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Measurement Techniques
Published in: Measurement Techniques 7/2011

01-10-2011

Mathematical model of the exact fraction method for the order of interference

Author: A. V. Zabelin

Published in: Measurement Techniques | Issue 7/2011

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Abstract

An improved method of interpreting the exact fraction method for the order of interference used in multiwavelength interferometry is examined. Optimal algorithms for choosing possible values of the integral orders of interference and a new, more exact method of calculating the result of two wavelength interference measurements are presented. The metrological problems of multiwavelength interferometry are shown to be closely related to the formalism of convergents of continued fractions in number theory.
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Literature
1.
J. Decker et al., “Increasing the range of unambiguity in step-height measurement with multiple wavelength interferometry – application to absolute long gauge block measurement,” Appl. Opt., 42, No. 28, 5670–5678 (2003).ADSCrossRef
2.
A. N. Korolev et al., “Measurement of the step height in the nanometer range using a laser microinterferometer,” Izmer. Tekhn., No. 4, 29–33 (2005); Measur. Techn., 48, No. 4, 352–358 (2005).
3.
K. Meiners-Hagen et al., “Multiwavelength interferometry for length measurements using diode lasers,” Measur. Sci. Rev., 9, No. 1, T. 3, 16–26 (2009).
4.
J. Decker, “Uncertainty evaluation for the measurement of gauge blocks by optical interferometry,” Metrologia, No. 34 (6), 479–493 (1997).
5.
C. Towers, D. Towers, and J. Jones, “Time efficient Chinese remainder theorem algorithm for full-field fringe phase analysis in multiwavelength interferometry,” Opt. Express, 9, No. 6, 1136–1143 (2004).ADSCrossRef
Metadata
Title
Mathematical model of the exact fraction method for the order of interference
Author
A. V. Zabelin
Publication date
01-10-2011
Publisher
Springer US
Published in
Measurement Techniques / Issue 7/2011
Print ISSN: 0543-1972
Electronic ISSN: 1573-8906
DOI
https://doi.org/10.1007/s11018-011-9799-4

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