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Related Concept Videos

Second Order systems I01:20

Second Order systems I

A servo system exemplifies a second-order system, featuring a proportional controller and load elements that ensure the output position aligns with the input position. The relationship between these components is described by a second-order differential equation. Applying the Laplace transform under zero initial conditions yields the transfer function, showing how inputs are converted to outputs in the system.
By reinterpreting the system, one can derive the closed-loop transfer function, which...
Second Order systems II01:18

Second Order systems II

In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
If  ζ...
Focusing of Light in the Eye01:16

Focusing of Light in the Eye

Light rays enter the eye through the cornea, a transparent dome-shaped tissue that is the eye's outermost layer. The cornea bends or refracts, light rays traveling to the pupil. The shape of the cornea determines how much of the light is bent and whether the image will be focused correctly on the retina at the back of the eye. Once the light has passed through both refraction layers, it converges into a single focal point onto a small area. This is where photoreceptors start transforming...
Properties of Enantiomers and Optical Activity02:24

Properties of Enantiomers and Optical Activity

It is essential to understand the difference between chiral and achiral interactions and the implications thereof in optical activity and their applications. Just as our feet, which are chiral, interact uniquely with chiral objects, such as a pair of shoes, but identically with achiral socks, enantiomers of a molecule exhibit different properties only when they interact with other chiral media. An example of a significant implication from this facet is the phenomenon known as optical activity,...
Linear time-invariant Systems01:23

Linear time-invariant Systems

A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be calculated...
Curvilinear Motion: Rectangular Components01:23

Curvilinear Motion: Rectangular Components

Curvilinear motion characterizes the movement of a particle or object along a curved path, notably evident when envisioning a car navigating a winding road. If the car starts at point A, its position vector is established within a fixed frame of reference, where the ratio of the position vector to its magnitude signifies the unit vector pointing in the position vector's direction.
As the car advances, its position evolves over time. Quantifying the car's velocity involves computing the time...

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Related Experiment Video

Updated: Jun 24, 2026

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
12:14

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

Published on: August 12, 2013

Optical system invariant to second-order aberrations.

Alexander B Samokhin1, Aleksey N Simonov, Michiel C Rombach

  • 1Applied Mathematics Department, Moscow Institute of Radio Engineering, Electronics and Automatics, 78 Vernadsky Prospekt, 117454, Moscow, Russia.

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|April 3, 2009
PubMed
Summary
This summary is machine-generated.

An approximate analytical expression for the optical transfer function (OTF) was derived for imaging systems with aberrations. This method analyzes broadband behavior using the stationary phase method, applicable to any pupil shape.

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Last Updated: Jun 24, 2026

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
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Published on: August 12, 2013

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05:14

Comparison of Agreement and Accuracy using Binocular Wavefront Optometer with Autorefractor and Phoropter

Published on: September 16, 2025

Area of Science:

  • Optics
  • Image Science
  • Optical Engineering

Background:

  • Imaging systems are susceptible to aberrations that degrade image quality.
  • The optical transfer function (OTF) is a key metric for characterizing imaging system performance.
  • Analyzing broadband behavior and aberration effects is crucial for optical system design.

Purpose of the Study:

  • To derive an approximate analytical expression for the two-dimensional incoherent optical transfer function (OTF).
  • To analyze the broadband behavior of imaging systems with a third-order phase mask.
  • To develop a method applicable to any pupil shape without requiring mathematical separability.

Main Methods:

  • Derivation of an approximate analytical expression for the OTF.
  • Application of the two-dimensional stationary phase method to analyze broadband behavior.
  • Investigation of systems invariant to second-order aberrations and incorporating third-order phase masks.

Main Results:

  • An analytical expression for the two-dimensional incoherent OTF was successfully derived.
  • The stationary phase method effectively analyzes broadband behavior for various pupil shapes.
  • The OTF remains well-defined and smooth at non-zero spatial frequencies with specific phase mask designs.

Conclusions:

  • The derived analytical OTF expression provides a valuable tool for evaluating imaging systems.
  • The stationary phase method offers a robust approach for analyzing aberration effects in broadband imaging.
  • Phase mask design, including third-order mixed terms, is critical for maintaining OTF quality.