The study on image theory and the retrieving algorithm of two-dimensional synthetic aperture microwave radiometer with circular antenna array is presented.Based upon simulated annealing algorithm

we will discuss two solutions of obtaining the ideal thinned array.One solution uses half-circle configuration with very much reduced number of elements and taking an image by rotating the array.The other solution selects element positions around the full circle to provide a roughly uniform coverage in the spatial frequency domain.The results show that both solutions have improved characteristics over the conventional design.For the half-circle case

if the integration time allows

with the rotation of the array and the limited time-shared measurements the number of elements can be further reduced to a great extent.For the full-circle case

the array can be thinned up to the least redundant number

which can never be reached by the most popular Y shaped array configuration under same spatial frequency coverage constraint.