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

Curvilinear Motion: Polar Coordinates01:27

Curvilinear Motion: Polar Coordinates

1.1K
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...
1.1K
Polar Coordinates01:24

Polar Coordinates

516
The polar coordinate system offers an alternative to the Cartesian coordinate system for specifying points in a plane, using a distance and an angle instead of x and y coordinates. This system is particularly advantageous in situations involving circular or rotational symmetry, such as in physics or engineering problems involving waves, oscillations, or orbital paths.Defining Polar CoordinatesIn polar coordinates, a point is represented as P(r, ��), where r is the radial distance...
516
Polar and Cylindrical Coordinates01:22

Polar and Cylindrical Coordinates

22.3K
The Cartesian coordinate system is a very convenient tool to use when describing the displacements and velocities of objects and the forces acting on them. However, it becomes cumbersome when we need to describe the rotation of objects. So, when describing rotation, the polar coordinate system is generally used.
22.3K
Graphs of Polar Equations01:17

Graphs of Polar Equations

398
The polar coordinate system represents points using a distance from a central point (the pole) and an angle from a reference direction (the polar axis). Unlike rectangular coordinates, polar coordinates are ideal for graphing curves with radial symmetry or periodic behavior.Some general forms of graphs in polar coordinates include the following:Equation of a Circle (Centered at the Pole):A graph where the radius remains constant for all angles traces a circle centered at the pole:Equation of a...
398
Polar Equations of Conics01:29

Polar Equations of Conics

307
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...
307
Geometry of Hyperbolas01:30

Geometry of Hyperbolas

602
A hyperbola consists of all points where the absolute difference of distances to two fixed points, called foci, remains constant. The standard equation isEach branch extends infinitely and approaches two asymptotes, which guide the curve’s behavior. The parameters a and b define key features: a measures the distance from the center to each vertex along the transverse axis, while b influences the slopes of the asymptotes. The asymptotes have equationsA rectangle centered at the origin with...
602

You might also read

Related Articles

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

Sort by
Same author

[Effect of fluoride ion on corrosion of two dental titanium alloys].

Hua xi kou qiang yi xue za zhi = Huaxi kouqiang yixue zazhi = West China journal of stomatology·2010
Same author

The phylogeny analysis of MyoG gene in different pig breeds.

Interdisciplinary sciences, computational life sciences·2010
Same author

[Treatment of early avascular necrosis of femoral head by core decompression combined with autologous bone marrow mesenchymal stem cells transplantation].

Zhongguo xiu fu chong jian wai ke za zhi = Zhongguo xiufu chongjian waike zazhi = Chinese journal of reparative and reconstructive surgery·2010
Same author

MicroRNAome of porcine pre- and postnatal development.

PloS one·2010
Same author

Hyperactive putamen in patients with paroxysmal kinesigenic choreoathetosis: a resting-state functional magnetic resonance imaging study.

Movement disorders : official journal of the Movement Disorder Society·2010
Same author

Danshensu has anti-tumor activity in B16F10 melanoma by inhibiting angiogenesis and tumor cell invasion.

European journal of pharmacology·2010

Related Experiment Video

Updated: Mar 21, 2026

Three-dimensional Super Resolution Microscopy of F-actin Filaments by Interferometric PhotoActivated Localization Microscopy iPALM
11:57

Three-dimensional Super Resolution Microscopy of F-actin Filaments by Interferometric PhotoActivated Localization Microscopy iPALM

Published on: December 1, 2016

11.3K

Absolute flatness testing of skip-flat interferometry by matrix analysis in polar coordinates.

Zhi-Gang Han, Lu Yin, Lei Chen

    Applied Optics
    |May 4, 2016
    PubMed
    Summary

    A novel matrix analysis method in polar coordinates enables accurate absolute testing of skip-flat interferometry. This efficient approach achieves 0.01 nm RMS accuracy for surface profile retrieval without iterative calculations.

    More Related Videos

    A Protocol for Real-time 3D Single Particle Tracking
    10:16

    A Protocol for Real-time 3D Single Particle Tracking

    Published on: January 3, 2018

    15.4K
    Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform
    06:25

    Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform

    Published on: February 12, 2014

    8.9K

    Related Experiment Videos

    Last Updated: Mar 21, 2026

    Three-dimensional Super Resolution Microscopy of F-actin Filaments by Interferometric PhotoActivated Localization Microscopy iPALM
    11:57

    Three-dimensional Super Resolution Microscopy of F-actin Filaments by Interferometric PhotoActivated Localization Microscopy iPALM

    Published on: December 1, 2016

    11.3K
    A Protocol for Real-time 3D Single Particle Tracking
    10:16

    A Protocol for Real-time 3D Single Particle Tracking

    Published on: January 3, 2018

    15.4K
    Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform
    06:25

    Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform

    Published on: February 12, 2014

    8.9K

    Area of Science:

    • Optics and Metrology
    • Surface Metrology
    • Interferometry

    Background:

    • Absolute testing of optical surfaces is crucial for high-precision metrology.
    • Skip-flat interferometry presents challenges in accurate surface profile retrieval.

    Purpose of the Study:

    • To introduce a new matrix analysis method for absolute testing of skip-flat interferometry.
    • To develop an efficient and accurate technique for retrieving absolute surface profiles.

    Main Methods:

    • Transforming wavefront maps from two cavity measurements into polar coordinates.
    • Applying matrix analysis in polar coordinates to retrieve the reflective flat's profile.
    • Converting the retrieved profile back to Cartesian coordinates for sample profile determination.

    Main Results:

    • Simulations demonstrate the method's capability to achieve high accuracy (0.01 nm RMS).
    • The approach utilizes closed mathematical formulas, avoiding polynomial fitting and iterative error evaluation.
    • The method provides an efficient solution for absolute testing in interferometry.

    Conclusions:

    • The presented matrix analysis in polar coordinates offers an efficient and accurate method for absolute skip-flat interferometry.
    • This technique simplifies the absolute profile retrieval process, enhancing precision metrology applications.