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The Gaussian function has a 1/e 2 diameter (2w as used in the text) about 1.7 times the FWHM.. At a position z along the beam (measured from the focus), the spot size parameter w is given by a hyperbolic relation: [1] = + (), where [1] = is called the Rayleigh range as further discussed below, and is the refractive index of the medium.
English: A gaussian beam transmitted through a lens with initial beam waist radius w 0 and distance z 0 from the lens and final beam waist radius w 0 ' and distance z 0 ' from the lens. Date 27 November 2021
Consequently, Gaussian functions are also associated with the vacuum state in quantum field theory. Gaussian beams are used in optical systems, microwave systems and lasers. In scale space representation, Gaussian functions are used as smoothing kernels for generating multi-scale representations in computer vision and image processing.
Gaussian beam width () as a function of the axial distance .: beam waist; : confocal parameter; : Rayleigh length; : total angular spread In optics and especially laser science, the Rayleigh length or Rayleigh range, , is the distance along the propagation direction of a beam from the waist to the place where the area of the cross section is doubled. [1]
Comparison of Gaussian (red) and Lorentzian (blue) standardized line shapes. The HWHM (w/2) is 1. Plot of the centered Voigt profile for four cases. Each case has a full width at half-maximum of very nearly 3.6. The black and red profiles are the limiting cases of the Gaussian (γ =0) and the Lorentzian (σ =0) profiles respectively.
English: Diagram of Gaussian beam waist parameters. Explains "Spot size" or "Focus Size", and "depth of focus". Date: 20 February 2009, 21:17 (UTC) Source ...
The shape of the laser beam depends on the type of resonator: The beam produced by stable, paraxial resonators can be well modeled by a Gaussian beam. In special cases the beam can be described as a single transverse mode and the spatial properties can be well described by the Gaussian beam, itself.
The NA of a Gaussian laser beam is then related to its minimum spot size ("beam waist") by NA ≃ λ 0 π w 0 , {\displaystyle {\text{NA}}\simeq {\frac {\lambda _{0}}{\pi w_{0}}},} where λ 0 is the vacuum wavelength of the light, and 2 w 0 is the diameter of the beam at its narrowest spot, measured between the e −2 irradiance points ("Full ...