A method of synthesising smooth aperture amplitude and phase distribut
ions from a prescribed far-field radiation pattern is proposed. A geom
etric optics (GO) solution of the problem, which gives a starting poin
t for the final physical optics (PO) optimisation, is obtained using t
he Monge-Ampere approach of Westcott. During PO optimisation a derivat
ive condition is invoked to control the smoothness of the aperture dis
tributions.