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

Double Integrals in Polar Coordinates01:27

Double Integrals in Polar Coordinates

Double integrals provide an effective method for calculating areas and other physical quantities distributed across two-dimensional regions. In engineering and design applications, curved geometries often appear in structures such as ponds, reservoirs, and circular foundations. When these regions possess circular symmetry, polar coordinates offer a more natural and efficient description than Cartesian coordinates. This coordinate system simplifies the integration process by representing points...
Triple Integrals in Rectangular Coordinates01:23

Triple Integrals in Rectangular Coordinates

Triple integrals provide a method for calculating the accumulated value of a function over a three-dimensional region. Common applications include computing volume, mass, and other physical quantities that vary with position. The fundamental idea is to partition a solid region into small rectangular boxes, evaluate the function at sample points within each box, and sum the contributions. As the partitions become finer, this triple Riemann sum approaches the exact value of the triple integral.In...
Line Integrals in the Plane01:25

Line Integrals in the Plane

Line integrals in the plane provide a method for evaluating quantities distributed along a curve, such as mass, work, or surface area. A curve C in the plane is commonly represented parametrically by x = x(t) and y = y(t), where the parameter t varies over an interval [a, b]. This representation allows geometric and physical quantities to be expressed in terms of a single variable, facilitating both analysis and computation.A line integral of a scalar function f(x, y) along a curve C is defined...
Double Integrals Over General Regions01:18

Double Integrals Over General Regions

Double integrals are often used to measure quantities distributed across two-dimensional regions, such as rainfall over a lake, heat across a metal plate, or population density over land. In many practical situations, the region of interest does not have straight boundaries and cannot be described conveniently as a rectangle. Instead, the region may have curved or irregular edges. To evaluate integrals over such domains, the region is embedded inside a larger rectangular region where...
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...
Substitutions in Multiple Integrals01:30

Substitutions in Multiple Integrals

Multiple integration is an important mathematical method used to calculate physical quantities distributed over a two-dimensional region, such as the total mass of an elliptical plate. In this process, the density function is evaluated throughout the entire region enclosed by the ellipse. The contributions from all points inside the boundary are then accumulated to determine the total mass.When integration is performed directly in rectangular coordinates, the elliptical boundary produces limits...

You might also read

Related Articles

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

Sort by
Same author

Meta-Entity Driven Triplet Mining for Aligning Medical Vision-Language Models.

IEEE journal of biomedical and health informatics·2026
Same author

scHyperLink: Revealing Cell-Type-Specific Gene Regulation with Hypergraph Neural Networks.

IEEE journal of biomedical and health informatics·2026
Same author

Light-orchestrated multi-step solid-phase picodroplet reactors.

bioRxiv : the preprint server for biology·2025
Same author

The impact of absorbable hemostatic agents on wound healing in an experimental penile fracture rat model.

BMC urology·2025
Same author

Corrigendum to "Natural language processing for defining linguistic features in schizophrenia: A sample from Turkish speakers" [Schizophr. Res. 266 (2024) 183-189].

Schizophrenia research·2024
Same author

Impedance matching in optically induced dielectrophoresis: Effect of medium conductivity on trapping force.

Applied physics letters·2024

Related Experiment Video

Updated: Jun 12, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Fast and accurate computation of two-dimensional non-separable quadratic-phase integrals.

Aykut Koç1, Haldun M Ozaktas, Lambertus Hesselink

  • 1Department of Electrical Engineering, Stanford University, Stanford, California 94305, USA. aykutkoc@stanford.edu

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|May 29, 2010
PubMed
Summary

We developed a fast algorithm for 2D non-separable linear canonical transforms (2D-NS-LCTs), crucial for modeling optical systems. This method ensures accurate computation with optimal sampling, improving efficiency for complex optical designs.

More Related Videos

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture
09:04

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture

Published on: February 23, 2018

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

Related Experiment Videos

Last Updated: Jun 12, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture
09:04

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture

Published on: February 23, 2018

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

Area of Science:

  • Optics and Photonics
  • Computational Mathematics
  • Signal Processing

Background:

  • Two-dimensional non-separable linear canonical transforms (2D-NS-LCTs), also known as quadratic-phase integrals, are fundamental for modeling diverse optical systems.
  • These systems include free-space propagation, graded-index media, thin lenses, and complex concatenations, presenting unique computational challenges compared to 1D or separable 2D cases.

Purpose of the Study:

  • To introduce a novel, fast, and accurate algorithm for the numerical computation of 2D-NS-LCTs.
  • To address the computational challenges posed by the non-separable nature of these transforms in two dimensions.
  • To provide a robust method for handling optical system modeling with improved efficiency and precision.

Main Methods:

  • Developed an algorithm with a computational complexity of approximately N log N, where N is the 2D space-bandwidth product.
  • Implemented precise tracking and control of space-bandwidth products throughout the computation.
  • Introduced an alternative definition of 2D-NS-LCTs, explicitly defining the kernel via ten parameters and linking them to ABCD matrix parameters.

Main Results:

  • Achieved a computational speed of N log N for 2D-NS-LCTs.
  • Ensured information-theoretically sufficient sampling for accurate reconstruction of continuous functions.
  • Provided a clear, parameter-based definition of the transform kernel and its relation to conventional optical system parameters.

Conclusions:

  • The presented algorithm offers a significant advancement in the efficient and accurate numerical computation of 2D-NS-LCTs.
  • This method enhances the modeling capabilities for a wide range of complex optical systems.
  • The explicit parameterization facilitates a deeper understanding and easier application of 2D-NS-LCTs in optical design and analysis.