P. A. Ermolaev

Read the full article 
Article in Russian


Data processing in the interferometer systems requires high-resolution and high-speed algorithms. Recurrence algorithms based on parametric representation of signals execute consequent processing of signal samples. In some cases recurrence algorithms make it possible to increase speed and quality of data processing as compared with classic processing methods. Dependence of the measured interferometer signal on parameters of its model and stochastic nature of noise formation in the system is, in general, nonlinear. The usage of nonlinear stochastic filtering algorithms is expedient for such signals processing. Extended Kalman filter with linearization of state and output equations by the first vector parameters derivatives is an example of these algorithms. To decrease approximation error of this method the second order extended Kalman filtering is suggested with additionally usage of the second vector parameters derivatives of model equations. Examples of algorithm implementation with the different sets of estimated parameters are described. The proposed algorithm gives the possibility to increase the quality of data processing in interferometer systems in which signals are forming according to considered models. Obtained standard deviation of estimated amplitude envelope does not exceed 4% of the maximum. It is shown that signal-to-noise ratio of reconstructed signal is increased by 60%.

Keywords: the second order extended Kalman filter, interferometer data analysis

1.          Malacara D. Optical Shop Testing. NY, Wiley, 1978, 862 p.
2.          Gurov I., Volynsky M. Interference fringe analysis based on recurrence computational algorithms. Optics and Lasers in Engineering, 2012, vol. 50, no. 4, pp. 514–521. doi: 10.1016/j.optlaseng.2011.07.015
3.          Van Kampen N. Stochastic Processes in Physics and Chemistry. North Holland, 1984, 464 p.
4.          Simon D. Using nonlinear Kalman filtering to estimate signals. Embedded Systems Design, 2006, vol. 19, no. 7, pp. 38–53.
5.          Volynshy M.A., Gurov I.P., Zakharov A.S. Dynamic analysis of the signals in optical coherent tomography by the method of nonlinear Kalman filtering. Journal of Optical Technology, 2008, vol. 75, no. 10, pp. 682–686.
6.          Simon D. Optimal state estimation: Kalman, H∞, and Nonlinear Approaches. NY, John Wiley & Sons, Inc., 2006, 526 p. doi: 10.1002/0470045345
7.          Kalman R.E. A new approach to linear filtering and prediction problems. Trans. ASME, J. Basic Eng., 1960, vol. 82, pp. 35–45.
8.          Gurov I., Ermolaeva E., Zakharov A. Analysis of low-coherence interference fringes by the Kalman filtering method. Journal of the Optical Society of America A, 2004, vol. 21, no. 2, pp. 242–251. doi: 10.1364/JOSAA.21.000242
9.          Gurov I.P. Opticheskaya kogerentnaya tomografiya: printsipy, problemy i perspektivy [Optical coherence tomography: basics, problems and prospects]. In Problemy kogerentnoi i nelineinoi optiki [Problems of coherence and nonlinear optocs] / Eds I.P. Gurov, S.A. Kozlov. St. Petersburg, SPbSU ITMO Publ., 2004, pp. 6–30.
10.       Gurov I., Volynsky M., Zakharov A. Evaluation of multilayer tissues in optical coherence tomography by the extended Kalman filtering method. Proc. SPIE - The International Society for Optical Engineering, 2007, vol. 6734, art. no. 67341P. doi: 10.1117/12.753425
11.       Dresel T., Häusler G., Ventzke H. Three-dimensional sensing of rough surfaces by coherence radar. Applied Optics, 1992, vol. 31, pp. 919–925.
12.       Deck L. de Groot P. High-speed non-contact profiler based on scanning white light interferometry. Applied Optics, 1994, vol. 33, no. 31, pp. 7334–7338.
13.       Fercher A. Optical coherence tomography. Journal of Biomedical Optics, 1996, vol. 1, no. 2, pp. 157–173.
14.       Gurov I.P., Zhukova E.V., Margaryants N.B. Issledovanie vnutrennei mikrostruktury materialov metodom opticheskoi kogerentnoi mikroskopii s perestraivaemoi dlinoi [Investigation of materials internal microstructure by optical coherence microscopy with a tunable wavelength]. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2012, no. 3 (79), pp. 40–45.
15.       Gurov I.P., Zhukova E.V., Levshina A.V. Primenenie metoda opticheskoi kogerentnoi tomografii dlya izucheniya predmetov iskusstva, vypolnennykh v tekhnike intarsii [Optical coherence tomography method application for art objects investigating performed in tarsia technique]. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2012, no. 3 (79), pp. 55–59.
16.       Volynshy M.A., Vorob’yeva E.A., Gurov I.P., Margaryants N.B. Beskontaktnyi kontrol’ mikroob”ektov metodami interferometrii maloi kogerentnosti i opticheskoi kogerentnoi tomografii [Remote testing of microlens with the use of low-coherence interferometry and optical coherence tomography]. Izv. vuzov. Priborostroenie,2011, vol. 54, no. 2, pp. 75–82.
17.       Yarlykov M.S. Statisticheskaya teoriya radionavigatsii [Statistical theory of radionavigation]. Moscow, Radio i svyaz' Publ., 1985, 344 p.
18.       Gurov I., Sheynihovich D. Interferometric data analysis based on Markov nonlinear filtering methodology. Journal of the Optical Society of America A, 2000, vol. 17, no. 1, pp. 21–27.
Copyright 2001-2017 ©
Scientific and Technical Journal
of Information Technologies, Mechanics and Optics.
All rights reserved.