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

Interference and Diffraction02:18

Interference and Diffraction

53.2K
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.
53.2K
Improper Integrals: Discontinuous Integrands01:28

Improper Integrals: Discontinuous Integrands

88
Evaluating Areas Under Curves with DiscontinuitiesA definite integral is considered improper when the integrand is discontinuous at one of the limits of integration. This occurs when the function is undefined or becomes infinite at an endpoint, making the corresponding region under the curve unbounded. Such behavior is commonly associated with vertical asymptotes at the boundary of the interval. To properly define and evaluate these integrals, a limiting process is used to determine whether a...
88
Determination of Crystal Structures01:29

Determination of Crystal Structures

39
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...
39
Substitution Rule Applied to Definite Integrals01:24

Substitution Rule Applied to Definite Integrals

129
When evaluating a definite integral whose integrand matches the structure of a composite function, the substitution method provides an efficient way to simplify the calculation. This method is based on reversing the chain rule from differentiation, allowing a complicated expression to be rewritten in a simpler form. When the integrand contains an inner function and its derivative, substitution naturally reduces the complexity of the problem.The core idea of substitution for definite integrals...
129
Approximate Integration01:24

Approximate Integration

92
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...
92
Improper Integrals: Infinite Intervals01:29

Improper Integrals: Infinite Intervals

185
An integral is classified as improper due to an infinite interval when at least one of its limits of integration extends to positive or negative infinity. In such cases, the region under the curve is unbounded, and standard techniques for evaluating definite integrals are not directly applicable. Instead, the improper integral is defined through a limiting process that allows one to determine whether the accumulated area remains finite despite the infinite domain.Application to Exponential...
185

You might also read

Related Articles

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

Sort by
Same author

Physical Parameters in High-Accuracy Spectrophotometry.

Journal of research of the National Bureau of Standards. Section A, Physics and chemistry·2021
Same author

A Study of the Polarization of Fluorescence of Ordered Systems With Application to Ordered Liquid Crystals.

Journal of research of the National Bureau of Standards. Section A, Physics and chemistry·2020
Same author

Reflection Correction for High-Accuracy Transmittance Measurements on Filter Glasses.

Journal of research of the National Bureau of Standards. Section A, Physics and chemistry·2020
Same author

Adaptation of a High-Accuracy Spectrophotometer for Ultraviolet Work.

Journal of research of the National Bureau of Standards. Section A, Physics and chemistry·2020
Same author

Polarization Effects on Fluorescence Measurements.

Journal of research of the National Bureau of Standards. Section A, Physics and chemistry·2020
Same author

Computation of Fresnel Integrals. II.

Journal of research of the National Institute of Standards and Technology·2016
Same journal

Precise Numerical Differentiation of Thermodynamic Functions with Multicomplex Variables.

Journal of research of the National Institute of Standards and Technology·2024
Same journal

Characterization of 3-Dimensional Printing and Casting Materials for use in Computed Tomography and X-ray Imaging Phantoms.

Journal of research of the National Institute of Standards and Technology·2024
Same journal

On The Quotient of a Centralized and a Non-centralized Complex Gaussian Random Variable.

Journal of research of the National Institute of Standards and Technology·2024
Same journal

Fast Methods for Finding Multiple Effective Influencers in Real Networks.

Journal of research of the National Institute of Standards and Technology·2024
Same journal

Disinfection of Respirators with Ultraviolet Radiation.

Journal of research of the National Institute of Standards and Technology·2024
Same journal

DNA Origami Design: A How-To Tutorial.

Journal of research of the National Institute of Standards and Technology·2024
See all related articles

Related Experiment Video

Updated: Mar 16, 2026

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

8.2K

Numerical Evaluation of Diffraction Integrals.

K D Mielenz1

  • 1Oakland, MD 21550.

Journal of Research of the National Institute of Standards and Technology
|August 24, 2016
PubMed
Summary
This summary is machine-generated.

This study presents a straightforward numerical integration method for diffraction integrals, offering accurate results with minimal assumptions. The technique simplifies calculations for various aperture types, enhancing computational efficiency in optics.

Keywords:
circular aperturediffractionhalf planenumerical integrationrecursion formulaslit

More Related Videos

Microfluidic Chips for In Situ Crystal X-ray Diffraction and In Situ Dynamic Light Scattering for Serial Crystallography
11:48

Microfluidic Chips for In Situ Crystal X-ray Diffraction and In Situ Dynamic Light Scattering for Serial Crystallography

Published on: April 24, 2018

15.3K
Author Spotlight: Advancing Protein Structure Analysis for Drug Development
07:08

Author Spotlight: Advancing Protein Structure Analysis for Drug Development

Published on: March 8, 2024

4.5K

Related Experiment Videos

Last Updated: Mar 16, 2026

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

8.2K
Microfluidic Chips for In Situ Crystal X-ray Diffraction and In Situ Dynamic Light Scattering for Serial Crystallography
11:48

Microfluidic Chips for In Situ Crystal X-ray Diffraction and In Situ Dynamic Light Scattering for Serial Crystallography

Published on: April 24, 2018

15.3K
Author Spotlight: Advancing Protein Structure Analysis for Drug Development
07:08

Author Spotlight: Advancing Protein Structure Analysis for Drug Development

Published on: March 8, 2024

4.5K

Area of Science:

  • Physics
  • Optics
  • Computational Physics

Background:

  • Diffraction integrals are fundamental in optics for understanding wave propagation.
  • Existing numerical methods can be computationally intensive or require specific assumptions.
  • Accurate calculation of diffracted fields is crucial for optical system design and analysis.

Purpose of the Study:

  • To introduce a simple, geometrically-based numerical integration method for diffraction integrals.
  • To demonstrate the method's applicability and accuracy across various diffraction scenarios.
  • To provide a computationally efficient alternative for calculating diffracted fields.

Main Methods:

  • A novel numerical integration approach based on geometrical considerations of wavefront contributions.
  • Application to Fresnel's diffraction integrals for circular apertures and apertures bounded by straight lines.
  • Development of a simple recursion formula for specific aperture geometries.

Main Results:

  • The method yields accurate results even with a small number of summation elements.
  • Accuracy can be improved by increasing summation elements or using Simpson's rule.
  • A simplified recursion formula eliminates repetitive summations for slit and half-plane apertures.

Conclusions:

  • The proposed numerical integration method is versatile, accurate, and computationally efficient for diffraction problems.
  • It offers a practical approach for analyzing diffraction patterns from various apertures.
  • The recursion formula significantly streamlines calculations for linear apertures.