Diffraction by circular apertures. 1: Method of linear phase and amplitude approximation.

Two methods are presented for efficient computation of the wave field that results when a spherical wave is diffracted by circular apertures. One method is based on the Kirchhoff diffraction integral, the other on the boundary-diffraction-wave (BDW) integral. In each method the integration domain is divided into sub-domains, and the amplitude and phase within each subdomain are linearized to make an analytical integration possible. Explicit and simple formulas are derived that specify the number of subdomains needed to obtain a desired accuracy for a given geometry and wavelength. Also we determine the number of subdomains needed in the BDW integral to obtain a sufficient accuracy in the vicinity of the shadow boundary. The speed of computation of each method is compared with that using direct numerical integration. As an illustration, the BDW method is used to compute the image field of a holographic lens.