Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Gauss's Law: Problem-Solving01:10

Gauss's Law: Problem-Solving

Gauss's law helps determine electric fields even though the law is not directly about electric fields but electric flux. In situations with certain symmetries (spherical, cylindrical, or planar) in the charge distribution, the electric field can be deduced based on the knowledge of the electric flux. In these systems, we can find a Gaussian surface S over which the electric field has a constant magnitude. Furthermore, suppose the electric field is parallel (or antiparallel) to the area vector...
Gauss's Law01:07

Gauss's Law

If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.
Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a uniform...
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...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Multispectral extended depth-of-field fluorescence microscopy with co-designed meta-optics and neural reconstruction.

Light, science & applications·2026
Same author

Reduced bone turnover in non-obese women with polycystic ovary syndrome: a cross-sectional study on procollagen-1 N-terminal peptide and beta-C terminal telopeptide.

Revista da Associacao Medica Brasileira (1992)·2026
Same author

Computer-generated holography using hybrid planar-spherical wave primitives.

Optics express·2026
Same author

Design and Characterization of Phosphatizing Coatings for Magnesium Implants.

ACS biomaterials science & engineering·2026
Same author

Comparative efficacy of corticosteroid injection, extracorporeal shock wave therapy, and radiofrequency ablation for chronic plantar fasciitis: a prospective randomized controlled trial.

BMC musculoskeletal disorders·2026
Same author

Total resection and reconstruction of collateral ligaments in severe elbow stiffness induced by heterotopic ossification: a novel approach and review of the literature.

JSES international·2026

Related Experiment Video

Updated: May 20, 2026

Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating
10:39

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

Published on: October 11, 2016

Scalar diffraction field calculation from curved surfaces via Gaussian beam decomposition.

Erdem Şahin1, Levent Onural

  • 1Department of Electrical and Electronics Engineering, Bilkent University, Ankara, Turkey. sahin@ee.bilkent.edu.tr

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|July 4, 2012
PubMed
Summary

This study presents a new method to analyze 3D diffraction fields on curved surfaces by decomposing signals into Gaussian beams. This approach accurately models complex wave propagation for smoother surfaces.

More Related Videos

Controlled Synthesis and Fluorescence Tracking of Highly Uniform Poly(N-isopropylacrylamide) Microgels
11:34

Controlled Synthesis and Fluorescence Tracking of Highly Uniform Poly(N-isopropylacrylamide) Microgels

Published on: September 8, 2016

Measurements of Long-range Electronic Correlations During Femtosecond Diffraction Experiments Performed on Nanocrystals of Buckminsterfullerene
08:44

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

Published on: August 22, 2017

Related Experiment Videos

Last Updated: May 20, 2026

Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating
10:39

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

Published on: October 11, 2016

Controlled Synthesis and Fluorescence Tracking of Highly Uniform Poly(N-isopropylacrylamide) Microgels
11:34

Controlled Synthesis and Fluorescence Tracking of Highly Uniform Poly(N-isopropylacrylamide) Microgels

Published on: September 8, 2016

Measurements of Long-range Electronic Correlations During Femtosecond Diffraction Experiments Performed on Nanocrystals of Buckminsterfullerene
08:44

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

Published on: August 22, 2017

Area of Science:

  • Optics and Photonics
  • Computational Electromagnetics
  • Wave Propagation

Background:

  • Analyzing three-dimensional (3D) diffraction fields on curved surfaces is computationally challenging.
  • Existing methods may struggle with the complexities of non-planar geometries.

Purpose of the Study:

  • To introduce a novel local signal decomposition method for analyzing 3D diffraction fields on curved surfaces.
  • To represent the 3D field as a sum of Gaussian beams for simplified propagation analysis.

Main Methods:

  • Decomposition of the field on a 2D curved surface into shifted and modulated Gaussian elementary signals.
  • Representation of the 3D diffraction field as a sum of Gaussian beams.
  • Propagation of Gaussian beams using an approximate expression derived from the Rayleigh-Sommerfeld diffraction model.
  • Treating Gaussian window functions on smooth curved surfaces as if on planar patches.

Main Results:

  • The proposed method decomposes the field into a sum of Gaussian beams.
  • Gaussian beams are propagated using an approximate Rayleigh-Sommerfeld model.
  • Simulation results demonstrate accurate 3D field solutions for surfaces meeting the smoothness assumption.

Conclusions:

  • The local signal decomposition method provides an accurate approach for analyzing 3D diffraction fields on curved surfaces.
  • The Gaussian beam representation simplifies the modeling of wave propagation in complex geometries.