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Related Concept Videos

Transformations of Functions II01:29

Transformations of Functions II

Transformations in mathematics alter the position or orientation of a function’s graph while preserving its fundamental shape. One important type of transformation is the horizontal shift, which involves modifying the input variable within a function’s equation. This operation affects where outputs occur along the horizontal axis but does not alter the function’s overall structure.A horizontal shift is achieved by replacing the input variable x with either x + c or x - c, where c is a constant.
Properties of Fourier Transform II01:24

Properties of Fourier Transform II

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.
The Frequency Shifting property of Fourier Transforms highlights that a shift in the frequency domain corresponds to a phase shift in the time domain. Mathematically, if x(t) has...
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...
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,...
Phase Changes01:19

Phase Changes

Phase transitions play an important theoretical and practical role in the study of heat flow. In melting or fusion, a solid turns into a liquid; the opposite process is freezing. In evaporation, a liquid turns into a gas; the opposite process is condensation.
A substance melts or freezes at a temperature called its melting point and boils or condenses at its boiling point. These temperatures depend on pressure. High pressure favors the denser form of the substance, so typically, high pressure...
Transformations of Functions III01:20

Transformations of Functions III

Transformations modify the graphical representation of a function without changing its fundamental form. One common transformation is reflection, which flips the graph across a designated axis. When the vertical coordinates of all points are multiplied by the negative one, the entire graph is mirrored over the horizontal axis. This transformation reverses the vertical orientation of peaks and troughs, akin to signal inversion in electrical systems, where a waveform is flipped, but the timing of...

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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

Phase-shifting algorithm by use of Hough transform.

Hongwei Guo1, Beiting Lü

  • 1Lab of Applied Optics and Metrology, Department of Precision Mechanical Engineering, Shanghai University, Shanghai 200072, China. hw-guo@yeah.net

Optics Express
|November 29, 2012
PubMed
Summary
This summary is machine-generated.

This study introduces a novel phase-shifting algorithm using Hough transform for accurate sinusoidal curve analysis. The method effectively removes noise and recovers phase maps from fringe patterns.

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Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
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Area of Science:

  • Optical metrology
  • Image processing
  • Signal analysis

Background:

  • Phase-shifting techniques are crucial for fringe pattern analysis.
  • Existing methods can be sensitive to noise and saturation.
  • Accurate extraction of sinusoidal parameters is essential for various applications.

Purpose of the Study:

  • To develop a robust phase-shifting algorithm for analyzing sinusoidal fringe patterns.
  • To improve the accuracy and reliability of phase map recovery.
  • To mitigate the effects of common image artifacts.

Main Methods:

  • A phase-shifting algorithm is proposed, leveraging the Hough transform.
  • Background intensity is removed by calculating pixel intensity differences.
  • Hough transform is applied to processed data for parameter extraction.

Main Results:

  • The algorithm successfully extracts sinusoidal parameters (phase, amplitude) for each pixel.
  • It demonstrates robustness against camera saturation and impulse noise.
  • Accurate phase map recovery is achieved in simulations and experiments.

Conclusions:

  • The proposed Hough transform-based phase-shifting algorithm offers a reliable solution for fringe pattern analysis.
  • It effectively eliminates gross errors, enhancing phase map accuracy.
  • This method provides a significant advancement in optical metrology and image processing.