Fresnel number

The Fresnel number  F , named after the physicist Augustin Jean Fresnel , is a dimensionless number that is used in optics , especially in diffraction . It describes how strong the diffraction of a light beam at a diaphragm is.

For an electromagnetic wave that passes through a diaphragm and hits a screen, the Fresnel number  F is defined as

${\displaystyle F={\frac {a^{2}}{L\cdot \lambda }}}$

With

• a the characteristic size of the aperture (e.g. its radius )
• L is the distance from the screen to the diaphragm
• λ is the wavelength .

Depending on the value of F , one can differentiate between the following cases:

• ${\displaystyle F\ll 1}$: Fraunhofer diffraction (e.g. aperture  a very small or beam path in the far field , i.e. distance  L very large)
• ${\displaystyle F\approx 1}$: Fresnel diffraction
• ${\displaystyle F\gg 1}$: Geometric optics (e.g. aperture  a very large or beam path in the near field , i.e. distance  L very small).

See also

• Fresnel integral
• Fresnel zone