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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

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...
Phase-lead and Phase-lag Controllers01:22

Phase-lead and Phase-lag Controllers

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

Time and frequency -Domain Interpretation of Phase-lag Control

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 finite,...
Properties of DTFT I01:24

Properties of DTFT I

In signal processing, Discrete-Time Fourier Transforms (DTFTs) play a critical role in analyzing discrete-time signals in the frequency domain. Various properties of the DTFTs such as linearity, time-shifting, frequency-shifting, time reversal, conjugation, and time scaling help understand and manipulate these signals for different applications.
The linearity property of DTFTs is fundamental. If two discrete-time signals are multiplied by constants a and b respectively, and then combined to...
Time and frequency -Domain Interpretation of PI Control01:27

Time and frequency -Domain Interpretation of PI Control

Proportional-Integral (PI) controllers are essential in many control systems to improve stability and performance. They are commonly used in everyday devices like thermostats to enhance system damping and reduce steady-state error. When the zero in the controller's transfer function is optimally placed, the system benefits significantly in terms of stability and accuracy.
Acting as a low-pass filter, the PI controller slows the system's response and extends settling times. This requires careful...
Alternating Series and Absolute Convergence01:28

Alternating Series and Absolute Convergence

A mass attached to a vertical spring can exhibit oscillatory motion as it moves above and below a central equilibrium point. In an ideal spring, the oscillations would continue indefinitely with constant amplitude. In a damped spring, however, resistive forces such as air resistance or internal friction gradually reduce the size of each swing. This behavior is often modeled by combining a sinusoidal function, which represents the repeated motion, with an exponential decay factor, which reduces...

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Related Experiment Video

Updated: Jun 25, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
08:39

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Published on: January 28, 2019

Deterministic convergence in iterative phase shifting.

Esteban Luna1, Luis Salas, Erika Sohn

  • 1Universidad Nacional Autónoma de México, Instituto de Astronomía, Observatorio Astronómico Nacional,Apartado Postal 877, Ensenada, B.C. 22800, México. eala@astrosen.unam.mx

Applied Optics
|March 12, 2009
PubMed
Summary
This summary is machine-generated.

This study introduces a new iterative phase shifting method that deterministically identifies convergence. This advancement improves accuracy in optical surface metrology and other phase shifting applications.

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Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform
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Last Updated: Jun 25, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
08:39

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Published on: January 28, 2019

Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform
06:25

Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform

Published on: February 12, 2014

Area of Science:

  • Optical Metrology
  • Interferometry
  • Surface Characterization

Background:

  • Iterative phase shifting methods in interferometry often lack a reliable convergence indicator.
  • Accurate phase computation is crucial for precise optical surface measurements.

Purpose of the Study:

  • To develop a novel iterative phase shifting method with deterministic convergence identification.
  • To enhance the accuracy and reliability of phase computation in interferometric measurements.

Main Methods:

  • A new iterative phase shifting algorithm was developed.
  • The method was implemented and tested using a home-built Fizeau interferometer.
  • Measurements were performed on optical surfaces polished to lambda/100 using the Hydra tool.

Main Results:

  • The new method deterministically identifies convergence, overcoming limitations of previous implementations.
  • Measurements of optical surfaces achieved an intrinsic quality better than 0.5 nm.
  • The technique demonstrated high precision in characterizing polished optical surfaces.

Conclusions:

  • The presented iterative phase shifting method offers a robust solution for determining convergence.
  • This technique significantly improves the accuracy of optical surface metrology.
  • Potential applications extend to fringe projection and other phase shifting techniques.