General phase-stepping algorithm with automatic calibration of phase steps

Wei, Chunlong; Chen, Mingyi; Wang, Zhijiang

doi:10.1117/1.602190

Cited by 21 publications

(6 citation statements)

References 8 publications

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“…First, the ellipse parameters had to be obtained by fitting the ellipse to the Lissajous representation of the detected data. The parameters of the ellipse and the detected data pairs are then used to calculate the optical phase using the modified phase-unwrapping equation (13). Finally, the optical phase is multiplied by a constant value u(t) = p(t) • λ/(4π ) to get the time-varying displacement.…”

Section: Methodsmentioning

confidence: 99%

“…For example, this can be done simply by following the practical realization given by Eom et al [11] while replacing their least-squares algorithm with the adapted code of Harker et al as described in section 2. The presented data processing is directly applicable in parallel research fields, especially in phase-shifting interferometry [12][13][14] and interferometric ellipsometry [15].…”

Section: Introductionmentioning

confidence: 99%

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Enhanced ellipse fitting in a two-detector homodyne quadrature laser interferometer

Požar¹,

Možina²

2011

Meas. Sci. Technol.

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The choice of fitting methods for elliptically scattered data obtained with displacement-measuring homodyne quadrature laser interferometers significantly influences the accuracy of the interferometer. This is especially important when the data contain a lot of noise or provide only a segment of the ellipse. The ellipse parameters extracted by the fitting are used either to correct the data or the basic arctangent phase-unwrapping function in order to enhance the accuracy of the measured displacement by reducing the common nonlinearities. We propose the use of linear, ellipse-specific, least-squares fitting that is further bias-corrected using a linear algorithm. This stable fitting method provides a good balance between the accuracy of the fit and the computational efficiency, and never returns corrupt, non-ellipse parameters. It is therefore applicable for an online, uniform fringe subdivision when there is a demand for sub-nanometric resolution. An experimental confirmation of the improvement over traditional fitting methods was carried out with a single-pass, two-detector homodyne quadrature laser interferometer. We were able to operate the interferometer with nanometric accuracy, provided the data draw out at least a quarter-arc of an ellipse.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Enhanced ellipse fitting in a two-detector homodyne quadrature laser interferometer

Požar¹,

Možina²

2011

Meas. Sci. Technol.

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“…The non-sinusoidal signal will include some higher harmonic components. Effectively, this means that using algorithms designed for sinusoidal signals [13][14][15][16][17][18][19][20][21] will yield incorrect results. The DFT method can calculate the phase maps for non-sinusoidal fringes as long as we increase the times of measurement.…”

Section: Introductionmentioning

confidence: 99%

Phase shifting method for non-sinusoidal interference fringes with phase shift error

Lian

Yang²,

Kudo

et al. 2019

Jpn. J. Appl. Phys.

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When applying phase shifting interferometry to practical phase measurement, the wave may become non-sinusoidal, and could include some phase shift errors. Prior phase shift algorithms are primarily used for sinusoidal cases, and can cause system errors when used for these non-sinusoidal interference. We propose two phase recovery methods for non-sinusoidal interference fringes: specifically, a least-squares-based fitting algorithm that eliminates system errors using a sufficient number of measured images, and a Fourier transform-based method that effectively suppresses system errors using a lower (or insufficient) number of images. Simulation and experimental results verify the efficacy of the proposed methods.

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“…A new general algorithm incorporates phase distributions composed of three least-squares fitting procedures for an analysis of real interferograms [8]. For the nonlinear phase shifter, the two-run-times-two-frame phase-shift method can be carried out in situ and is applicable to any phase shifter [9].…”

Section: Introductionmentioning

confidence: 99%

High-precision self-adaptive phase-calibration method for wavelength-tuning interferometry

Zhu

Zhao

Dong

et al. 2017

Meas. Sci. Technol.

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We introduce a high-precision self-adaptive phase-calibration method for performing wavelength-tuning interferometry. Our method is insensitive to the nonlinearity of the phase shifter, even under random control. Intensity errors derived from laser voltage changes can be restrained by adopting this approach. Furthermore, this method can effectively overcome the influences from the background and modulation intensities in the interferogram, regardless of the phase structure. Numerical simulations and experiments are implemented to verify the validity of this high-precision calibration method.

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General phase-stepping algorithm with automatic calibration of phase steps

Cited by 21 publications

References 8 publications

Enhanced ellipse fitting in a two-detector homodyne quadrature laser interferometer

Enhanced ellipse fitting in a two-detector homodyne quadrature laser interferometer

Phase shifting method for non-sinusoidal interference fringes with phase shift error

High-precision self-adaptive phase-calibration method for wavelength-tuning interferometry

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