Improved high-order ambiguity-function method for the estimation of phase from interferometric fringes.

Interferometers often encode the information on the measurand in the phase of a fringe pattern, which is usually recorded by an imaging device. Accuracy of measurements carried out by interferometric techniques is thus strongly dependent on the accuracy with which the underlying phase distribution of these fringe patterns is estimated. Fringe analysis methods, which have been developed to accomplish this task, are in general characterized by their performance in terms of both accuracy of phase estimation and associated computational complexity. We propose an improved high-order ambiguity-function-based fringe-analysis method that is demonstrated to provide an accurate and direct estimation of the unwrapped phase distribution in a highly computationally efficient manner. Presented simulation and experimental results in digital holographic interferometry depict the potential utility of the proposed method.

[1]  Jingang Zhong,et al.  Spatial carrier-fringe pattern analysis by means of wavelet transform: wavelet transform profilometry. , 2004, Applied optics.

[2]  M. Takeda,et al.  Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry , 1982 .

[3]  Serhat Özder,et al.  Continuous wavelet transform analysis of projected fringe patterns , 2004 .

[4]  Sai Siva Gorthi,et al.  Numerical analysis of fringe patterns recorded in holographic interferometry using high-order ambiguity function , 2009 .

[5]  David R. Burton,et al.  Spatial carrier fringe pattern demodulation by use of a two-dimensional continuous wavelet transform , 2006 .

[6]  José A. Gómez-Pedrero,et al.  Algorithm for fringe pattern normalization , 2001 .

[7]  J. Marroquín,et al.  Demodulation of a single interferogram by use of a two-dimensional regularized phase-tracking technique. , 1997, Applied optics.

[8]  L R Watkins,et al.  Determination of interferometer phase distributions by use of wavelets. , 1999, Optics letters.

[9]  Qian Kemao,et al.  Windowed Fourier transform for fringe pattern analysis. , 2004, Applied optics.

[10]  R. O. Schmidt,et al.  Multiple emitter location and signal Parameter estimation , 1986 .

[11]  Werner Jüptner,et al.  Digital recording and numerical reconstruction of holograms , 2002 .

[12]  Benjamin Friedlander,et al.  A modification of the discrete polynomial transform , 1998, IEEE Trans. Signal Process..

[13]  Mariano Rivera,et al.  Fast phase recovery from a single closed-fringe pattern. , 2008, Journal of the Optical Society of America. A, Optics, image science, and vision.

[14]  Seah Hock Soon,et al.  Phase-shifting windowed Fourier ridges for determination of phase derivatives. , 2003, Optics letters.

[15]  Thomas Kailath,et al.  ESPRIT-estimation of signal parameters via rotational invariance techniques , 1989, IEEE Trans. Acoust. Speech Signal Process..

[16]  Sai Siva Gorthi,et al.  Piecewise polynomial phase approximation approach for the analysis of reconstructed interference fields in digital holographic interferometry , 2009 .

[17]  Bernard Mulgrew,et al.  Iterative frequency estimation by interpolation on Fourier coefficients , 2005, IEEE Transactions on Signal Processing.