ANNULAR ARRAY IMAGING WITH FULL-APERTURE RESOLUTION

The problem of imaging with an annular array of transducers by employing all pairs of transducer elements around the circumference of the annulus as transmitters and receivers is considered. If theta(t) and theta(r) are, respectively, the angular locations of a pair of transmitting and receiving elements, then weighting the received signal with the positive weight 2\sin (theta(t) - theta(r)\ before coherent summation results in an image point spread function of the form J1 (R)/R. This corresponds to the point spread function of a full circular (area) aperture. Moreover, it is shown that the diameter of this synthetic aperture is twice that of the annulus. A more general weighting function is also derived that results in a point spread function of the form J(n) (R)/R(n), n = 1,2,..., which is shown to correspond to an apodized circular aperture of diameter twice that of the annulus.