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Related Concept Videos

Spherical Coordinates01:23

Spherical Coordinates

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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Triple Integrals in Spherical Coordinates

Triple integrals in spherical coordinates provide an efficient method for evaluating volumes over regions with central symmetry, such as spheres. Instead of describing points by rectangular coordinates, spherical coordinates use three variables: 𝜌, 𝜃, and 𝜑. Here, 𝜌 is the distance from the origin, 𝜃 is the angle in the xy-plane measured from the positive x-axis, and 𝜑 is the angle measured downward from the positive z-axis.To derive the volume of a sphere, the solid region can be divided...
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In-phase-contrast microscopes, interference between light directly passing through a cell and light refracted by cellular components is used to create high-contrast, high-resolution images without staining. It is the oldest and simplest type of microscope that creates an image by altering the wavelengths of light rays passing through the specimen. Altered wavelength paths are created using an annular stop in the condenser. The annular stop produces a hollow cone of...
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Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
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Spherical particle sizing by optical correlation using ternary phase-amplitude filters.

M S Marshall, R E Benner

    Applied Optics
    |August 20, 2010
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces novel ternary phase-amplitude filters for accurately sizing opaque spherical particles across various size ranges. These filters, derived from classical matched filters, enhance particle sizing in optical correlators.

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    Area of Science:

    • Optics
    • Particle characterization
    • Digital image processing

    Background:

    • Accurate particle sizing is crucial in various scientific and industrial applications.
    • Classical matched filters have limitations in handling complex particle characteristics.
    • Ternary phase-amplitude filters offer potential for improved optical correlation performance.

    Purpose of the Study:

    • To develop and evaluate advanced ternary phase-amplitude filters for sizing opaque spherical particles.
    • To investigate the impact of spatial frequency and cutoff frequency on particle sizing accuracy.
    • To demonstrate the effectiveness of these filters across a wide range of particle sizes.

    Main Methods:

    • Utilizing computer simulations and experimental data to validate filter performance.
    • Deriving nearly unlimited spatial frequency ternary phase-amplitude filters from classical matched filters.
    • Employing limited-order ternary phase-amplitude filters for smaller particle size ranges.
    • Testing filters on opaque spherical particles in size ranges from 5 to 400 microm.

    Main Results:

    • Demonstrated successful sizing of opaque spherical particles using ternary phase-amplitude filters.
    • Showcased the effectiveness of unlimited spatial frequency filters for particles 100-400 microm.
    • Highlighted the critical influence of cutoff frequency on optical correlator performance for smaller particles.
    • Achieved accurate sizing for particles in the 100-400, 15-100, and 5-25 microm ranges using limited-order filters.

    Conclusions:

    • Ternary phase-amplitude filters are effective tools for sizing opaque spherical particles.
    • The choice of filter order and cutoff frequency is critical for accurate sizing, especially for smaller particles.
    • This work advances optical particle sizing techniques with practical implications for various fields.