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    Summary
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    This study introduces a fast, accurate method for real-time phase detection using spatial carrier phase-shifting interferometry and dynamic mode decomposition. The technique enables efficient single-frame phase demodulation, crucial for dynamic measurements.

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    Area of Science:

    • Optical Metrology
    • Interferometry
    • Signal Processing

    Background:

    • Real-time phase detection is critical for dynamic measurements in various scientific and engineering fields.
    • Traditional phase-shifting interferometry methods can be time-consuming and computationally intensive.
    • Developing efficient single-frame phase demodulation algorithms remains a significant challenge.

    Purpose of the Study:

    • To present a novel, fast, and precise spatial carrier phase-shifting interferometry method for real-time phase detection.
    • To utilize the dynamic mode decomposition strategy for accurate phase measurement from a single interferogram.
    • To analyze the performance and robustness of the proposed method under various influencing factors.

    Main Methods:

    • Generation of phase-shifted sub-interferograms from a spatial carrier interferogram.
    • Application of dynamic mode decomposition (DMD), a non-iterative algorithm, for phase extraction.
    • Numerical simulations and experimental validation to assess the method's accuracy and efficiency.
    • Performance analysis considering factors like noise level, carrier frequency, and direction.

    Main Results:

    • The proposed method achieves fast and accurate phase demodulation from a single interferogram.
    • Dynamic Mode Decomposition effectively extracts phase information without iterative processes.
    • The algorithm demonstrates robustness against varying levels of random noise and carrier frequency parameters.
    • Experimental results confirm the efficiency and precision of the single-frame phase measurement technique.

    Conclusions:

    • The developed spatial carrier phase-shifting interferometry combined with DMD offers an efficient and accurate solution for dynamic real-time phase measurement.
    • This non-iterative, single-frame approach overcomes limitations of traditional methods.
    • The technique provides a valuable tool for applications requiring rapid and precise phase detection.