Explicit derivation of the Fraunhofer diffraction formula for oblique incidence

TL;DR

This paper analytically derives the Fraunhofer diffraction formulae for oblique incidence of plane waves on various apertures within the Rayleigh-Sommerfeld scalar diffraction framework, aiding optics education.

Contribution

It provides explicit derivations of diffraction formulas for oblique incidence, which were not previously detailed in this context.

Findings

Explicit formulas for oblique incidence diffraction

Derivations for single-slit, circular aperture, and diffraction grating

Educational utility for optics courses

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 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.