NUMERICAL-SOLUTION OF THE HUYGENS-FRESNEL-KIRCHHOFF DIFFRACTION OF SPHERICAL WAVES BY A CIRCULAR APERTURE

Using the rigorous wave-front formulation for scaler wave diffraction of Kraus [J. Opt. Sec, Am, A 6, 1196 (1989); 9, 1132 (1992)], it is sh own that the two-dimensional integral used to calculate the diffractio n of spherical waves by a circular aperture may be reduced to a one-di mensional integral by choosing an appropriate coordinate frame. Both t he two-dimensional integral and the one-dimensional integral must be e valuated numerically, but because each dimension must be sampled at ap proximately N locations to calculate accurately the integral (where N is the number of wavelengths across the aperture) the two-dimensional integration will require of the order of N-2 evaluations of the integr and, whereas the one-dimensional integration will require of the order of only N evaluations, a substantial decrease in computing time for a pertures that are large compared with optical wavelengths.