  Light diffraction at an aperture is a basic problem that has generated a
tremendous amount of interest in optics. Some of the most significant
diffraction results are the Fresnel-Kirchhoff and Rayleigh-Sommerfeld formulas.
These theories are based on solving the wave equation using Green's theorem and
result in slightly different expressions depending on the particular boundary
conditions employed. In this paper, we propose another approach for solving the
diffraction by a thin screen, which includes apertures, gratings,
transparencies etc. We show that, applying the first order Born approximation
to 2D objects, we obtain a general diffraction formula, without angular
approximations. We discuss several common approximations and place our results
in the context of existing theories.
