Spatial carrier phase-shifting algorithm based on principal component analysis method

A non-iterative spatial phase-shifting algorithm based on principal component analysis (PCA) is proposed to directly extract the phase from only a single spatial carrier interferogram. Firstly, we compose a set of phase-shifted fringe patterns from the original spatial carrier interferogram shifting by one pixel their starting position. Secondly, two uncorrelated quadrature signals that correspond to the first and second principal components are extracted from the phase-shifted interferograms by the PCA algorithm. Then, the modulating phase is calculated from the arctangent function of the two quadrature signals. Meanwhile, the main factors that may influence the performance of the proposed method are analyzed and discussed, such as the level of random noise, the carrier-frequency values and the angle of carrier-frequency of fringe pattern. Numerical simulations and experiments are given to demonstrate the performance of the proposed method and the results show that the proposed method is fast, effectively and accurate. The proposed method can be used to on-line detection fields of dynamic or moving objects.

[1]  J Vargas,et al.  Phase-shifting interferometry based on principal component analysis. , 2011, Optics letters.

[2]  Peter John Bryanston-Cross,et al.  Spatial phase stepping method of fringe-pattern analysis , 1995 .

[3]  Qian Kemao,et al.  Windowed Fourier transform for fringe pattern analysis: theoretical analyses. , 2008, Applied optics.

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

[5]  Yong Li,et al.  Principal component analysis of multiple-beam Fizeau interferograms with random phase shifts. , 2011, Optics express.

[6]  Malgorzata Kujawinska,et al.  Spatial-carrier phase-shifting technique of fringe pattern analysis , 1991, Other Conferences.

[7]  Qian Kemao,et al.  Real-time 2D parallel windowed Fourier transform for fringe pattern analysis using Graphics Processing Unit. , 2009, Optics express.

[8]  YongKeun Park,et al.  Real-time quantitative phase imaging with a spatial phase-shifting algorithm. , 2011, Optics letters.

[9]  Huaixin Chen,et al.  Algorithm for near-field reconstruction based on radial-shearing interferometry. , 2005, Optics letters.

[10]  Jiancheng Xu,et al.  Spatial carrier phase-shifting algorithm based on least-squares iteration. , 2008, Applied optics.

[11]  J H Massig,et al.  Fringe-pattern analysis with high accuracy by use of the fourier-transform method: theory and experimental tests. , 2001, Applied optics.

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

[13]  M. Takeda,et al.  Fourier transform profilometry for the automatic measurement of 3-D object shapes. , 1983, Applied optics.

[14]  K A Nugent,et al.  Interferogram analysis using an accurate fully automatic algorithm. , 1985, Applied optics.

[15]  W. Macy,et al.  Two-dimensional fringe-pattern analysis. , 1983, Applied optics.

[16]  D J Bone,et al.  Fringe-pattern analysis using a 2-D Fourier transform. , 1986, Applied optics.

[17]  J Vargas,et al.  Analysis of the principal component algorithm in phase-shifting interferometry. , 2011, Optics letters.

[18]  F Roddier,et al.  Interferogram analysis using Fourier transform techniques. , 1987, Applied optics.

[19]  Dong Liu,et al.  Real time diagnosis of transient pulse laser with high repetition by radial shearing interferometer. , 2007, Applied optics.

[20]  Krzysztof Patorski,et al.  Analysis of systematic errors in spatial carrier phase shifting applied to interferogram intensity modulation determination. , 2007, Applied optics.

[21]  Weimin Jin,et al.  Phase extraction from randomly phase-shifted interferograms by combining principal component analysis and least squares method. , 2011, Optics express.

[22]  P. Ronney,et al.  Modified Fourier transform method for interferogram fringe pattern analysis. , 1997, Applied optics.

[23]  Manuel Servin,et al.  A Novel Technique for Spatial Phase-shifting Interferometry , 1995 .

[24]  Jingang Zhong,et al.  Phase retrieval of optical fringe patterns from the ridge of a wavelet transform. , 2005, Optics letters.

[25]  Qi Yang,et al.  Local frequency estimation for the fringe pattern with a spatial carrier: principle and applications. , 2007, Applied optics.

[26]  José A. Ferrari,et al.  Multiple phase-shifted interferograms obtained from a single interferogram with linear carrier , 2007 .

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