An alternate way to teach Fourier Optics

Scalar diffraction theory is usually introduced using the classical Green function approach as a solution to a boundary value problem. I propose a different approach first proposed by Duffieux and later put on a solid mathematical foundation by Arsac. and which exploits the close connection between Fourier theory and linear systems theory; it is based on elementary distribution theory, where scalar diffraction appears naturally as a convolution of the diffracting screen with an optical propagator. All the classical expressions such as Rayleigh's integral formula and the Kirchhoff-Sommerfeld diffraction integral are easily derived as special cases. The fact that diffraction appears naturally as a convolution facilitates the integration of diffraction theory with linear systems theory, which has come to play a major role in fourier optics