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
Rearranging, and simplifying
The constant term
In antenna applications, the Rayleigh distance is often given as four times this value, i.e.
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.