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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]
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.
Rayleigh distance in optics is the axial distance from a radiating aperture to a point at which the path difference between the axial ray and an edge ray is λ / 4. An approximation of the Rayleigh Distance is =, in which Z is the Rayleigh distance, D is the aperture of radiation, λ the wavelength. This approximation can be derived as follows.
The rayleigh is a unit of photon flux, used to measure faint light emitted in the sky, such as airglow and auroras. It was first proposed in 1956 by Donald M. Hunten, Franklin E. Roach, and Joseph W. Chamberlain. [1] It is named for Robert Strutt, 4th Baron Rayleigh (1875–1947). [2] Its symbol is R (also used for the röntgen, an unrelated unit).
In fluid mechanics, the Rayleigh number (Ra, after Lord Rayleigh [1]) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free (or natural) convection. [2] [3] [4] It characterises the fluid's flow regime: [5] a value in a certain lower range denotes laminar flow; a value in a higher range, turbulent flow.
In that case, the angular resolution of an optical system can be estimated (from the diameter of the aperture and the wavelength of the light) by the Rayleigh criterion defined by Lord Rayleigh: two point sources are regarded as just resolved when the principal diffraction maximum (center) of the Airy disk of one image coincides with the first ...
Rayleigh waves; Rayleigh (unit), a unit of photon flux named after the 4th Baron Rayleigh; Rayl, rayl or Rayleigh, two units of specific acoustic impedance and characteristic acoustic impedance, named after the 3rd Baron Rayleigh; Rayleigh criterion in angular resolution; Rayleigh distribution; Rayleigh fading; Rayleigh law on low-field ...
In probability theory and statistics, the Rayleigh distribution is a continuous probability distribution for nonnegative-valued random variables. Up to rescaling, it coincides with the chi distribution with two degrees of freedom .