Mathematical model of the exact fraction method for the order of interference
- 359 Downloads
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.
Keywordsmultiwavelength interferometry exact fraction method for the order of interference Chinese remainder theorem convergents of continued fractions euclidean algorithm
- 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).Google Scholar
- 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).Google Scholar
- 4.J. Decker, “Uncertainty evaluation for the measurement of gauge blocks by optical interferometry,” Metrologia, No. 34 (6), 479–493 (1997).Google Scholar