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Fast algorithm based on the Hilbert transform for high-speed absolute distance measurement using a frequency scanning

Xiuming Li, Fajie Duan, Xiao Fu

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    A new fast algorithm improves distance measurement accuracy in frequency scanning interferometry. This method is nearly twice as fast as conventional techniques, offering precise results for micrometer-scale measurements.

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    Area of Science:

    • Optics and Photonics
    • Metrology

    Background:

    • Frequency scanning interferometry (FSI) measures absolute distances from micrometers to centimeters.
    • Existing methods like Fast Fourier Transform (FFT) and fringe counting lack accuracy with limited sampling points.
    • Conventional Hilbert transform offers better accuracy but is computationally intensive due to arctangent calculations and phase unwrapping.

    Purpose of the Study:

    • To develop a faster and accurate algorithm for distance demodulation in FSI.
    • To overcome the limitations of existing FFT and conventional Hilbert transform methods.
    • To enhance the speed and precision of absolute distance measurements.

    Main Methods:

    • A novel, fast algorithm based on the Hilbert transform was developed.
    • The algorithm avoids computationally expensive arctangent calculations and phase unwrapping.
    • It processes interference signals to recover phase and distance information.

    Main Results:

    • The proposed algorithm achieved a measurement speed of 1 kHz, completing in 40 µs.
    • It demonstrated a standard deviation of 0.062 µm at approximately 16 mm distance.
    • The new method is almost twice as fast as the conventional Hilbert transform with minimal accuracy loss.

    Conclusions:

    • The developed algorithm significantly enhances the speed and accuracy of FSI distance measurements.
    • It provides a more efficient alternative to FFT and conventional Hilbert transform methods.
    • This advancement is crucial for high-speed, precise metrology applications.