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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 FWHM of the Gaussian profile is = (). The FWHM of the Lorentzian profile is =. An approximate relation (accurate to within about 1.2%) between the widths of the Voigt, Gaussian, and Lorentzian profiles is: [10]
A simple answer is to sample the continuous Gaussian, yielding the sampled Gaussian kernel. However, this discrete function does not have the discrete analogs of the properties of the continuous function, and can lead to undesired effects, as described in the article scale space implementation .
The 1/e 2 width is important in the mathematics of Gaussian beams, in which the intensity profile is described by () = (). The American National Standard Z136.1-2007 for Safe Use of Lasers (p. 6) defines the beam diameter as the distance between diametrically opposed points in that cross-section of a beam where the power per unit area is 1/e (0 ...
The equations below assume a beam with a circular cross-section at all values of z; this can be seen by noting that a single transverse dimension, r, appears.Beams with elliptical cross-sections, or with waists at different positions in z for the two transverse dimensions (astigmatic beams) can also be described as Gaussian beams, but with distinct values of w 0 and of the z = 0 location for ...
If the source has a Gaussian spectrum with FWHM spectral width , then a path offset of will reduce the fringe visibility to 50%. It is important to note that this is a roundtrip coherence length — this definition is applied in applications like OCT where the light traverses the measured displacement twice (as in a Michelson interferometer ).
In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is [ 2 ] [ 3 ] f ( x ) = 1 2 π σ 2 e − ( x − μ ) 2 2 σ 2 . {\displaystyle f(x)={\frac {1}{\sqrt {2\pi \sigma ^{2 ...
A graph of the function () = and the area between it and the -axis, (i.e. the entire real line) which is equal to . The Gaussian integral , also known as the Euler–Poisson integral , is the integral of the Gaussian function f ( x ) = e − x 2 {\displaystyle f(x)=e^{-x^{2}}} over the entire real line.