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The Fourier Transform (FT) is an essential mathematical tool in signal processing, transforming a time-domain signal into its frequency-domain representation. This transformation elucidates the relationship between time and frequency domains through several properties, each revealing unique aspects of signal behavior.
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Related Experiment Video

Updated: Sep 29, 2025

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
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Frequency-shifting technique for pixelwise absolute phase retrieval.

Zhaoshuai Qi, Xiaolin Liu, Xiaojun Liu

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    |March 25, 2022
    PubMed
    Summary
    This summary is machine-generated.

    Frequency shifting eliminates phase periodicity in fringe projection profilometry, enabling direct absolute phase retrieval without phase unwrapping. This new method offers comparable performance to traditional phase shifting and phase unwrapping techniques.

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    Area of Science:

    • Optics and Photonics
    • Metrology
    • 3D Imaging

    Background:

    • Phase shifting (PS) is standard for phase retrieval in fringe projection profilometry.
    • PS techniques are limited by sine wave periodicity, causing wrapped phases that necessitate phase unwrapping (PU).

    Purpose of the Study:

    • To introduce a novel frequency shifting (FS) technique for absolute phase retrieval.
    • To eliminate phase periodicity and the need for phase unwrapping in fringe projection profilometry.

    Main Methods:

    • A new frequency shifting (FS) technique is proposed for phase retrieval.
    • The FS method aims to directly obtain absolute phase without wrapping.

    Main Results:

    • The proposed frequency shifting technique effectively eliminates phase periodicity.
    • Experimental results demonstrate comparable performance to combined PS and PU methods.
    • The FS technique achieves absolute phase retrieval in a single step with fewer projections.

    Conclusions:

    • Frequency shifting is a more general and effective technique for absolute phase retrieval.
    • This method simplifies 3D profilometry by removing the need for phase unwrapping.
    • The FS technique offers a promising alternative for accurate and efficient 3D surface measurement.