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Interferometric data analysis based on Markov nonlinear filtering methodology

Summary: Interferometric data analysis based on Markov
nonlinear filtering methodology
Igor P. Gurov and Denis V. Sheynihovich
Saint Petersburg Institute of Fine Mechanics and Optics (Technical University), 14 Sablinskaya Street,
Saint Petersburg 197101, Russia
Received March 15, 1999; revised manuscript received July 15, 1999; accepted August 2, 1999
For data processing in conventional phase shifting interferometry, Fourier transform, and least-squares-fitting
techniques, a whole interferometric data series is required. We propose a new interferometric data processing
methodology based on a recurrent nonlinear procedure. The signal value is predicted from the previous step
to the next step, and the prediction error is used for nonlinear correction of an a priori estimate of the param-
eters phase, visibility, or frequency of interference fringes. Such a recurrent procedure is correct on the con-
dition that the noise component be a Markov stochastic process realization. The accuracy and stability of the
recurrent Markov nonlinear filtering algorithm were verified by computer simulations. It was discovered that
the main advantages of the proposed methodology are dynamic data processing, phase error minimization, and
high noise immunity against the influence of non-Gaussian noise correlated with the signal and the automatic
solution of the phase unwrapping problem. © 2000 Optical Society of America [S0740-3232(99)01012-1]
OCIS codes: 050.5080, 070.6020, 030.4280, 100.5070.
The phase restoration of interference fringes is widely
used in wave-front analysis,1­3


Source: Arleo, Angelo - Laboratory of Neurobiology of Adaptive Processes, Université Pierre-et-Marie-Curie, Paris 6


Collections: Biology and Medicine