Low-sidelobe pattern synthesis using two-dimensional boundary arrays

Consider a simply-connected f i n i t e a p e r t u r e i n a two-dimensional plane, bounded by a convex boundary . In th i s paper we show that by using information acquired only on the boundary points we can synt h e s i z e beam pa t t e rns ob ta inab le f rom any apod iza t ion ove r t he en tire ape r tu re . Wild [l] w a s the f i r s t t o p r o p o s e a beam s y n t h e s i s t e c h n i q u e o f t h i s n a t u r e , f o r a c i r c u l a r a r r a y a c t i n g i n the receive mode in incoherent imaging. More recent ly Luthra and Kassam [2] ex tended Wi ld ' s , r e su l t t o cohe ren t imag ing us ing the c i r cu la r a r r ay e l emen t s i n bo th t r ansmi t and r ece ive modes.