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Comparative analysis of interferogram noise filtration using wavelet transform and spin filtering algorithms

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The aim of this paper is to analyze 2D fringe pattern denoising performed by two chosen methods based on quasi-1D two-arm spin filter and 2D discrete wavelet transform (DWT) signal decomposition and thresholding. The ultimate aim of this comparison is to estimate which algorithm is better suited for high-accuracy measurements by phase shifting interferometry (PSI) with the phase step evaluation using the lattice site approach. The spin filtering method proposed by Yu et al. (1994) was designed to minimize possible fringe blur and distortion. The 2D DWT also presents such features due to a lossless nature of the signal wavelet decomposition. To compare both methods, a special 2D histogram introduced by Gutman and Weber (1998) is used to evaluate intensity errors introduced by each of the presented algorithms.
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  • Institute of Micromechanics and Photonics, Warsaw University of Technology, 8 Św. Andrzeja Boboli Str., 02-525 Warsaw, Poland, b.zielinski@mchtr.pw.edu.pl
Bibliografia
  • [1] D. W. Robinson and G. T. Reid: Interferogram Analysis: Digital Fringe Pattern Measurement Techniques. Taylor & Francis Ltd, London, 2002.
  • [2] D. L. Donoho: De-noising by soft-thresholding. IEEE T. Inform. Theory 41, 613-627 (1995).
  • [3] Q. F. Yu: Spin filtering processes and automatic extraction of fringe centerlines in digital inteferometric patterns. Appl. Opt. 27, 3782-3784, 1988.
  • [4] Q. Yu, X. Liu and K. Andresen: New spin filters for interferometric fringe patterns and grating patterns. Appl. Opt. 33, 3705-3711, 1994.
  • [5] A. Styk and K. Patorski: Identification of nonlinear recording error in phase shifting interferometry. Opt. Lasers Eng. 45, 265-273, 2007.
  • [6] K. Patorski, A. Styk, L. Bruno and P. Szwaykowski: Detection and assessment of the nonuniform phase displacement error in temporal phase shifting interferometry. Opt. Express 14, 5232-5249, 2006.
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  • [8] Q. Kemao: Windowed Fourier transform for fringe pattern analysis. Appl. Opt. 43, 2695-2702, 2004.
  • [9] J. P. Antoine, R. Murenzi and S. T. Ali: Two-dimensional Wavelets and their Relatives. Cambridge University Press, Cambridge, 2004.
  • [10] I. Daubechies: Ten Lectures on Wavelets. SIAM, Philadelphia, 1992.
  • [11] D. L. Donoho and I.M. Johnstone: Ideal spatial adaptation by wavelet shrinkage. Biometrika 81, 425-455, 1994.
  • [12] L. Salbut, K. Patorski, M. Jóźwik, J. Kacperski, C. Gorecki, A. Jacobelli and T. Dean: Active microelements testing by interferometry using time-average and quasistroboscopic techniques. Proc. SPIE 5145, 23-32, 2003.
  • [13] K. G. Larkin: Efficient nonlinear algorithm for envelope detection in white light interferometry. J. Opt. Soc. Am. A13, 832-843, 1996.
  • [14] A. Styk and K. Patorski: Analysis of systematic errors in spatial carrier phase shifting applied to interferogram intensity modulation determination. Appl. Opt. 46, 4613-4624, 2007.
  • [15] K. Patorski, Z. Sienicki and A. Styk: The phase shifting method contrast calculations in time average interferometry error analysis. Opt. Eng. 44, 065601, 2005.
  • [16] K. Patorski and A. Styk: Interferogram intensity modulation calculations using temporal phase shifting: error analysis. Opt. Eng. 45, 085602, 2006.
  • [17] B. Gutman and H. Weber: Phase-shifter calibration and error detection in phase-shifting applications: a new method. Appl. Opt. 37, 7624-7631, 1998.
  • [18] T. Kreis: Handbook of Holographic Interferometry. Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2005.
  • [19] J. Schwieder, R. Burow, K.-E. Elsser, J. Grzanna, R. Spolarczyk and K. Merkel: Digital wave-front measuring interferometry: some systematic error sources. Appl. Opt. 22, 3421-3432, 1983.
  • [20] M. Hansen and B. Yu: Wavelet thresholding via MDL for natural images. IEEE T. Inform. Theory 46, 1778-1788, 2000.
  • [21] A. Buades, B. Coll and J. M. Morel: A review of image denoising algorithms, with a new one. Multiscale Model. Sim. (SIAM) 4, 490-530, 2005.
  • [22] D. C. Ghiglia and M. D. Pritt: Two-Dimensional Phase Unwrapping: Theory, Algorithms and Software. Wiley-Interscience, New York, 1998.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BWAD-0018-0017
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