Abstract: Kirchhoff's complex spatial convolution formula is developed as a new algorithm for radiation from a aperture. It is based on hte idea of analytic ectention that the original aperture field is extended to a complex plane.and then the kirchhoff's complex spatial-convolution formula makes up an indirect and rigorous representation of radiation from a plane aperture.Numerical tests confirm its correctness and efficiency.

Key words: aperture radiation, complex ray, lirchhoff's formula