Abstract
We introduce the algorithm for the direct phase estimation from the single noisy interferometric pattern. The method, named implicit smoothing spline (ISS), can be regarded as a formal generalization of the smoothing spline interpolation for the case when the interpolated data is given implicitly. We derive the necessary equations, discuss the properties of the method and address its application for the direct estimation of the continuous phase in both classical interferometry and digital speckle pattern interferometry (DSPI). The numerical illustrations of the algorithm performance are provided to corroborate the high quality of the results.
Highlights
In optical metrological systems the measured quantity modifies such light beam parameters as its amplitude, propagation direction, frequency, phase and polarization state
While there exist other algorithms aiming at direct phase estimation, such as the regularized phase tracking (RPT) algorithms family, there are fundamental differences between the proposed technique and other methods considered in the literature, namely
The quality of the retrieved phase is evaluated with the root mean square error (RMS), mean absolute value of the error (MAE) and the maximum error value (Peak), all given in radians
Summary
In optical metrological systems the measured quantity modifies such light beam parameters as its amplitude (intensity), propagation direction, frequency, phase and polarization state. Instead of tackling the task of the noise removal from the intensity fringe image as an image enhancement technique, we address the direct estimation of the phase distribution with the newly introduced algorithm named implicit smoothing spline (ISS). In this way the error in the sought phase distribution can be minimized directly, unlike in the methods aiming at the intensity pattern filtering. It constitutes a new framework for the phase demodulation and with very small number of parameters that need to be specified, the method is not difficult to automatize
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