Abstract
In phase-shifting interferometry with unknown phase shifts, a normalization and orthogonalization phase-shifting algorithm (NOPSA) is proposed to achieve phase retrieval. The background of interferogram is eliminated through using the orthogonality of complex sinusoidal function; and the influence of phase shifts deviation on accuracy of phase retrieval is avoided through both normalization and orthogonalization processing. Compared with the current algorithms with unknown phase shifts, the proposed algorithm reveals significantly faster computation speed, higher accuracy, better stability and non-sensitivity of phase shifts deviation.
Highlights
Good consistency while the phase shifts is changed in a large range, but they need to eliminate the background through filtering processing in advance, otherwise, the error of phase retrieval is large
By using the whole interferogram or local interferogram for computation, a normalization and orthogonalization phase-shifting algorithm (NOPSA or local normalization and orthogonalization phase-shifting algorithm (LNOPSA)) is proposed to achieve phase retrieval, in which three or more phase-shifting interferograms with unknown phase shifts are employed, the background of interferogram is eliminated through using the orthogonality of complex sinusoidal function in advance, and the accurate phase can be achieved rapidly through both the normalization and orthogonalization processing
Each sequence includes 4-frame phase-shifting interferograms, and the corresponding phase distributions with and without phase shifts deviation (PSD) are calculated by different algorithms
Summary
Good consistency while the phase shifts is changed in a large range, but they need to eliminate the background through filtering processing in advance, otherwise, the error of phase retrieval is large. 2-PSA based on the orthonormalization processing is introduced to three–frame interferograms, the accuracy of phase retrieval can be further improved. By using the whole interferogram or local interferogram for computation, a normalization and orthogonalization phase-shifting algorithm (NOPSA or LNOPSA) is proposed to achieve phase retrieval, in which three or more phase-shifting interferograms with unknown phase shifts are employed, the background of interferogram is eliminated through using the orthogonality of complex sinusoidal function in advance, and the accurate phase can be achieved rapidly through both the normalization and orthogonalization processing. All computations are performed with the CPU of Intel(R) Core(TM) 2 Duo and the 3 GB memory, and with the software package of MATLAB
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