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Discrete Fourier Transform01:15

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The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...
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Updated: Oct 2, 2025

Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating
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S-transform application in phase extraction of spectrally resolved interferometry measuring step height.

Wentao Luo, Yu He, Yan Tang

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    |February 24, 2022
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    Summary

    The S-transform is a feasible method for phase extraction in spectrally resolved white-light interferometry, outperforming Fourier and wavelet transforms for step height measurements.

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    Area of Science:

    • Metrology and Surface Characterization
    • Optical Measurement Techniques
    • Signal Processing

    Background:

    • Spectrally resolved interferometry is crucial for micro/nano-scale geometric measurements.
    • Accurate phase extraction is essential for white-light interferometry.
    • Traditional methods like Fourier and wavelet transforms have limitations.

    Purpose of the Study:

    • To evaluate the S-transform for phase extraction in spectrally resolved white-light interferometry.
    • To compare the S-transform's performance against Fourier and wavelet transforms for step height measurement.

    Main Methods:

    • Utilized the S-transform for phase extraction from spectrally resolved white-light interferometry signals.
    • Applied the method to measure step height.
    • Compared results with Fourier transform and wavelet transform methods.

    Main Results:

    • The S-transform demonstrated feasibility in phase extraction for spectrally resolved interferometry.
    • It proved effective for measuring step height.
    • Performance was validated against established transform methods.

    Conclusions:

    • The S-transform is a viable and effective technique for phase extraction in spectrally resolved white-light interferometry.
    • It offers advantages for micro/nano-scale geometric measurements, particularly for step height analysis.