Rayleigh distance 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 formula_1, 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 formula_2, opposite formula_3and hypotenuse formula_4. According to Pythagorean theorem, formula_5. Rearranging, and simplifying formula_6 The constant termformula_7 can be neglected. In antenna applications, the Rayleigh distance is
Wave shoaling the product of the wave energy density with the group velocity, between two wave rays is a conserved quantity (i.e. a constant when following the energy of a wave packet from one location to another). Under stationary conditions the total energy transport must be constant along the wave ray – as first shown by William Burnside in 1915. For waves affected by refraction and shoaling (i.e. within the geometric optics approximation), the rate of change of the wave energy transport is: where formula_13 is the co-ordinate along the wave ray and formula_14 is the energy flux per unit crest length.