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Concept
Nombre de Fresnel
Résumé
The Fresnel number (F), named after the physicist Augustin-Jean Fresnel, is a dimensionless number occurring in optics, in particular in scalar diffraction theory.
For an electromagnetic wave passing through an aperture and hitting a screen, the Fresnel number F is defined as
where
is the characteristic size (e.g. radius) of the aperture
is the distance of the screen from the aperture
is the incident wavelength.
Conceptually, it is the number of half-period zones in the wavefront amplitude, counted from the center to the edge of the aperture, as seen from the observation point (the center of the imaging screen), where a half-period zone is defined so that the wavefront phase changes by when moving from one half-period zone to the next.
An equivalent definition is that the Fresnel number is the difference, expressed in half-wavelengths, between the slant distance from the observation point to the edge of the aperture and the orthogonal distance from the observation point to the center of the aperture.
The Fresnel number is a useful concept in physical optics. The Fresnel number establishes a coarse criterion to define the near and far field approximations. Essentially, if Fresnel number is small – less than roughly 1 – the beam is said to be in the far field. If Fresnel number is larger than 1, the beam is said to be near field. However this criterion does not depend on any actual measurement of the wavefront properties at the observation point.
The angular spectrum method is an exact propagation method. It is applicable to all Fresnel numbers.
A good approximation for the propagation in the near field is Fresnel diffraction. This approximation works well when at the observation point the distance to the aperture is bigger than the aperture size. This propagation regime verifies .
Finally, once at the observation point the distance to the aperture is much bigger than the aperture size, propagation becomes well described by Fraunhofer diffraction. This propagation regime verifies .
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