-shifting algorithms for the interferometric measurement of form error, diameter variation and refractive index inhomogeneity of fused silica spheres, Proceedings of the 12th International Conference of the European Society for Precision Engineering and Nanotechnology, Stockholm, SE (Accessed June 22, 2024)

Issues

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Created September 8, 2012, Updated October 12, 2021