Fresnel number

The Fresnel number F, named after the physicist Augustin-Jean Fresnel, is a dimensionless number occurring in optics, in particular in diffraction theory.

For an electromagnetic wave passing through an aperture and hitting a screen, the Fresnel number F is defined as

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

where

$a\!$ is the characteristic size (e.g. radius) of the aperture

$L\!$ is the distance of the screen from the aperture

$\lambda\!$ is the incident wavelength.

Depending on the value of F the diffraction theory can be simplified into two special cases:

• Fraunhofer diffraction for $F \ll 1$
• Fresnel diffraction for $F \gtrsim 1$

In case of $F \gg 1$, laws of geometrical optics are applied.

The agreement on this limit does not seem universal, for elaboration on this controversy see this article's discussion page. Intermediate values of the Fresnel number necessitate a more detailed analysis based on the scalar diffraction theory.

See also

• Fresnel integral
• Fresnel zone
• Fraunhofer distance