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Related Concept Videos

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.
Phase-lag controllers do not place a pole at zero, but instead influence the steady-state error by amplifying any...
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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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Understanding the working function of different types of controllers can be illustrated with practical analogies, such as adjusting a stereo's volume equalizer. Cranking up the bass involves a phase-lead controller, which functions as a high-pass filter, while increasing the treble uses a phase-lag controller, which acts as a low-pass filter. PD controllers, similar to high-pass filters, enhance the system's response to high-frequency components. PI controllers, akin to low-pass...
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The Phase Rule01:20

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The phase rule describes the relationship between the variance (degrees of freedom), the number of components, and the number of phases in a system at equilibrium.Variance is a concept that denotes the number of independent intensive properties (properties are those that do not depend on the amount of material in the system), such as temperature, pressure, and composition, that can be altered without impacting the number of phases in equilibrium.In a single-component system, such as pure water,...
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Related Experiment Video

Updated: May 1, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
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Generalized phase-shifting algorithm for inhomogeneous phase shift and spatio-temporal fringe visibility variation.

Rigoberto Juarez-Salazar, Carlos Robledo-Sanchez, Fermin Guerrero-Sanchez

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    |March 26, 2014
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    Summary

    A new cascade least-squares algorithm accurately extracts wrapped phase from fringe patterns, even with unknown surface shifts. This robust method enhances phase computing in automated applications.

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    Area of Science:

    • Optical metrology
    • Image processing
    • Phase analysis

    Background:

    • Wrapped phase extraction is crucial for 3D surface analysis.
    • Inhomogeneous surface phase shifts pose significant challenges.
    • Existing methods often struggle with unknown or varying phase shifts.

    Purpose of the Study:

    • To propose a novel cascade least-squares scheme for wrapped phase extraction.
    • To address challenges posed by unknown and inhomogeneous surface phase shifts.
    • To develop a robust and computationally efficient algorithm for fringe-pattern analysis.

    Main Methods:

    • Utilizing a parameter estimation approach for fringe-pattern processing.
    • Developing a cascade least-squares algorithm.
    • Employing computer simulations and experimental validation.

    Main Results:

    • Successful phase extraction is demonstrated even with nonlinear piezoelectric materials or miscalibrated phase shifters.
    • The algorithm shows robustness against inhomogeneous phase shifts.
    • The proposed method achieves accurate phase computing.

    Conclusions:

    • The cascade least-squares scheme provides a reliable method for wrapped phase extraction.
    • The algorithm's robustness, efficiency, and user-free execution make it suitable for automated applications.
    • This technique advances fringe-pattern analysis in optical metrology.