Diffraction of apertured Gaussian beams: solution by expansion in Chebyshev polynomials

Abstract

A differential equation satisfied by the diffraction integral as a function of the off-axis coordinate in the observation plane is derived and its solution is obtained by expansion in Chebyshev polynomials. The resulting series provides an analytic expression for the diffraction integral and is convenient for fast numerical computation. The efficiency of this approach allows us to use it in optimization of optical systems in which diffraction effects must be taken into consideration.