A general resolution for the optimum element locations o（?） weighted thinning array and the grating lobe level of the optimum array are firstly presented. Special attention is then paid to the array weighted by general raised cosine function. The properties of the optimum thinning array with this weighting are analyzed. The closed-form expressions for the efficiency index

grating lobe level

beamwidth and clean region width are also given. As a result

a simple design method of optimum thinning arrays with any desired nearby （mainlobe） sidelobe level and clean region width is obtained. Finally

an application of the thinned arrays is briefly discussed.