Explicit derivation of the Fraunhofer diffraction formula for oblique incidence

Abstract

We have analytically explored the Rayleigh-Sommerfeld scalar diffraction for oblique incidence. We have explicitly derived the Fraunhofer diffraction formulae for oblique incidence of a plane scalar wave on various apertures, such as single-slit, circular aperture and diffraction grating. Such derivations in the background of Rayleigh-Sommerfeld scalar diffraction theory would be important for an undergraduate course on optics.