A synthetic-aperture imaging system using an annular array of transducer elements is analyzed. The aperture is assumed to consist of N elements, where each element serves both as a source and receiver of sound, giving rise to N2 amplitude and phase measurements around the annular circumference. Because of source-receiver reciprocity, however, (1/2)N(N - 1) of these measurements [where (1/2)N(N - 1) is the number of element pairs on the annulus] are redundant, giving a total of N2 - (1/2)N(N - 1) = (1/2)N(N + 1) independent measurements. It is shown how suitable processing of these measurements can yield a high-resolution image of a reflecting object in a plane parallel to the annulus and located within its Fresnel region. Moreover, the resultant resolution is shown to be equivalent to that of a full circular aperture twice the diameter of the annulus. This approach differs from the J2 synthesis of Wild (1965) in that the annular array acts as a source as well as a receiver and that no assumptions regarding the spatial coherence of the reflecting object are required. Numerical reconstructions based on simulated data are presented. Possible areas of application of the annular imaging system include medical ultrasonic imaging, underwater acoustic imaging and microwave imaging.