The simultaneous suppression of phase shift error and harmonics in the phase shifting interferometry using carrier squeezing interferometry

The phase shift errors and the harmonics are the most common types of errors in the phase shifting interferometry. Although there are many suppression techniques for these two errors, it is hard to suppress them simultaneously. In this paper the carrier squeezing interferometry is used to solve this problem, where the data of phase shifting interferograms with linear carrier are re-arranged to acquire a spatial–temporal fringes image. In the frequency domain of the image the lobes of harmonics and phase shift errors and the lobe of the phase are separated, so the correct phase can be extracted by filtering. The algorithm is validated by both simulations and the experiments, with the phase retrieving accuracy greater than λ/400 and λ/200 (RMS value), respectively. The spatial uniform phase shift errors and harmonics can be suppressed by this method, using only four phase shifting interferograms.

[1]  J. García‐Márquez,et al.  Phase-shifting algorithms for a finite number of harmonics: first-order analysis by solving linear systems. , 2012, Journal of the Optical Society of America. A, Optics, image science, and vision.

[2]  Haitao He,et al.  Gamma correction for digital fringe projection profilometry. , 2004, Applied optics.

[3]  K Creath,et al.  Extended averaging technique for derivation of error-compensating algorithms in phase-shifting interferometry. , 1995, Applied optics.

[4]  L. Ugarte,et al.  Weakly Lefschetz symplectic manifolds , 2004, math/0404479.

[5]  Bongtae Han,et al.  Advanced iterative algorithm for phase extraction of randomly phase-shifted interferograms. , 2004, Optics letters.

[6]  L. Deck Suppressing phase errors from vibration in phase-shifting interferometry. , 2009, Applied optics.

[7]  D. J. Brangaccio,et al.  Digital wavefront measuring interferometer for testing optical surfaces and lenses. , 1974, Applied optics.

[9]  Lei Chen,et al.  Carrier squeezing interferometry: suppressing phase errors from the inaccurate phase shift. , 2011, Optics letters.

[10]  A. Tralle,et al.  On simply connected K-contact non-Sasakian manifolds , 2013, 1305.2591.

[11]  Zhaoyang Wang,et al.  Generic gamma correction for accuracy enhancement in fringe-projection profilometry. , 2010, Optics letters.

[12]  Peter de Groot,et al.  Derivation of algorithms for phase-shifting interferometry using the concept of a data-sampling window. , 1995, Applied optics.

[13]  W. V. Hodge,et al.  The Theory and Applications of Harmonic Integrals , 1941 .

[14]  Baoli Yao,et al.  Phase-shift extraction for generalized phase-shifting interferometry. , 2009, Optics letters.

[15]  Jun Ma,et al.  Phase extraction from optical interferograms in presence of intensity nonlinearity and arbitrary phase shifts , 2011 .

[16]  Seah Hock Soon,et al.  Phase extraction from arbitrary phase-shifted fringe patterns with noise suppression , 2010 .

[17]  J. Marrero,et al.  Examples of compact K-contact manifolds with no Sasakian metric , 2013, 1311.3270.

[18]  E. Rees,et al.  On the Fundamental Group of a Complex Algebraic Manifold , 1987 .

[19]  Robert E. Gompf A new construction of symplectic manifolds , 1995 .

[20]  Rihong Zhu,et al.  A fast and accurate gamma correction based on Fourier spectrum analysis for digital fringe projection profilometry , 2012 .

[21]  J. Schwider,et al.  Digital wave-front measuring interferometry: some systematic error sources. , 1983, Applied optics.

[22]  J A Quiroga,et al.  Spatial carrier interferometry from M temporal phase shifted interferograms: Squeezing Interferometry. , 2008, Optics express.

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

[24]  D. Malacara Optical Shop Testing , 1978 .

[25]  J. M. Huntley Suppression of phase errors from vibration in phase-shifting interferometry , 1998 .

[26]  Jean-Luc Brylinski,et al.  A differential complex for Poisson manifolds , 1988 .

[27]  Katsuyuki Okada,et al.  Simultaneous calculation of phase distribution and scanning phase shift in phase shifting interferometry , 1991 .