Skip to Main Content
A planar array of sensors is required to collect the signals coming from a 3-D scene to generate volumetric underwater acoustic images. The method most frequently used to process the acquired signals is a digital beamforming algorithm. In general, owing to the high number of sensors and beam signals, the computational load is prohibitive for real-time image generation. In the literature, a frequency-domain beamforming technique based on the chirp zeta transform (CZT), which is efficient and computationally advantageous, has been introduced for linear and planar arrays working in the far field. This paper proposes an extension of the CZT beamforming that has been specifically devised to cope with the requirements of volumetric sonar imaging. In particular, the processing of wideband signals collected by a planar array and generated by a scene placed in both near-field and far-field conditions is enabled with a computational load that is one or two orders of magnitude lower than that of the traditional frequency-domain and time-domain beamforming implementations. To attain this result, the Fresnel delay approximation, a useful definition of steering angles, and the setting up of multiple focal regions are adopted. In addition, a computationally convenient technique to generate cubic resolution cells is introduced.