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Phase-lag controllers are widely used in control systems to improve stability and reduce steady-state errors. A dimmer switch controlling the brightness of a light bulb serves as a practical example of phase-lag control, gradually adjusting the bulb's brightness. Mathematically, phase-lag control or low-pass filtering is represented when the factor 'a' is less than 1.
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Related Experiment Video

Updated: Mar 18, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
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Dynamic phase measurement based on spatial carrier-frequency phase-shifting method.

Linbo Huang, Xiaoxu Lu, Jiaosheng Li

    Optics Express
    |July 14, 2016
    PubMed
    Summary
    This summary is machine-generated.

    A new method combines spatial carrier-frequency phase-shifting (SCPS) and Fourier transforms for faster dynamic phase measurement from single images. This technique accurately retrieves phase shifts without prior calibration, enabling real-time analysis.

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    Area of Science:

    • Optical Metrology
    • Interferometry
    • Phase Measurement

    Background:

    • Dynamic phase measurement is crucial for observing transient phenomena.
    • Existing spatial carrier-frequency phase-shifting (SCPS) methods often require prior calibration.
    • Efficient phase retrieval from single interferograms remains a challenge.

    Purpose of the Study:

    • To develop a novel, rapid phase retrieval method for dynamic phase measurement.
    • To eliminate the need for carrier-frequency calibration in SCPS techniques.
    • To enable accurate phase retrieval from a single spatial carrier-frequency interferogram (SCFI).

    Main Methods:

    • Constructing four-frame phase-shifting sub-interferograms from a single SCFI using the SCPS technique.
    • Employing Fourier transform methods for rapid extraction of accurate phase shifts.
    • Utilizing a least-squares algorithm for wrapped phase retrieval.

    Main Results:

    • Accurate phase shifts were extracted rapidly without carrier-frequency calibration.
    • The proposed method demonstrated high accuracy comparable to traditional SCPS.
    • Phase variations during water droplet evaporation and drug-induced cell apoptosis were successfully measured.

    Conclusions:

    • The novel method offers a significant improvement in processing speed for dynamic phase measurement.
    • It effectively combines SCPS and Fourier transform methods for efficient phase retrieval.
    • The technique facilitates broader applications in real-time optical metrology and biological studies.