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Time and frequency -Domain Interpretation of Phase-lag Control01:21

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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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Updated: Jun 24, 2025

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"Hidden phase" in two-wavelength adaptive optics.

Milo W Hyde, Jack E McCrae, Matthew Kalensky

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    This summary is machine-generated.

    Two-wavelength adaptive optics (AO) systems can be improved by accounting for the "hidden phase" effect in moderate atmospheric turbulence. This hidden phase is only correlated over a narrow wavelength band, limiting its benefit in two-wavelength AO systems.

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    Area of Science:

    • Astronomy
    • Optical Engineering
    • Atmospheric Physics

    Background:

    • Two-wavelength adaptive optics (AO) systems utilize different wavelengths for sensing and compensation.
    • Traditional AO analysis assumes weak scintillation, neglecting the
    • hidden phase
    • which arises from atmospheric aberrations.

    Purpose of the Study:

    • Investigate the impact of the hidden phase on two-wavelength AO performance.
    • Determine the wavelength dependency of the hidden phase correlation.

    Main Methods:

    • Wave optics simulations were conducted to model atmospheric turbulence.
    • The hidden-phase correlation coefficient was analyzed as a function of wavelengths and scintillation strength.

    Main Results:

    • The hidden phase is found to be correlated over a narrow wavelength band, unlike the least-squares phase.
    • An approximate expression for the hidden-phase correlation coefficient was derived.
    • The average hidden-phase correlation linewidth was found to be approximately 0.35 µm for wavelengths between 1-3 µm.

    Conclusions:

    • The hidden phase's limited wavelength correlation restricts its benefit in two-wavelength AO systems.
    • For wavelength differences greater than ~0.35 µm, correcting the hidden phase offers minimal improvement over standard AO.
    • This finding has implications for optimizing two-wavelength AO system design.