Research on methods of regression analysis and nonlinear programming for calibrating a goniometer

Korolev, A.N., Lukin, A.Y., Venediktov, V.Y., Ivashchenko, E.M.

Publication in Journal of Optical Technology

For Russian citation (Opticheskii Zhurnal):

Королёв А.Н., Лукин А.Я., Венедиктов В.Ю., Иващенко Е.М. Исследование методов регрессионного анализа и нелинейного программирования в задачах калибровки на гониометре // Оптический журнал. 2022. Т. 89. № 6. С. 53–63. http://doi.org/10.17586/1023-5086-2022-89-06-53-63

Korolev A.N., Lukin A.Ya., Venediktov V.Yu., Ivashchenko E.M. Research on methods of regression analysis and nonlinear programming for calibrating a goniometer [in Russian] // Opticheskii Zhurnal. 2022. V. 89. № 6. P. 53–63. http://doi.org/10.17586/1023-5086-2022-89-06-53-63

For citation (Journal of Optical Technology):

A. N. Korolev, A. Ya. Lukin, V. Yu. Venediktov, and E. M. Ivashchenko, "Research on methods of regression analysis and nonlinear programming for calibrating a goniometer," Journal of Optical Technology. 89(6), 346-352 (2022). https://doi.org/10.1364/JOT.89.000346

Abstract:

Subject of study. This study is devoted to solving the calibration problems of a goniometer built using a holographic angle sensor and an autocollimator. Method. Methods of regression analysis and nonlinear programming are studied in relation to the problems of calibration of a goniometer and determination of the systematic error of its angle sensor to introduce corrections in the measurement results. Main results. The methods of regression analysis and nonlinear programming are applied to the problem of goniometer calibration. It is shown that using regression analysis can reduce the error from to 0.15^′′ to 0.01^′′. The application of nonlinear programming makes it possible to determine the systematic error of the angle sensor included in the goniometer. In two cycles of measurements, the error is at the level of hundredths of an arc second. The possibility of using nonlinear programming for determining the angles of deviation of optical polygon faces from the nominal values is demonstrated. Practical significance. The application of regression analysis to the problem of calibration of a goniometer enables the error range to be reduced by more than an order of magnitude. The use of nonlinear programming simplifies the procedure for determining the systematic error of its angle sensor.

Keywords:

goniometer, calibration, angle measurement, regression analysis, nonlinear programming

Acknowledgements:

The research was supported by the grant of RFS No. 20-19-00412.

OCIS codes: 120.0120, 230.0230

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