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Related Concept Videos

Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
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...
Application of Linearization and Approximation01:29

Application of Linearization and Approximation

A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...
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-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...

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Related Experiment Video

Updated: Jun 8, 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

Approximating fully complex spatial modulation with pseudorandom phase-only modulation.

R W Cohn, M Liang

    Applied Optics
    |October 12, 2010
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a novel, noniterative method for creating phase-only transparencies to generate desired diffraction patterns. This approach simplifies complex transparency design, offering a direct translation for optical applications.

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    Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform
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    Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform

    Published on: February 12, 2014

    Generation and Coherent Control of Pulsed Quantum Frequency Combs
    06:42

    Generation and Coherent Control of Pulsed Quantum Frequency Combs

    Published on: June 8, 2018

    Related Experiment Videos

    Last Updated: Jun 8, 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

    Generation and Coherent Control of Pulsed Quantum Frequency Combs
    06:42

    Generation and Coherent Control of Pulsed Quantum Frequency Combs

    Published on: June 8, 2018

    Area of Science:

    • Optics and Photonics
    • Computational Imaging
    • Diffractive Optics

    Background:

    • Diffraction patterns are formed in the Fourier plane by input-plane transparencies.
    • Achieving desired diffraction patterns often requires complex-valued transmittance.
    • Current design methods rely on computationally intensive optimization techniques.

    Purpose of the Study:

    • To develop a noniterative procedure for designing phase-only transparencies.
    • To directly translate desired complex transmittance into a practical phase-only transparency.
    • To evaluate the accuracy of the generated diffraction patterns.

    Main Methods:

    • Introduced a noniterative design procedure.
    • Employed pseudorandom phase selection at each pixel, with distribution standard deviation linked to desired amplitude.
    • Derived statistical expressions to analyze approximation errors.

    Main Results:

    • Successfully demonstrated a direct translation from complex to phase-only transmittance.
    • The pseudorandom phase selection method allows for efficient generation of phase transparencies.
    • Statistical analysis provided a means to quantify the errors between desired and achieved diffraction patterns.

    Conclusions:

    • The proposed noniterative method offers a practical alternative to complex optimization for designing phase-only transparencies.
    • This technique simplifies the creation of optical elements for generating specific diffraction patterns.
    • The derived statistical expressions are valuable for predicting and understanding the performance of the designed transparencies.