Abstract: Sparse antenna array design is of great importance in aperture synthesis radiometers （ASR）. For non-re- dundant baseline distribution and the simplicity of mechanical structure and instrumental manufacture, the circular array, as a promising configuration of ASR, has received more and more attention. Two methods for optimal thinned circular arrays are proposed to achieve the least redundancy in baseline length （ modulus of baseline vector）. One is half-circle thinning based on restricted difference set （RDS） , the other is full-circle thinning based on cyclic difference set （CDS）. Both methods can greatly reduce the numbers of the elements and channels and provide analytical solutions for the element positions of thinned circular arrays. With the rotation of the array and time-shared measurement, the thinned circular arrays resulting for both methods can obtain the same spatial frequency coverage as that of UCA.