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Based on the Rayleigh–Sommerfeld diffraction integral, the diffraction of converging spherical waves at a circular aperture is studied in a general case. The expression for the intensity near focus of strongly converging spherical diffracted waves is derived, which reduces to the well known result expressed in terms of Lommel functions for the case of weakly converging spherical diffracted waves. The intensity distributions at the geometrical focal plane and along the axis are given. Numerical comparative examples are presented to illustrate the more general applicability of our results. [ABSTRACT FROM AUTHOR]