# Rayleigh distance

**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. Consider a right angled triangle with sides adjacent , opposite and hypotenuse . According to Pythagorean theorem,

.

Rearranging, and simplifying

The constant term can be neglected.

In antenna applications, the Rayleigh distance is often given as four times this value, i.e. [1] which corresponds to the border between the Fresnel and Fraunhofer regions and denotes the distance at which the beam radiated by a reflector antenna is fully formed (although sometimes the Rayleigh distance it is still given as per the optical convention e.g.[2]).

Actually, Rayleigh distance is also a distance beyond which the distribution of the diffracted light energy no longer changes according to the distance Z from the aperture. It is the reduced Fraunhofer diffraction limitation.

Lord Rayleigh's paper on the subject was published in 1891.[3]

- Kraus, J (2002).
*Antennas for all applications*. McGraw Hill. p. 832. ISBN 0-07-232103-2. - "Radar Tutorial".
- On Pinhole Photography