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Error-compensating algorithms in phase-shifting interferometry: a comparison by error analysis
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DOI：10.1016/S0143-8166(99)00017-2.png)
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Abstract
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In this paper, two families of phase-shifting algorithms with pi/2 phase steps are studied. In family I, three new algorithms are derived by using the averaging technique based on the Surrel six-sample algorithm with phase shifts of pi/2. Family II includes four well-known algorithms derived by the averaging technique based on the conventional four-sample algorithm with pi/2 phase steps. A polynomial model of phase-shift errors used to describe general expressions for calculation of the correct object phase via the Fourier spectra analysing method as a function of the harmonic order in the fringe signal is presented. The error-compensating properties of the algorithms in families I and II are investigated by the Fourier spectra analysing method. It is found that the averaging technique, when used in any of the algorithm with pi/2 phase steps, can improve the phase-shifting algorithm property: it is insensitive to phase-shift error when the fringe signal contains the first harmonic, but it can't be used to enhance the phase-shifting algorithm properties when the fringe signal contains higher order harmonics (n greater than or equal to 2). P-V (peak-valley) phase errors are calculated by the computer simulation and tables and plots are presented, from which the algorithms in families I and II are compared. It is shown that the algorithms in family I are more insensitive to phase-shift errors when the fringe signal contains the second harmonic and the algorithms in family II are more insensitive to phase-shift errors when the fringe signal is a sinusoidal waveform. (C) 1999 Elsevier Science Ltd. All rights reserved.
Keywords:
interferometry
phase-shifting algorithm
fringe analysis
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