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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.
The Voigt profile is normalized: (;,) =,since it is a convolution of normalized profiles. The Lorentzian profile has no moments (other than the zeroth), and so the moment-generating function for the Cauchy distribution is not defined.
For example, the blue star shows that the Hubble Space Telescope is almost diffraction-limited in the visible spectrum at 0.1 arcsecs, whereas the red circle shows that the human eye should have a resolving power of 20 arcsecs in theory, though 20/20 vision resolves to only 60 arcsecs (1 arcminute)
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). The FWHM method may be difficult to apply when the spectrum has a complex shape.
The diameter of the seeing disk, most often defined as the full width at half maximum (FWHM), is a measure of the astronomical seeing conditions. It follows from this definition that seeing is always a variable quantity, different from place to place, from night to night, and even variable on a scale of minutes.
The presence of other molecules close to the molecule involved affects both line width and line position. It is the dominant process for liquids and solids. An extreme example of this effect is the influence of hydrogen bonding on the spectra of protic liquids. Observed spectral line shape and line width are also affected by instrumental factors.
For c = 2 the constant before the standard deviation in the frequency domain in the last equation equals approximately 1.1774, which is half the Full Width at Half Maximum (FWHM) (see Gaussian function). For c = √ 2 this constant equals approximately 0.8326. These values are quite close to 1.
The other half of the flux is outside this circle. The half flux diameter unit is pixels. [2] The lower the half flux diameter value the better the seeing is and the sharper the image. It is a similar measurement to full width at half maximum (FWHM), but is a more robust measurement [3] especially for stars out of focus.