Approximation of Stochastic Quasi-Periodic Responses of Limit Cycles in Non-Equilibrium Systems under Periodic Excitations and Weak Fluctuations

Guo, Kongming; Xu, Yang

doi:10.3390/e19060280

Cited by 3 publications

(1 citation statement)

References 25 publications

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“…From the early phase-shift algorithm including the Hariharan algorithm and the Schwider algorithm to the current frequency-conversion phase-shift algorithm including the iterative algorithm and the principal element analysis method, we can come to a conclusion that the research of the frequency conversion phase shift algorithm has become the trend of modern phase-shift interferometry research [1]. Although the principal element analysis (PCA) and Advanced iterative algorithm (AIA) can be used to recover the phase information from a large number of phase-shifted interferogram efficiently [2][3][4][5], a series of error sources and the complexity of measured surface do exist in the actual measuring process [6,7]. And the traditional phase-shift interference algorithm exposes some drawbacks, such as the effect of noise and phase shift error on phase extraction precision of stochastic phase-shift algorithm [8], the influence of the background intensity and modulation system on phase-shift algorithm, and slow rate of operation as well as low precision of the result [3,9,10].…”

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confidence: 99%

Measurement of step surface contour based on variable sampling phase shift interference phase extraction algorithm based on selective sampling

Zhang

Huang

Xiong

2020

Preprint

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Variable frequency phase shift interferometry is widely applied in optical precision measurement, with the accuracy of phase extraction’s direct impact on that of phase shift interferometry. In the variable-frequency phase-shift interferometry, the commonly used phase-shifting devices are prone to phase shift errors, because the ordinary equal-step phase extraction algorithm, which can be merely used to measure simple and smooth surface, influences the accuracy of phase extraction resulting in measuring error, and causes inefficiency led by the long time the iterative process lasts for when applied in complex stepped surfaces measurement. As a sort of step-by-step phase-shifting phase extraction algorithm based on selective sampling is used to measure the step surface contour, the interference image is firstly sampled at equal intervals to reduce the iterative calculation, and in view of the fact that the phase calibration of the test system is not required in this algorithm, the measured phase is given by using the alternating iterative method despite the unknown phase and unknown phase shift amount. The phase extraction accuracy and iteration time among traditional iterative algorithm, four-step phase shift algorithm and the variable phase shift phase interpolation algorithm based on selective sampling are compared in the simulation and experiment. It is shown that the variable frequency phase shifting interference phase extraction algorithm based on selective sampling has shorter operation time, less error and higher accuracy than traditional iterative algorithm in measuring complex step surface.

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