Full width at half maximum in the context of Beam width


Full width at half maximum in the context of Beam width

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⭐ Core Definition: Full width at half maximum

In a distribution, full width at half maximum (FWHM) is the difference between the two values of the independent variable at which the dependent variable is equal to half of its maximum value. In other words, it is the width of a spectrum curve measured between those points on the y-axis which are half the maximum amplitude.Half width at half maximum (HWHM) is half of the FWHM if the function is symmetric.The term full duration at half maximum (FDHM) is preferred when the independent variable is time.

FWHM is applied to such phenomena as the duration of pulse waveforms and the spectral width of sources used for optical communications and the resolution of spectrometers.The convention of "width" meaning "half maximum" is also widely used in signal processing to define bandwidth as "width of frequency range where less than half the signal's power is attenuated", i.e., the power is at least half the maximum. In signal processing terms, this is at most −3 dB of attenuation, called half-power point or, more specifically, half-power bandwidth.When half-power point is applied to antenna beam width, it is called half-power beam width.

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Full width at half maximum in the context of Astronomical seeing

In astronomy, seeing is the degradation of the image of an astronomical object due to turbulence in the atmosphere of Earth that may become visible as blurring, twinkling or variable distortion. The origin of this effect is rapidly changing variations of the optical refractive index along the light path from the object to the detector.Seeing is a major limitation to the angular resolution in astronomical observations with telescopes that would otherwise be limited through diffraction by the size of the telescope aperture.Today, many large scientific ground-based optical telescopes include adaptive optics to overcome seeing.

The strength of seeing is often characterized by the angular diameter of the long-exposure image of a star (seeing disk) or by the Fried parameter r0. The diameter of the seeing disk is the full width at half maximum of its optical intensity. An exposure time of several tens of milliseconds can be considered long in this context. The Fried parameter describes the size of an imaginary telescope aperture for which the diffraction limited angular resolution is equal to the resolution limited by seeing. Both the size of the seeing disc and the Fried parameter depend on the optical wavelength, but it is common to specify them for 500 nanometers.A seeing disk smaller than 0.4 arcseconds or a Fried parameter larger than 30 centimeters can be considered excellent seeing. The best conditions are typically found at high-altitude observatories on small islands, such as those at Mauna Kea or La Palma.

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Full width at half maximum in the context of H band (infrared)

In infrared astronomy, the H band refers to an atmospheric transmission window centred on 1.65 micrometres with a Full width at half maximum of 0.35 micrometres (in the near-infrared).

Save for a limited amount of absorption by water vapor, Earth's atmosphere is highly translucent at the wavelengths covered by the H band. The window is also notably less likely to be contaminated by infrared excess than other bands.

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Full width at half maximum in the context of Spectral width

In telecommunications, spectral width is the width of a spectral band, i.e., the range of wavelengths or frequencies over which the magnitude of all spectral components is significant, i.e., equal to or greater than a specified fraction of the largest magnitude.

In fiber-optic communication applications, the usual method of specifying spectral width is the full width at half maximum (FWHM). This is the same convention used in bandwidth, defined as the frequency range where power drops by less than half (at most −3 dB).

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