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

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...
Deflection of a Beam01:19

Deflection of a Beam

Accurately determining beam deflection and slope under various loading conditions in structural engineering is crucial for ensuring safety and structural integrity. Singularity functions offer a streamlined approach to analyzing beams, especially when multiple loading functions complicate the bending moment equation.
Singularity functions, described in an earlier lesson, are powerful mathematical tools that represent discontinuities within a function commonly encountered in structural loading...
Integration by Parts: Problem Solving01:29

Integration by Parts: Problem Solving

Smart speakers process voice commands by modeling audio inputs as piecewise functions and analyzing them through integration against trigonometric functions, such as cosine. This mathematical approach is fundamental in signal processing, where complex sound waves are decomposed into simpler frequency components.Consider a definite integral involving a piecewise function multiplied by a cosine function. Because the function is defined differently over separate intervals, the integral is split...
Linear Differential Equations01:27

Linear Differential Equations

The integrating factor method provides a systematic way to solve first-order linear differential equations, especially those that cannot be handled by separation of variables. This method is particularly useful in modeling time-dependent physical systems influenced by both constant inputs and resistive forces. A common example is the motion of a car subjected to a constant engine force while experiencing air resistance proportional to its velocity.In such scenarios, Newton’s second law yields a...
Approximate Integration01:24

Approximate Integration

In many practical and theoretical contexts, the exact value of a definite integral may be inaccessible. This limitation typically arises when the antiderivative of a function is either unknown or cannot be expressed in a closed mathematical form. Alternatively, it can occur when a function is defined not by a formula but by a finite set of empirical data points, such as those collected during experiments. In these cases, approximate integration techniques provide a valuable solution.One of the...

You might also read

Related Articles

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

Sort by
Same author

Automated Segmentation of Augmented Bone After Transalveolar Sinus Floor Elevation Using Deep Learning.

International dental journal·2026
Same author

Parallel overlapping-domain decomposition FDFD for modeling of large-scale complex nanostructures.

Optics express·2025
Same author

A perfectly matched layer-boundary integral equation method for wave scattering in a two-layer medium of a step-like interface.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2025
Same author

Perturbation Theory for Resonant States near a Bound State in the Continuum.

Physical review letters·2025
Same author

Spectral Galerkin mode-matching method for applications in photonics.

Physical review. E·2024
Same author

Bifurcation of bound states in the continuum in periodic structures.

Optics letters·2024
Same journal

Multi-module collaborative optimization-driven fast speckle correlation imaging in variable environments.

Journal of the Optical Society of America. A, Optics, image science, and vision·2026
Same journal

Secrecy performance analysis of NOMA-UWOC systems over a vertically stratified WGG oceanic turbulence channel.

Journal of the Optical Society of America. A, Optics, image science, and vision·2026
Same journal

Backscattering of plane waves in a composite system containing a rough surface and anisotropic scatterers.

Journal of the Optical Society of America. A, Optics, image science, and vision·2026
Same journal

Aspherical surface construction methods based on extended Jacobi polynomials.

Journal of the Optical Society of America. A, Optics, image science, and vision·2026
Same journal

OCT sidelobe suppression method based on dual-path phase sinusoidal modulation and minimum value fusion.

Journal of the Optical Society of America. A, Optics, image science, and vision·2026
Same journal

Optical design concepts using wavelength-selective diffractive optics to enable miniaturized multimodal endoscopic imaging across separated spectral ranges.

Journal of the Optical Society of America. A, Optics, image science, and vision·2026
See all related articles

Related Experiment Video

Updated: May 22, 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

High order integral equation method for diffraction gratings.

Wangtao Lu1, Ya Yan Lu

  • 1Joint Advanced Research Center of University of Science and Technology of China and City University of Hong Kong, Suzhou, Jiangsu, China.

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|May 8, 2012
PubMed
Summary
This summary is machine-generated.

This study enhances the boundary integral equation Neumann-to-Dirichlet map (BIE-NtD) method for diffraction gratings. The improved BIE-NtD method offers higher accuracy and numerical stability for analyzing dielectric gratings.

More Related Videos

In situ Grazing Incidence Small Angle X-ray Scattering on Roll-To-Roll Coating of Organic Solar Cells with Laboratory X-ray Instrumentation
06:49

In situ Grazing Incidence Small Angle X-ray Scattering on Roll-To-Roll Coating of Organic Solar Cells with Laboratory X-ray Instrumentation

Published on: March 2, 2021

Fabrication of High Contrast Gratings for the Spectrum Splitting Dispersive Element in a Concentrated Photovoltaic System
12:08

Fabrication of High Contrast Gratings for the Spectrum Splitting Dispersive Element in a Concentrated Photovoltaic System

Published on: July 18, 2015

Related Experiment Videos

Last Updated: May 22, 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

In situ Grazing Incidence Small Angle X-ray Scattering on Roll-To-Roll Coating of Organic Solar Cells with Laboratory X-ray Instrumentation
06:49

In situ Grazing Incidence Small Angle X-ray Scattering on Roll-To-Roll Coating of Organic Solar Cells with Laboratory X-ray Instrumentation

Published on: March 2, 2021

Fabrication of High Contrast Gratings for the Spectrum Splitting Dispersive Element in a Concentrated Photovoltaic System
12:08

Fabrication of High Contrast Gratings for the Spectrum Splitting Dispersive Element in a Concentrated Photovoltaic System

Published on: July 18, 2015

Area of Science:

  • Optics and Photonics
  • Computational Electromagnetics

Background:

  • Conventional integral equation methods for diffraction gratings rely on lattice sums for quasi-periodic Green's functions.
  • The boundary integral equation Neumann-to-Dirichlet map (BIE-NtD) method offers an alternative by avoiding these complex functions.

Purpose of the Study:

  • To present numerical improvements to the BIE-NtD method for enhanced accuracy and stability.
  • To refine the computation of tangential derivatives and boundary condition matching in diffraction grating analysis.

Main Methods:

  • Implementation of a revised numerical formulation for the BIE-NtD method.
  • Development of advanced techniques for computing tangential derivatives at material interfaces.
  • Improved methods for matching boundary conditions with surrounding homogeneous regions.

Main Results:

  • The improved BIE-NtD method demonstrates high-order accuracy for dielectric gratings.
  • Numerical examples confirm the enhanced stability and precision of the revised formulation.
  • The method effectively handles both in-plane and conical diffraction scenarios.

Conclusions:

  • The enhanced BIE-NtD method provides a more accurate and stable approach for diffraction grating analysis.
  • This improved technique simplifies the evaluation of quasi-periodic Green's functions, facilitating easier implementation.