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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...
Reflection of Waves01:07

Reflection of Waves

When a wave travels from one medium to another, it gets reflected at the boundary of the second medium. A common example of this is when a person yells at a distance from a cliff and hears the echo of their voice. The sound waves (longitudinal waves) traveling in the air are reflected from the bounding cliff. Similarly, flipping one end of a string whose other end is tied to a wall causes a pulse (transverse wave) to travel through the string, which gets reflected upon reaching the wall. In...
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...
Propagation of Waves01:07

Propagation of Waves

When a wave propagates from one medium to another, part of it may get reflected in the first medium, and part of it may get transmitted to the second medium. In such a case, the interface of the two mediums can be considered as a boundary that is neither fixed nor free.
Consider a scenario where a wave propagates from a string of low linear mass density to a string of high linear mass density. In such a case, the reflected wave is out of phase with respect to the incident wave, however the...
Interference: Path Lengths01:10

Interference: Path Lengths

Consider two sources of sound, that may or may not be in phase, emitting waves at a single frequency, and consider the frequencies to be the same.
Two special sources may be considered when they are in phase. This can be easily achieved by feeding the two sources from the same source. An example would be synchronizing the two speakers by feeding them with the same source, such as the sound waves produced by a tuning fork. This setup ensures that the two sources have the same frequency and are...

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Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating
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Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating

Published on: October 11, 2016

Edge diffraction of a convergent wave.

A C Livanos, N George

    Applied Optics
    |February 6, 2010
    PubMed
    Summary
    This summary is machine-generated.

    This study presents closed-form solutions for diffraction patterns from circular apertures and infinite edges under convergent waves. Findings are visualized with photographs and computer-generated graphs for edge transform patterns.

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    Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating
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    Published on: October 11, 2016

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    Area of Science:

    • Optics and Photonics
    • Wave Diffraction Phenomena

    Background:

    • Understanding diffraction patterns is crucial in optical system design.
    • Previous models often simplify aperture shapes or incident wave characteristics.

    Purpose of the Study:

    • Derive closed-form solutions for focal plane diffraction patterns.
    • Analyze diffraction from a partial circular aperture and an infinite edge.
    • Visualize and present key features of edge transform patterns.

    Main Methods:

    • Analytical derivation of diffraction patterns.
    • Utilized closed-form solutions for specific illumination conditions (unit amplitude convergent wave, Gaussian amplitude convergent wave).
    • Experimental validation using photographic imaging and computational modeling for graphical representation.

    Main Results:

    • Closed-form solutions were successfully obtained for both scenarios.
    • Key features of the edge transform patterns were identified and documented.
    • Photographic and graphical data corroborate the theoretical findings.

    Conclusions:

    • The derived solutions provide accurate models for diffraction in the studied configurations.
    • This work enhances the understanding of wave propagation and diffraction at aperture discontinuities.
    • The presented visualizations aid in the interpretation and application of diffraction theory.