Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

What is a Mode?

What is a Mode?

The mode is one of the commonly used measures of a central tendency. It is defined as the most frequent value in a data set.
There can be more than one mode in a data set if multiple values have the same highest frequency. For instance, suppose that the Statistics exam scores of 20 students are: 50; 53; 59; 59; 63; 63; 72; 72; 72; 72; 72; 76; 78; 81; 83; 84; 84; 84; 90; 93. Here, the mode is 72, as it occurs most frequently, five times.
A data set with two modes is called bimodal. For example,...

Vector Representation of Complex Numbers

Vector Representation of Complex Numbers

Complex numbers, represented in Cartesian coordinates, can also be visualized as vectors. These vectors can be expressed in polar form, emphasizing their magnitude and angle. When a complex number is input into a function, the output is another complex number, highlighting the function's zero point from which the vector representation can originate.
Consider a function defined as the product of the complex factors in the numerator divided by the product of the complex factors in the denominator.

State Space Representation

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...

Area Computation by the Alternative Coordinate Method

Area Computation by the Alternative Coordinate Method

The alternative coordinate method, also known as the Shoelace Formula, is a technique for determining the area of a traverse using Cartesian coordinates. This method relies on the sequential arrangement of x and y coordinates for each point of the shape, ensuring accuracy and ease of application.In this approach, each corner's x and y coordinates are listed as fractions, with the x-coordinate as the numerator and the y-coordinate as the denominator. These coordinates are arranged sequentially...

Linear Approximation in Frequency Domain

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.

Vector Algebra: Method of Components

Vector Algebra: Method of Components

It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
In many applications, the magnitudes and directions of...

You might also read

Related Articles

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

Sort by

Same author

Oblique line scan illumination enables expansive, accurate and sensitive single-protein measurements in solution and in living cells.

Nature methods·2025

Same author

Joint Reconstruction of Absorbed Optical Energy Density and Sound Speed Distributions in Photoacoustic Computed Tomography: A Numerical Investigation.

IEEE transactions on computational imaging·2017

Same author

Discrete imaging models for three-dimensional optoacoustic tomography using radially symmetric expansion functions.

IEEE transactions on medical imaging·2014

Same author

TRANSDUCER FIELD IMAGING USING ACOUSTOGRAPHY.

Advances in acoustics and vibration·2013

Same author

Photoacoustic computed tomography correcting for heterogeneity and attenuation.

Journal of biomedical optics·2012

Same author

Numerical investigation of the effects of shear waves in transcranial photoacoustic tomography with a planar geometry.

Journal of biomedical optics·2012

Same journal

Gaussian-modulated continuous-variable quantum key distribution over 60 km fiber using an integrated silicon photonic receiver.

Optics letters·2026

Same journal

E2E-OCT: end-to-end joint learning model using optical coherence tomography images for vocal cord leukoplakia diagnosis.

Optics letters·2026

Same journal

Holographic generation of panoramic 3D scenes by concave ellipsoidal mirror reflection.

Optics letters·2026

Same journal

Dual-pilot phase recovery with pair-wise maximum-ratio combining for coherent PONs.

Optics letters·2026

Same journal

Mapping the whispering gallery modes of a CaF<sub>2</sub> disk resonator with half-tapered fibers to estimate the fundamental mode volume.

Optics letters·2026

Same journal

Quantitative estimation of deep-subwavelength scale via dark-field scattering axial energy concentration decay profiles.

Optics letters·2026

See all related articles

Search research articles

Related Experiment Video

Updated: Jun 24, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Computationally efficient coherent-mode representations.

Brynmor J Davis¹, Robert W Schoonover

¹The Beckman Institute for Advanced Science and Technology, Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA. bryn@illinois.edu

|April 3, 2009

Summary

This summary is machine-generated.

A new LDL decomposition method offers an efficient alternative to traditional eigenvalue decomposition for calculating coherent-mode representations. This approach significantly improves computational efficiency for partially coherent fields, especially those with low coherence.

More Related Videos

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Related Experiment Videos

Last Updated: Jun 24, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Area of Science:

Optics and Photonics
Computational Physics

Background:

Traditional coherent-mode representations (CMRs) rely on eigenvalue decomposition of the cross-spectral density matrix.
Numerical calculations of CMRs can be computationally intensive, limiting efficiency for certain applications.

Purpose of the Study:

To introduce an efficient alternative modal representation for partially coherent fields.
To reduce storage requirements and improve the speed of calculations involving CMRs.

Main Methods:

Utilized LDL decomposition as an alternative to eigenvalue decomposition for modal representation.
Analyzed the impact of LDL decomposition on storage requirements and computational efficiency.

Main Results:

Achieved significant reduction in storage requirements, proportional to the ratio of coherence length to source width.
Demonstrated substantial improvements in the efficiency of numerical calculations for partially coherent propagation effects.

Conclusions:

LDL decomposition provides a computationally efficient method for representing partially coherent fields.
This method is particularly advantageous for analyzing low-coherence fields and reduces computational burden.