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

Vector Algebra: Method of Components01:08

Vector Algebra: Method of Components

18.5K
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...
18.5K
Group Polarization01:01

Group Polarization

38.3K
Group polarization is the strengthening of an original group attitude following the discussion of views within a group (Teger & Pruitt, 1967). That is, if a group initially favors a viewpoint, after discussion the group consensus is likely a stronger endorsement of the viewpoint. Conversely, if the group was initially opposed to a viewpoint, group discussion would likely lead to stronger opposition.
38.3K
Vector Components in the Cartesian Coordinate System01:29

Vector Components in the Cartesian Coordinate System

26.3K
Vectors are usually described in terms of their components in a coordinate system. Even in everyday life, we naturally invoke the concept of orthogonal projections in a rectangular coordinate system. For example, if someone gives you directions for a particular location, you will be told to go a few km in a direction like east, west, north, or south, along with the angle in which you are supposed to move. In a rectangular (Cartesian) xy-coordinate system in a plane, a point in a plane is...
26.3K
Polar Equations of Conics01:29

Polar Equations of Conics

123
A conic section can be defined in polar coordinates as the set of all points whose distance from a fixed point, known as the focus, bears a constant ratio to their distance from a fixed line, known as the directrix. This constant ratio is called the eccentricity. This definition unifies all types of conic sections—ellipses, parabolas, and hyperbolas—under a single framework. When the focus is positioned at the origin of the polar coordinate system, a single polar equation can...
123
Curvilinear Motion: Polar Coordinates01:27

Curvilinear Motion: Polar Coordinates

731
In polar coordinates, the motion of a particle follows a curvilinear path. The radial coordinate symbolized as 'r,' extends outward from a fixed origin to the particle, while the angular coordinate, 'θ,' measured in radians, represents the counterclockwise angle between a fixed reference line and the radial line connecting the origin to the particle.
The particle's location is described using a unit vector along the radial direction. Deriving the particle's position...
731
Potential Due to a Polarized Object01:29

Potential Due to a Polarized Object

655
A neutral atom consists of a positively charged nucleus surrounded by a negatively charged electron cloud. When placed in an external electric field, the external electric force pulls the electrons and nucleus apart, opposite to the intrinsic attraction between the nucleus and the electrons. The opposing forces balance each other with a slight shift between the center of masses of the nucleus and the electron cloud, resulting in a polarized atom. On the other hand, a few molecules, like water,...
655

You might also read

Related Articles

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

Sort by
Same author

Quantitative single-cell analysis of PML-RARα oncogene-induced DNA damage along cell cycle progression.

Methods (San Diego, Calif.)·2026
Same author

Advancing Italian biophysics: insights from the 27th SIBPA congress.

European biophysics journal : EBJ·2026
Same author

Confocal and multiphoton microscopy: A selective review.

Journal of microscopy·2026
Same author

Antisecretory Factor in rat cerebellar granule cells augments inhibitory current via GABA<sub>A</sub> receptors: a mechanism for vertigo reduction in Menière's disease?

European biophysics journal : EBJ·2026
Same author

Wavefront estimation through structured detection in laser scanning microscopy.

Biomedical optics express·2026
Same author

Cancer cell identification in tissue imaging via phasor map analysis in polarization-resolved two-photon excitation fluorescence microscopy.

Biomedical optics express·2026
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: Dec 16, 2025

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
07:56

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

8.8K

Eigenvectors of polarization coherency matrices.

Colin J R Sheppard, Artemi Bendandi, Aymeric Le Gratiet

    Journal of the Optical Society of America. A, Optics, Image Science, and Vision
    |July 2, 2020
    PubMed
    Summary
    This summary is machine-generated.

    This study presents an algebraic method for calculating eigenvectors of coherency matrices. The approach combines characteristic polynomials and adjugate matrices for efficient analysis of polarization properties.

    More Related Videos

    Author Spotlight: Non-Invasive Imaging of Complex Bio-Structures Using Polarization-Sensitive Two-Photon Microscopy
    05:54

    Author Spotlight: Non-Invasive Imaging of Complex Bio-Structures Using Polarization-Sensitive Two-Photon Microscopy

    Published on: September 8, 2023

    1.6K
    Generation and Coherent Control of Pulsed Quantum Frequency Combs
    06:42

    Generation and Coherent Control of Pulsed Quantum Frequency Combs

    Published on: June 8, 2018

    9.5K

    Related Experiment Videos

    Last Updated: Dec 16, 2025

    A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
    07:56

    A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

    Published on: September 5, 2019

    8.8K
    Author Spotlight: Non-Invasive Imaging of Complex Bio-Structures Using Polarization-Sensitive Two-Photon Microscopy
    05:54

    Author Spotlight: Non-Invasive Imaging of Complex Bio-Structures Using Polarization-Sensitive Two-Photon Microscopy

    Published on: September 8, 2023

    1.6K
    Generation and Coherent Control of Pulsed Quantum Frequency Combs
    06:42

    Generation and Coherent Control of Pulsed Quantum Frequency Combs

    Published on: June 8, 2018

    9.5K

    Area of Science:

    • Optics and Photonics
    • Mathematical Physics

    Background:

    • Coherency matrices are fundamental in polarization optics for describing light.
    • Calculating eigenvectors of these matrices is crucial for characterizing polarization states.
    • Recent algorithmic advancements motivate re-evaluation of existing methods.

    Purpose of the Study:

    • To develop an efficient algebraic method for computing eigenvectors of 2D, 3D, and 4D coherency matrices.
    • To provide simplified expressions for the characteristic decomposition of coherency matrices.
    • To leverage recent algorithms for improved computational efficiency.

    Main Methods:

    • The study employs a combination of characteristic polynomial evaluation and adjugate matrix computation.
    • Diagonal terms of the coherency matrix are expressed using the characteristic polynomial of reduced matrices.
    • Off-diagonal elements are also analyzed using analogous polynomial forms.

    Main Results:

    • A novel algebraic approach for eigenvector calculation is presented.
    • Diagonal coherency matrix terms are derived as functions of eigenvalues via characteristic polynomials.
    • Simple expressions for pure components in characteristic decomposition are obtained.

    Conclusions:

    • The proposed method offers an efficient algebraic pathway for coherency matrix eigenvector analysis.
    • This work contributes to a deeper understanding of light polarization characterization.
    • The findings are applicable to various optical systems and measurements involving polarized light.