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In a scalar treatment, the three dimensional irradiance distribution in the focal region of a monochromatic convergent uniform spherical wave diffracted at a circular aperture in an opaque screen is calculated by the direct integration of the Rayleigh-Sommerfeld diffraction integral of the first kind by a matrix method that uses a two dimensional form of Simpson's 1/3 rule. The method described can be used for both large and small Fresnel numbers and for large numerical apertures, off axis beams, filters and aberrations. By operating on matrices using the software package Matlab, the calculations can be done in minutes on a fast PC computer. [ABSTRACT FROM AUTHOR]