Adaptive filtering of white-light interferometry fringe patterns

Tests are carried out of an on-line adaptive filtering scheme based on the least-mean-square (LMS) algorithm and are specifically aimed at enhancing the performance of fringe order identification in white-light interferometry (WLI) over a wide range of signal-to-noise ratios (SNR's). Additional capability is also provided in accurately pinpointing the central fringe with a minimum resolution of 1/13 of a fringe width anywhere over the middle 1000 pixels of a 1024-pixel CCD array. Computer simulations and subsequent measurements have demonstrated the superiority of this scheme over the less efficient centroid-based method previously reported.

[1]  B. Widrow,et al.  Stationary and nonstationary learning characteristics of the LMS adaptive filter , 1976, Proceedings of the IEEE.

[2]  B. Widrow,et al.  Adaptive noise cancelling: Principles and applications , 1975 .

[3]  R. Ulrich,et al.  Fiber-optic displacement sensor with 0.02 μm resolution by white-light interferometry , 1990 .

[4]  James V. Candy,et al.  Signal Processing: Model Based Approach , 1986 .

[5]  J. Nagumo,et al.  A learning method for system identification , 1967, IEEE Transactions on Automatic Control.

[6]  Richard W. Harris,et al.  A variable step (VS) adaptive filter algorithm , 1986, IEEE Trans. Acoust. Speech Signal Process..

[7]  G. Ungerboeck Theory on the speed of convergence in adaptive equalizers for digital communication , 1972 .

[8]  Kenneth T. V. Grattan,et al.  The Application of Super-Resolution Adaptive Algorithms to Fringe Order Estimation in All-Optical-Fibre Interferometric Sensors , 1995 .

[9]  B. T. Meggitt,et al.  Novel electronic scanner for coherence multiplexing in a quasi-distributed pressure sensor , 1990 .

[10]  B. T. Meggitt,et al.  Digital signal-processing techniques for electronically scanned optical-fiber white-light interferometry. , 1992, Applied optics.

[11]  B. T. Meggitt,et al.  Electronically scanned optical-fiber Young's white-light interferometer. , 1991, Optics letters.

[12]  Norbert Wiener,et al.  Extrapolation, Interpolation, and Smoothing of Stationary Time Series, with Engineering Applications , 1949 .

[13]  Peter M. Clarkson,et al.  A class of order statistic LMS algorithms , 1992, IEEE Trans. Signal Process..

[14]  Simon Haykin,et al.  Adaptive filter theory (2nd ed.) , 1991 .

[15]  William A. Gardner Nonstationary learning characteristics of the LMS algorithm , 1987 .

[16]  R. Gitlin,et al.  On the required tap-weight precision for digitally implemented, adaptive, mean-squared equalizers , 1979, The Bell System Technical Journal.

[17]  C. Caraiscos,et al.  A roundoff error analysis of the LMS adaptive algorithm , 1984 .

[18]  John M. Cioffi,et al.  Limited-precision effects in adaptive filtering , 1987 .

[19]  R. Dandliker,et al.  Noise-resistant Signal Processing For Electronically Scanned White-Light Interferometry , 1992, 8th Optical Fiber Sensors Conference.