A fast algorithm to compute a scattering pattern produced by a two-dimensional object is presented. Rather than by use of an approximation, this algorithm is derived by decomposition of the spherical nature of a radiation pattern into the sum of plane waves. Thus it precludes the phase errors that exist in approximationbased Fresnel holograms. Moreover, the amount of computation required in this method is shown to be significantly smaller than that of a well-known ray-tracing method; excellent performance, as good as one could obtain with the ray-tracing method, is achieved. Implementation results as well as sampling constraints are also presented.