Related Experiment Video

Updated: May 7, 2026

Four-Dimensional CT Analysis Using Sequential 3D-3D Registration
05:05

Four-Dimensional CT Analysis Using Sequential 3D-3D Registration

Published on: November 23, 2019

Three-dimensional nonparaxial beams in parabolic rotational coordinates

Dongmei Deng, Yuanmei Gao, Juanying Zhao

    Optics Letters
    |October 2, 2013
    PubMed
    Summary

    We present novel three-dimensional nonparaxial optical beams with parabolic symmetries, derived from the nonparaxial Helmholtz equation. Experimental generation using computer-generated holography confirms theoretical predictions of beam patterns.

    More Related Videos

    Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence12:34

    Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence

    Published on: June 24, 2016

    Measuring 3D In-vivo Shoulder Kinematics using Biplanar Videoradiography06:09

    Measuring 3D In-vivo Shoulder Kinematics using Biplanar Videoradiography

    Published on: March 12, 2021

    Related Concept Videos

    Centroid for the Paraboloid of Revolution01:16

    Centroid for the Paraboloid of Revolution

    The paraboloid of revolution is an axially symmetric surface generated by rotating a parabola around its axis. This shape has several applications in mechanical engineering due to its advantageous structural properties, such as strength against stress concentration points and rotational symmetry.
    The centroid for the paraboloid of revolution is the point where all the mass of the paraboloid is concentrated. This centroid is important for engineering applications, as it determines how forces are...
    Design of Prismatic Beams for Bending01:23

    Design of Prismatic Beams for Bending

    The design of prismatic beams, structural elements with a uniform cross-section, focuses on ensuring safety and structural integrity under load. The design process begins by determining the allowable stress, either from material properties tables, or by dividing the material's ultimate strength by a safety factor. This safety factor is essential for accommodating uncertainties, and varies depending on the material—timber, steel, or concrete—with each having unique strength and stress...
    Perpendicular-Axis Theorem01:16

    Perpendicular-Axis Theorem

    The perpendicular-axis theorem states that the moment of inertia of a planar object about an axis perpendicular to its plane is equal to the sum of the moments of inertia about two mutually perpendicular concurrent axes lying in the plane of the body.
    Consider a circular disc of mass M and radius R lying along an x-y plane. The origin lies at the center of the disc, and the z-axis is perpendicular to the disc's plane. All three axes coincide at the disc's center. The moment of inertia of this...
    Polar and Cylindrical Coordinates01:22

    Polar and Cylindrical Coordinates

    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.
    Load along a Single Axis01:29

    Load along a Single Axis

    In structural engineering, the analysis of beams subjected to varying loads is a critical aspect of understanding the behavior and performance of these structural elements. A common scenario involves a beam subjected to a combination of different load distributions.
    Consider a beam of length L subjected to a varying load, which is a combination of parabolic and trapezoidal load distribution along the x-axis. In this case, it is essential to determine the resultant loads, their locations, and...
    Beams with Symmetric Loadings01:15

    Beams with Symmetric Loadings

    The moment-area method is an analytical tool used in structural engineering to determine the slope and deflection of beams under various loads. Consider a cantilever with a concentrated load and moment at the free end. The first step is constructing a free-body diagram to calculate the reactions at the fixed end. Next, the bending moment diagram is plotted to visualize how the bending moment varies along the beam's length, focusing on points where the bending moment equals zero.
    The M/EI...