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Related Concept Videos

Time and frequency -Domain Interpretation of Phase-lead Control01:24

Time and frequency -Domain Interpretation of Phase-lead Control

116
Phase-lead controllers are commonly used in various control systems to enhance response speed and stability. Adjusting the brightness on a television screen offers a practical example of phase-lead control. When contrast is enhanced, a phase-lead controller is employed. Mathematically, phase-lead control is identified when the first parameter is smaller than the second.
The design of phase-lead control involves the strategic placement of poles and zeros to balance steady-state error and system...
116
Time and frequency -Domain Interpretation of Phase-lag Control01:21

Time and frequency -Domain Interpretation of Phase-lag Control

126
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.
Phase-lag controllers do not place a pole at zero, but instead influence the steady-state error by amplifying any...
126

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Related Experiment Video

Updated: Jul 31, 2025

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
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High-order spatial phase shift method realizes modulation analysis through a single-frame image.

Yuliang Long, Yan Tang, Xiaolong Cheng

    Applied Optics
    |May 3, 2023
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    Summary
    This summary is machine-generated.

    This study introduces a high-order spatial phase shift algorithm for modulation analysis in structured illumination microscopy. The method accurately measures discontinuous surfaces, overcoming limitations of previous frequency-domain techniques.

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    Area of Science:

    • Microscopy
    • Optical Imaging
    • Surface Metrology

    Background:

    • Structured illumination microscopy (SIM) requires accurate modulation distribution retrieval.
    • Existing frequency-domain methods lose high-frequency information, causing analytical errors.
    • Spatial area phase-shifting methods improve precision but smooth discontinuous topography.

    Purpose of the Study:

    • To develop a robust modulation analysis method for discontinuous surfaces using single-frame images.
    • To enhance the measurement accuracy of complex and discontinuous topographies in SIM.
    • To address the smoothing effect of previous methods on step-like structures.

    Main Methods:

    • Proposed a high-order spatial phase shift algorithm for single-frame modulation analysis.
    • Implemented a residual optimization strategy to handle complex topographies.
    • Validated the method through simulations and experimental measurements.

    Main Results:

    • The high-order spatial phase shift algorithm accurately analyzes modulation distribution on discontinuous surfaces.
    • The residual optimization strategy enables precise measurement of complex topographies.
    • Achieved higher precision measurements compared to existing frequency-domain and spatial methods.

    Conclusions:

    • The proposed high-order spatial phase shift algorithm offers robust and precise modulation analysis for discontinuous surfaces.
    • This technique significantly improves the measurement capabilities of modulation-based SIM systems for complex topographies.
    • The method provides a valuable advancement for quantitative phase imaging and surface metrology.