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Related Concept Videos

Curvilinear Motion: Polar Coordinates01:27

Curvilinear Motion: Polar Coordinates

415
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...
415
Polar and Cylindrical Coordinates01:22

Polar and Cylindrical Coordinates

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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.
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Related Experiment Video

Updated: Aug 12, 2025

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

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Polar coordinate Fourier single-pixel imaging.

Guan Wang, Huaxia Deng, Mengchao Ma

    Optics Letters
    |February 1, 2023
    PubMed
    Summary

    This study introduces circular Fourier patterns for single-pixel imaging, improving efficiency in circular fields of view. This innovation enhances imaging performance for circular visual areas and foveated imaging applications.

    Area of Science:

    • Optics and Photonics
    • Computational Imaging

    Background:

    • Traditional single-pixel imaging relies on Cartesian Fourier patterns, which are ill-suited for circular display areas.
    • Circular fields of view are common in computed optical imaging systems.

    Purpose of the Study:

    • To adapt single-pixel imaging for circular fields of view using novel circular Fourier patterns.
    • To enhance imaging efficiency in circular visual areas.

    Main Methods:

    • Developed circular patterns based on two-dimensional Fourier transforms in polar coordinates.
    • Implemented polar coordinate Fourier single-pixel imaging.

    Main Results:

    • The proposed circular patterns significantly improved imaging efficiency from 63.66% to 100%.

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  • Demonstrated the effectiveness of polar coordinate Fourier transforms for circular imaging.

    • Conclusions:

    • Polar coordinate Fourier single-pixel imaging effectively addresses the limitations of Cartesian patterns in circular fields of view.
    • The method shows promise for applications in circular field-of-view imaging and foveated imaging.