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Related Concept Videos

Polar Coordinates01:24

Polar Coordinates

189
The polar coordinate system offers an alternative to the Cartesian coordinate system for specifying points in a plane, using a distance and an angle instead of x and y coordinates. This system is particularly advantageous in situations involving circular or rotational symmetry, such as in physics or engineering problems involving waves, oscillations, or orbital paths.Defining Polar CoordinatesIn polar coordinates, a point is represented as P(r, ��), where r is the radial distance...
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Group Polarization01:01

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Group polarization is the strengthening of an original group attitude following the discussion of views within a group (Teger & Pruitt, 1967). That is, if a group initially favors a viewpoint, after discussion the group consensus is likely a stronger endorsement of the viewpoint. Conversely, if the group was initially opposed to a viewpoint, group discussion would likely lead to stronger opposition.
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NMR Spectrometers: Resolution and Error Correction01:14

NMR Spectrometers: Resolution and Error Correction

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When magnetic nuclei in a sample achieve resonance and undergo relaxation, the signal detected in NMR is an approximately exponential free induction decay. Fourier transform of an exponential decay yields a Lorentzian peak in the frequency domain. Lorentzian peaks in an NMR spectrum are defined by their amplitude, full width at half maximum, and position, where the peak width is governed by the spin-spin relaxation time alone. In real experiments, however, the applied magnetic field is rendered...
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Accuracy and Precision01:52

Accuracy and Precision

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Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value.  Highly accurate...
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Graphs of Polar Equations01:17

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The polar coordinate system represents points using a distance from a central point (the pole) and an angle from a reference direction (the polar axis). Unlike rectangular coordinates, polar coordinates are ideal for graphing curves with radial symmetry or periodic behavior.Some general forms of graphs in polar coordinates include the following:Equation of a Circle (Centered at the Pole):A graph where the radius remains constant for all angles traces a circle centered at the pole:Equation of a...
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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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Alignment precision of polarization components.

Nathan Hagen, Prathan Buranasiri, Yukitoshi Otani

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    Achieving high angular precision during optical system alignment is feasible, making postprocessing correction for azimuthal errors unnecessary. This study demonstrates millidegree precision is attainable with standard mounts and an optical signal model.

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    Area of Science:

    • Optical Engineering
    • Polarization Optics
    • Metrology

    Background:

    • Postprocessing correction methods for azimuthal alignment errors in optical systems are discussed in recent polarization literature.
    • Achieving high angular precision during system alignment is often considered challenging, necessitating postprocessing corrections.

    Purpose of the Study:

    • To demonstrate that high angular precision alignment is achievable during system setup, rendering postprocessing correction unnecessary.
    • To estimate the achievable alignment precision for linear polarizers and waveplates in polarization systems.
    • To show that an optical signal model can enable alignment precision limited by optical component quality, not mechanical limitations.

    Main Methods:

    • Estimation of alignment precision for linear polarizers and waveplates.
    • Utilizing an optical signal model for system alignment.
    • Analysis of precision limitations imposed by optics and detectors versus mechanical components.

    Main Results:

    • High angular precision alignment is achievable during system setup, eliminating the need for postprocessing correction.
    • Millidegree alignment precision is possible using ordinary rotational mounts.
    • Alignment precision is primarily limited by the quality of optical components and detectors, not the mechanical setup.

    Conclusions:

    • Postprocessing correction for azimuthal alignment errors is unnecessary when high precision is achieved during initial system alignment.
    • Advanced alignment techniques utilizing optical signal models allow for unprecedented precision with standard equipment.
    • The quality of optical elements and detectors dictates the ultimate alignment precision, surpassing mechanical limitations.