Two methods for determination of the effective wavenumber of Gaussian beams in absolute gravimeters

• Autorzy: Křen P. , Pálinkáš V.

Identyfikatory

DOI

10.24425/mms.2018.124876

• Języki publikacji: EN

Abstrakty

EN

This paper presents two methods for evaluation of the effective wavenumber of nearly-Gaussian beams in laser interferometers that can be used for determination of a so called diffraction correction in absolute gravimeters. The first method, that can be simply used in situ, is an empirical procedure based on the evaluation of the variability of g measurements against the amount of light limited by an iris diaphragm and transmitted to a photodetector. However, precision of this method depends on the beam quality similarly as in the case of the conventional method based on measurement of a beam width. The second method, that is more complex, is based on beam profiling in various distances and on calculation of the effective wavenumber using the second spatial derivative of a non-ideal beam field envelope. The measurement results achieved by both methods are presented on an example of two absolute gravimeters and the determined diffraction corrections are compared with the results obtained by measurements of beam width. Agreement of methods within about 1 μGal have been obtained with average diffraction corrections slightly exceeding +2 μGal for three FG5(X) gravimeter configurations.

Słowa kluczowe

EN

diffraction correction; effective wavenumber; interferometer; Gaussian beam; absolute gravimeter

• Wydawca: Komitet Metrologii i Aparatury Naukowej PAN
• Czasopismo: Metrology and Measurement Systems
• Rocznik: 2018
• Tom: Vol. 25, nr 4
• Strony: 701--713
• Opis fizyczny: Bibliogr. 15 poz., rys., tab., wykr., wzory

Twórcy

autor

Křen P.

• Czech Metrology Institute, Okružní 31, 63800 Brno, Czech Republic

autor

Pálinkáš V.

• Research Institute of Geodesy, Topography and Cartography, Geodetic Observatory Pecný, 25165 Ondˇrejov 244, Czech Republic

Bibliografia

• [1] Monchalin, J.P., Kelly, M.J., Thomas, J.E., Kurnit, N.A., Szöke, A., Zernike, F., Lee, P.H., Javan, A. (1981). Accurate laser wavelength measurement with a precision two-beam scanning Michelson interferometer. Appl Opt., 20(5), 736-57.
• [2] Sasso, C.P., Massa, E., and Mana, G. (2016). Diffraction effects in length measurements by laser interferometry. Optics Express, 24(6), 6522-6531.
• [3] Niebauer, T.M., Sasagawa, G.S., Faller, J.E., Hilt, R., Klopping, F. (1995). A new generation of absolute gravimeters. Metrologia, 32, 159-180.
• [4] vanWestrum, D., Niebauer, T.M. (2003). The diffraction correction for absolute gravimeters. Metrologia, 40, 258-263.
• [5] Robertsson, L. (2007). On the diffraction correction in absolute gravimetry. Metrologia, 44, 35-39.
• [6] Jiang, Z., et al. (2012). The 8th International Comparison of Absolute Gravimeters 2009: the first Key Comparison (CCM.G-K1) in the field of absolute gravimetry. Metrologia, 49, 666-684.
• [7] Trimeche, A., Langlois, M., Merlet, S., Pereira Dos Santos, F. (2017). Active Control of Laser Wavefronts in Atom Interferometers. Phys. Rev. Applied, 7, 034016.
• [8] Mana, G., Massa, E., Sasso, C., Andreas, B., Kuetgens, U. (2017). A new analysis for diffraction correction in optical interferometry. Metrologia, 54, 559-565.
• [9] Azuma, Y., et al. (2015). Improved measurement results for the Avogadro constant using a 28 Si-enriched crystal. Metrologia, 52, 360-375.
• [10] Fujii, K., Bettin, H., Becker, P., Massa, E., Rienitz, O., Pramann, A., Nicolaus, A., Kuramoto, N., Busch, I., Borys, M. (2016). Realization of the kilogram by the XRCD method. Metrologia, 53, A19-A45.
• [11] Zhan, Q. (2004). Second-order tilted wave interpretation of the Gouy phase shift under high numerical aperture uniform illumination. Opt. Com., 242, 351-360.
• [12] Andreas, B., Fujii, K., Kuramoto, N., Mana, G. (2012). The uncertainty of the phase-correction in sphere-diameter measurements. Metrologia, 49, 479-486.
• [13] Křen, P., Pálinkáš, V., Mašika, P. (2016). On the effect of distortion and dispersion in fringe signal of the FG5 absolute gravimeters. Metrologia, 53, 27-40.
• [14] Křen, P., Pálinkáš, V., Mašika P., Val’ko, M. (2018). FFT swept filtering, a bias-free method for processing fringe signals in absolute gravimeters. Accepted in Journal of Geodesy.
• [15] Mana, G., Massa, E., Rovera, A. (2001). Accuracy of laser beam center and width calculations. Appl Opt., 40(9), 1378-1385.

Uwagi

EN

1. The project "Advanced processing of absolute gravity measurements and investigation of systematic instrumental effects” is funded by the Czech Science Foundation (GA ČR) as grant no. 16-14105S and it is also supported by ČMI and VÚGTK.

PL

2. Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).