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    A novel phase calculation method using discrete Fourier series (DFS) significantly enhances phase-shifting algorithm precision. This approach reduces phase error by up to 85%, improving accuracy in optical metrology applications.

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    Area of Science:

    • Optical Metrology
    • Signal Processing

    Background:

    • Traditional phase-shifting algorithms are susceptible to nonsinusoidal waveform errors.
    • Accurate phase calculation is crucial for quantitative analysis in optical measurement techniques.

    Purpose of the Study:

    • To propose a phase calculation method that mitigates nonsinusoidal effects.
    • To enhance the precision of existing phase-shifting algorithms.
    • To validate the proposed method through simulations and experimental verification.

    Main Methods:

    • Utilizing discrete Fourier series (DFS) to extract fundamental coefficients from N samples.
    • Reconstructing four images with π/2 intervals using extracted coefficients.
    • Applying the method to improve traditional phase-shifting algorithm accuracy.

    Main Results:

    • The discrete Fourier series (DFS) method effectively eliminates nonsinusoidal characteristics.
    • Phase error reduction of approximately 85% compared to a four-step algorithm.
    • Phase error reduction of approximately 70% compared to a 16-step algorithm.
    • Experimental validation using moiré fringe and projecting fringe techniques.

    Conclusions:

    • The proposed DFS-based phase calculation method offers superior accuracy.
    • This technique significantly improves upon conventional phase-shifting algorithms.
    • The method is robust and effective for various optical fringe analysis applications.