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UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS Guest
2024-11-23 17:54 |
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Conference: Bucharest University Faculty of Physics 2022 Meeting
Section: Solid State Physics and Materials Science, Optics, Spectroscopy, Plasma and Lasers
Title:
Impure geometric progression of synthetic frequencies: a well-defined and precision-optimized method for absolute distance measurement
Authors:
Petre Cătălin LOGOFĂTU
Affiliation:
National Institute for Laser, Plasma and Radiation Physics, Laser Dept., str. Atomiștilor nr. 409, CP MG-36, Măgurele, jud. Ilfov, Romania, 077125
E-mail
petre.logofatu@inflpr.ro
Keywords:
Absolute length measurement, multiwavelength interferometry, synthetic frequency
Abstract:
The method for the determination of the absolute distance from the excess ratios of multiwavelength interferometry, invented by Benoît in 1898 [1], was seriously confronted with the problem of ambiguity and the lack of a analytical formula for calculations. From the beginning it was intuitively known that the ambiguity may be removed by using a large number of frequencies and selecting frequencies that are not in an obvious rapport with each other, such as a small integer ratio. But only much later sufficient theoretical progress was made toward the elimination in principle of the ambiguity [2] and finding an analytical formula for the absolute distance [3]. I offer here a solution for the elimination of the ambiguities at the ends of the period, which are not dealt in reference [2], a true analytical formula for the determination of the absolute distance, (reference [3] offers only an easily implemented computer procedure, not really an analytical function) and other improvements. My method is proven rigorously to be well-defined (i.e. non-ambiguous) and optimized for precision. It is shown here that my method is the boundary between ambiguity and precision. There are more precise methods, but they are ambiguous; there are also other non-ambiguous methods, but they are less precise.
References:
[1] R. Benoît, “Application des phénomènes d’interférence à des déterminations métrologiques,” Journal de Physique Théorique et Appliquée, 7(1), 57 (1898) (in French).
[2] C. E. Towers, D. P. Towers, J. D. C. Jones, “Optimum frequency selection in multifrequency interferometry,” Optics Letters 28(11), 887 (2003).
[3] C. R. Tilford, “Analytical procedure for determining lengths from fractional fringes,” Appl. Opt., 16(7), 1857 (1977).
Acknowledgement:
Acknowledgments. This work was supported by Romanian Ministry of Education and Research, under Romanian National Nucleu Program LAPLAS VI – contract no. 16N/2019.
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