This paper investigates Fresnel diffraction from plane-wave gaussian beams truncated by circular apertures. Kirchhoff’s integral has been evaluated analytically and (analytical) expressions are derived, in terms of infinite series, for the irradiance and total power of the diffracted field. Some graphs are presented for Fraunhofer conditions. The results obtained greatly reduce the labor of numerically computing the irradiance and the power.
G. OLUREMI OLAOFE, "Diffraction by Gaussian Apertures," J. Opt. Soc. Am. 60, 1654-1657 (1970)