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Related Concept Videos

Interference and Diffraction02:18

Interference and Diffraction

Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.
X-ray Crystallography02:18

X-ray Crystallography

The size of the unit cell and the arrangement of atoms in a crystal may be determined from measurements of the diffraction of X-rays by the crystal, termed X-ray crystallography.
Diffraction
Diffraction is the change in the direction of travel experienced by an electromagnetic wave when it encounters a physical barrier whose dimensions are comparable to those of the wavelength of the light. X-rays are electromagnetic radiation with wavelengths about as long as the distance between neighboring...
Determination of Crystal Structures01:29

Determination of Crystal Structures

In the late 1800s, the revelation that light extended beyond visible wavelengths led to the discovery of X-rays by Wilhelm Roentgen. Recognized as high-energy electromagnetic radiation with short wavelengths, X-rays prompted exploration into their interaction with crystals. Max von Laue proposed in 1912 that the periodic arrangement of atoms, ions, or molecules in crystals would cause them to diffract X-rays, a hypothesis confirmed through experiments with copper sulfate and zinc sulfide...
X-ray Diffraction of Biological Samples01:10

X-ray Diffraction of Biological Samples

X-ray diffraction or XRD is an analytical tool that utilizes X-rays to study ordered structures such as crystalline organic and inorganic samples, polycrystalline materials, proteins, carbohydrates, and drugs.
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Polar Coordinates: Problem Solving01:27

Polar Coordinates: Problem Solving

Directional radiation patterns are central to antenna analysis, as they illustrate how signal strength varies with direction. These patterns are often modeled using polar plots, where the radial distance from the origin represents signal intensity at a given angle. A commonly used idealized form is the four-lobed rose curve, which captures the concept of directional beams in a simplified mathematical form.The four-lobed rose curve, described by r = cos⁡(2θ), features four symmetric lobes, each...
Electric Field of a Charged Disk01:23

Electric Field of a Charged Disk

The simplest case of a surface charge distribution is the uniformly charged disk. Calculating its electric field also helps us calculate the electric field of a large plane of charge.
The system's symmetry is in the cylindrical directions across the plane of the charge. As a result, the electric fields created by various surface charge elements nullify each other in the direction parallel to the surface. Thereby, the resulting electric field is perpendicular to the plane. Since the disk is...

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Related Experiment Video

Updated: Jun 12, 2026

Measurements of Long-range Electronic Correlations During Femtosecond Diffraction Experiments Performed on Nanocrystals of Buckminsterfullerene
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Measurements of Long-range Electronic Correlations During Femtosecond Diffraction Experiments Performed on Nanocrystals of Buckminsterfullerene

Published on: August 22, 2017

Diffraction from a circular aperture: on-axis field strength.

R E English, N George

    Applied Optics
    |May 22, 2010
    PubMed
    Summary
    This summary is machine-generated.

    This study presents an analytical solution for the on-axis field strength of uniformly illuminated circular apertures. New calculations are also provided for tapered illuminations, advancing optical analysis.

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    Last Updated: Jun 12, 2026

    Measurements of Long-range Electronic Correlations During Femtosecond Diffraction Experiments Performed on Nanocrystals of Buckminsterfullerene
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    Published on: October 11, 2016

    Area of Science:

    • Optics and electromagnetics
    • Wave propagation and diffraction

    Background:

    • Understanding electromagnetic field distribution is crucial in optical system design.
    • Circular apertures are fundamental components in various optical instruments.

    Purpose of the Study:

    • To derive an analytical result for the on-axis field strength of a uniformly illuminated circular aperture.
    • To present novel calculations for circular apertures with non-uniform, tapered illuminations.

    Main Methods:

    • Analytical derivation using diffraction integral methods.
    • Numerical computation for tapered illumination profiles.

    Main Results:

    • An exact analytical expression for the on-axis field strength for uniform illumination.
    • Detailed field strength calculations for several tapered illumination functions.

    Conclusions:

    • The derived analytical result provides a benchmark for optical field calculations.
    • The new calculations for tapered illuminations offer practical tools for designing optical systems with improved performance.