The complete Rayleigh–Sommerfeld scalar diffraction formula contains (1−<i>ikR</i>) in the integrand. Usually the wavelength is small compared with the distance of the observation point from the aperture and (1−<i>ikR</i>) is approximated by −<i>ikR</i> alone. Other approximations usually made in the Rayleigh–Sommerfeld formula are addressed as well. Closed-form solutions, without approximations, are possible wherein interesting consequences of these approximations become apparent.
© 2004 Optical Society of America
(050.1940) Diffraction and gratings : Diffraction
(050.1960) Diffraction and gratings : Diffraction theory
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(260.1960) Physical optics : Diffraction theory
Arvind S. Marathay and John F. McCalmont, "On the usual approximation used in the Rayleigh-Sommerfeld diffraction theory," J. Opt. Soc. Am. A 21, 510-516 (2004)