Forming First-and Second-Order Cardioids with Multimode Hydrophones

This paper compares and contrasts the performance of cylindrical multimode hydrophones that can form first- and second-order cardioids. The basic theory of directional sensors (i.e., pressure-gradient hydrophones of order 0, 1, and 2) is presented along with an analysis of the directivity index as it pertains to first- and second-order cardioids. The theory of cylindrical multimode hydrophones is presented which relates the n=0, 1, and 2 circumferential modes to the pressure gradient having orders 0, 1, and 2. Electronic beam steering of second-order cardioids is also covered. A case study is presented on a cylindrical multimode hydrophone consisting of a radially-poled piezoelectric ring having four segments. Lastly a brief discussion is presented concerning the augmentation of the directivity index resulting from the physical aperture of the hydrophone