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Time and frequency -Domain Interpretation of Phase-lead Control01:24

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Phase-lead controllers are commonly used in various control systems to enhance response speed and stability. Adjusting the brightness on a television screen offers a practical example of phase-lead control. When contrast is enhanced, a phase-lead controller is employed. Mathematically, phase-lead control is identified when the first parameter is smaller than the second.
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Phase rectification for two-plus-one phase-shifting fringe projection technique via harmonic coefficient estimation.

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    This study introduces a new phase rectification method for two-plus-one phase-shifting fringe projection. It effectively removes harmonic errors without photometric calibration, improving measurement accuracy.

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    Area of Science:

    • Optical Metrology
    • 3D Measurement Technologies
    • Computational Imaging

    Background:

    • The two-plus-one phase-shifting fringe projection technique offers rapid 3D measurements with minimal fringe patterns.
    • Harmonic errors caused by system luminance nonlinearities hinder the practical application of this technique.
    • Existing methods often require complex photometric calibration to address these errors.

    Purpose of the Study:

    • To propose and validate a novel phase rectification method for the two-plus-one phase-shifting technique.
    • To eliminate harmonic-induced phase artifacts without the need for photometric calibration.
    • To preserve the integrity of phase map edges during error correction.

    Main Methods:

    • Analysis of the frequency response of the two-plus-one phase-shifting algorithm.
    • Reconstruction of a complex fringe pattern to estimate harmonic coefficients from its spectrum.
    • Development of a nonlinear phase mapping process using a look-up table for phase rectification.

    Main Results:

    • Successful estimation of harmonic coefficients based on the algorithm's frequency response.
    • Effective rectification of erroneous phase values to true phase values via a look-up table.
    • Demonstrated removal of harmonic-induced phase artifacts in both simulations and experiments.

    Conclusions:

    • The proposed method accurately removes harmonic errors in fringe projection without photometric calibration.
    • The technique preserves fine details and edges in the phase map, unlike methods that cause blurring.
    • This advancement enhances the practical applicability of rapid 3D measurement techniques.