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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

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

Time and frequency -Domain Interpretation of Phase-lag Control

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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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Phase-lead and Phase-lag Controllers01:22

Phase-lead and Phase-lag Controllers

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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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Time-Domain Interpretation of PD Control01:07

Time-Domain Interpretation of PD Control

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Proportional-Derivative (PD) control is a widely used control method in various engineering systems to enhance stability and performance. In a system with only proportional control, common issues include high maximum overshoot and oscillation, observed in both the error signal and its rate of change. This behavior can be divided into three distinct phases: initial overshoot, subsequent undershoot, and gradual stabilization.
Consider the example of control of motor torque. Initially, a positive...
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Gain01:15

Gain

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Gain and phase shift are properties of linear circuits that describe the effect a circuit has on a sinusoidal input voltage or current. The circuit's behavior that contains reactive elements will depend on the frequency of the input sinusoid. As a result, it is observed that the gain and phase shift will all be frequency functions.
Gain:
Suppose Vin is the input and Vout is the output signal to a circuit.
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Phase Contrast and Differential Interference Contrast Microscopy01:26

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Phase-Contrast Microscopes
In-phase-contrast microscopes, interference between light directly passing through a cell and light refracted by cellular components is used to create high-contrast, high-resolution images without staining. It is the oldest and simplest type of microscope that creates an image by altering the wavelengths of light rays passing through the specimen. Altered wavelength paths are created using an annular stop in the condenser. The annular stop produces a hollow cone of...
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Related Experiment Video

Updated: Jun 17, 2025

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
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Theory and application of robust linear phase-shift algorithm for phase-shift deflectometry method.

Song Yang1, Xianyong Zhu2, Zhirui Cao3

  • 1School of Mechanical and Aerospace Engineering, Jilin University, Changchun, 130025, Jilin, China.

Scientific Reports
|August 8, 2024
PubMed
Summary

A new Robust Linear Phase-Shift (RLPS) algorithm effectively suppresses Gamma distortion and phase detuning errors in optical measurements. This advanced algorithm offers superior stability and accuracy compared to traditional N-step Discrete Fourier Transform (N-DFT) methods.

Keywords:
Detuning errorGamma distortionPhase shift algorithmPhase-shift deflectometry

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Area of Science:

  • Optical metrology
  • Signal processing

Background:

  • N-step Discrete Fourier Transform (N-DFT) algorithms are widely used for phase-shift analysis.
  • These algorithms face challenges with Gamma distortion and phase detuning, limiting measurement accuracy.
  • Simultaneous suppression of multiple error sources remains a key challenge in optical metrology.

Purpose of the Study:

  • To analyze the error propagation characteristics of N-step DFT algorithms.
  • To design a novel algorithm capable of simultaneously suppressing Gamma distortion and phase detuning.
  • To evaluate the performance of the new algorithm against existing methods through simulations and experiments.

Main Methods:

  • Theoretical analysis based on polynomial theory to study error propagation in N-DFT.
  • Design and implementation of a Robust Linear Phase-Shift (RLPS) algorithm.
  • Performance evaluation using the Manuel Servin method, spectral response analysis, and detuning robustness tests.
  • Physical experiments using inclined plane and concave mirrors to validate algorithm performance.

Main Results:

  • N-DFT algorithms cannot simultaneously suppress Gamma distortion and phase detuning.
  • The RLPS algorithm demonstrates simultaneous suppression of both error types.
  • RLPS exhibits superior stability and accuracy over N-DFT and exponential algorithms, particularly in gradient measurement, peak-to-valley (PV), and root-mean-square (RMS) error reduction.
  • Physical experiments confirm RLPS improves measurement stability and accuracy under detuning and without Gamma calibration.

Conclusions:

  • The RLPS algorithm provides a significant advancement in optical metrology by overcoming the limitations of N-DFT.
  • RLPS offers enhanced stability and accuracy, crucial for precise optical surface measurements.
  • The developed algorithm is robust to detuning and Gamma distortion, simplifying measurement procedures.