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Related Concept Videos

Gauss's Law: Cylindrical Symmetry01:20

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A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
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Understanding the motion of particles is a fundamental aspect of classical mechanics, and the choice of the coordinate system plays a pivotal role in unraveling the complexities of their dynamics.
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One of the distinctive characteristics of circular shafts is their ability to maintain their cross-sectional integrity under torsion. In other words, each cross-section continues to exist as a flat, unaltered entity, simply rotating like a solid, rigid slab. To understand the distribution of shearing stress within such a shaft, consider a cylindrical section inside this circular shaft. This section has a length of L and a radius of R, with one end fixed. The radius of the cylindrical section is...
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A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a...
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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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Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
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Implementation of a Reference Interferometer for Nanodetection
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Self-referenced interferometer for cylindrical surfaces.

Martin Šarbort, Šimon Řeřucha, Miroslava Holá

    Applied Optics
    |February 3, 2016
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    Summary
    This summary is machine-generated.

    A novel self-referenced interferometric method accurately measures the shape of hollow cylindrical tubes using an axicon lens. This technique offers a simple, robust approach for precise dimensional analysis of tubular components.

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    Area of Science:

    • Optical Metrology
    • Precision Engineering
    • Wavefront Sensing

    Background:

    • Accurate shape measurement of hollow cylindrical components is crucial in various engineering fields.
    • Traditional interferometric methods can be complex and sensitive to environmental disturbances.
    • Existing techniques may face challenges in measuring long or delicate tubes.

    Purpose of the Study:

    • To introduce a new, simple, and robust self-referenced interferometric method for shape measurement of hollow cylindrical tubes.
    • To demonstrate the effectiveness of using a single axicon lens to generate reference and object waves.
    • To validate the method's capability for measuring tubes of varying dimensions.

    Main Methods:

    • A self-referenced interferometer utilizing a single axicon lens to generate conical waves.
    • The central part of the conical wave serves as the reference, and the peripheral part as the object wave.
    • Digital camera acquisition of interferograms with a circular carrier fringe pattern.
    • Spatial synchronous detection for interference phase demodulation.

    Main Results:

    • Successful implementation of a self-referenced interferometer for hollow cylinder shape measurement.
    • Demonstration of a closed-fringe pattern with a circular carrier in the interferogram.
    • Experimental validation of the method on hollow cylindrical tubes up to 600 mm in length.

    Conclusions:

    • The proposed interferometric method is simple, robust, and effective for shape measurement of hollow cylindrical tubes.
    • The use of an axicon lens provides a straightforward way to generate the necessary wave components.
    • This technique shows promise for non-contact, high-precision dimensional analysis in industrial applications.