The Fresnel numberF, named after the physicist Augustin-Jean Fresnel, is a dimensionless number occurring in optics, in particular in diffraction theory. Augustin Fresnel Augustin-Jean Fresnel (pronounced fray-NELL) (May 10, 1788 – July 14, 1827), was a French physicist who contributed significantly to the establishment of the wave theory of light and optics. ... In dimensional analysis, a dimensionless number (or more precisely, a number with the dimensions of 1) is a pure number without any physical units. ... Table of Opticks, 1728 Cyclopaedia Optics ( appearance or look in ancient Greek) is a branch of physics that describes the behavior and properties of light and the interaction of light with matter. ... To meet Wikipedias quality standards, this article or section may require cleanup. ...
For an electromagnetic wave passing through an aperture and hitting a screen, the Fresnel number is defined as Electromagnetic radiation is a propagating wave in space with electric and magnetic components. ... a big (1) and a small (2) aperture For other uses, see Aperture (disambiguation). ...
where λ is wavelength, a is the characteristic size (e.g. radius) of the aperture, and L is the distance of the screen from the aperture. The wavelength is the distance between repeating units of a wave pattern. ... Remote Authentication Dial In User Service (RADIUS) is an AAA (authentication, authorization and accounting) protocol for applications such as network access or IP mobility. ...
Depending on the value of F the diffraction theory can be simplified into two special cases:
Values in between require a more detailed analysis based on the scalar diffraction theory. Fresnel diffraction is the diffraction pattern of an electromagnetic wave obtained a small number of wavelengths away from the diffracting object (often a source or aperture). ... Fraunhofer diffraction is diffraction of light through an aperture for small values of the Fresnel number, F<<1. ...
interval of time during which the eye could be impressed, there would be opportunity for any number of rearrangements of phase, due either to motions of the particles or to irregularities in their modes of vibration.
The narrowness of the bright line of light seen in the spectroscope, and the possibility of a large number of Fresnel's bands, depend upon precisely the same conditions; the one is in truth as much an interference phenomenon as the other.
In Fresnel's experiment, whether carried out with the mirrors or with the biprism, the corresponding parts of the images are on the same side; that is, the right of one corresponds to the right of the other, and the left of the one to the left of the other.
A large Fresnelnumber (well above 1) of a resonator means that diffraction losses at the end mirrors are small for typical mode sizes (i.e., not close a stability limit of the cavity, where mode sizes can diverge).
Conversely, a small Fresnelnumber means that diffraction losses can be significant – particularly for high-order cavity modes, so that diffraction-limited operation may be favored.
Most laser cavities have a rather large Fresnelnumber, although rather small Fresnelnumbers occur in unstable cavities, which are sometimes applied for high power lasers.
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