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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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Linear Approximation in Frequency Domain01:26

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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
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Gauss's Law01:07

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If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.
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A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the instrument response levels, using the substance and its concentrations as standards. Alternatively, or additionally, an equation is fitted to the calibration curve plot and subsequently used to calculate the unknown concentrations of other samples reliably.
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Gauss's Law: Spherical Symmetry01:26

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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...
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The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
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Gaussian profile estimation in one dimension: erratum.

Nathan Hagen, Matthew Kupinski, Eustace L Dereniak

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    Summary
    This summary is machine-generated.

    This erratum addresses and corrects inaccuracies previously published in Applied Optics. The corrections ensure the scientific record is accurate for future research and reference.

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    Area of Science:

    • Optics
    • Photonics

    Background:

    • Published research requires rigorous accuracy.
    • Ensuring the integrity of scientific literature is paramount.

    Purpose of the Study:

    • To formally correct errors in a previously published article.
    • To provide an accurate reference for the scientific community.

    Main Methods:

    • Identification of specific errors in the original publication.
    • Detailed description of the corrections to be made.

    Main Results:

    • The erratum provides a clear and concise list of all identified errors.
    • Corrected values and statements are presented to replace the erroneous information.

    Conclusions:

    • The erratum rectifies the inaccuracies, ensuring the reliability of the scientific record.
    • This ensures the continued utility of the research for the optics and photonics fields.