This paper discusses the synthesis of optimum thinning arrays by nonuniform spacings in the sense of Dolph-Chebyshev. Having derived the equations of optimum element distribution

we analyze the exponentially spaced arrays

which arc optimum when the elements are isotropic and equally weighted. The formulae for estimating the sidelobe envelope and beamwidth of the array pattern are obtained. Also

the relationship between the nearby side-lobe level and the array parameters is given. These results allow us to design a desired array with minimal elements. Finally

a comparative study on some "optimum" arrays shows that the exponentially spaced array is the best one of them.