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 Z = D 2 2 λ {displaystyle Z={frac {D^{2}}{2lambda }}} , 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 Z {displaystyle Z} , opposite D 2 {displaystyle {frac {D}{2}}} and hypotenuse Z + λ 4 {displaystyle Z+{frac {lambda }{4}}} . According to Pythagorean theorem, 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 Z = D 2 2 λ {displaystyle Z={frac {D^{2}}{2lambda }}} , 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 Z {displaystyle Z} , opposite D 2 {displaystyle {frac {D}{2}}} and hypotenuse Z + λ 4 {displaystyle Z+{frac {lambda }{4}}} . According to Pythagorean theorem, ( Z + λ 4 ) 2 = Z 2 + ( D 2 ) 2 {displaystyle {ig (}Z+{frac {lambda }{4}}{ig )}^{2}=Z^{2}+{ig (}{frac {D}{2}}{ig )}^{2}} .