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    A new algorithm enhances microscopic vibration measurement precision for self-mixing interferometers. This method achieves high accuracy, improving data collection in scientific research.

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    Area of Science:

    • * Optical Metrology
    • * Vibration Analysis
    • * Interferometry

    Background:

    • * Self-mixing interferometers are valuable tools for microscopic measurements.
    • * Improving measurement precision and simplifying instrument installation are key challenges.
    • * Existing methods may require complex setups or lack sufficient accuracy for certain applications.

    Purpose of the Study:

    • * To introduce an envelope extraction Fourier transform algorithm for enhanced measurement precision.
    • * To facilitate the installation and application of equivalent wavelength self-mixing interferometers.
    • * To enable accurate microscopic vibration measurement.

    Main Methods:

    • * Development of an envelope extraction Fourier transform algorithm.
    • * Application of the algorithm to self-mixing interferometer data.
    • * Validation using simulated and experimental vibration signals.

    Main Results:

    • * Theoretical precision of approximately 21 nm achieved without modulation.
    • * Minimum measurable vibration amplitude determined to be approximately 87 nm.
    • * Algorithm's validity confirmed through simulations and experimental measurements.

    Conclusions:

    • * The proposed algorithm significantly improves measurement precision in self-mixing interferometry.
    • * The method offers a practical solution for microscopic vibration analysis.
    • * This advancement supports more accurate and accessible optical metrology applications.