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This paper proposes a novel approximation for the delays of digital near-field beamforming based on a planar array. An optimized algorithm for the underwater 3-D sonar imaging system based on the novel approximation will also be described. The algorithm is applied to both an evenly spaced planar array and an unevenly spaced planar array. A data path for the optimized algorithm will be illustrated. Comparisons of the memory and the computational requirements between the optimized algorithm and the direct method (DM) beamforming will be presented. Comparisons of the proposed approximation and the Fresnel approximation will also be demonstrated. This paper illustrates that the proposed approximation enlarges the validity region of the system's view scene as compared with the Fresnel approximation. The optimized algorithm has the advantage of reducing the memory requirements for parameter storage comparing with DM beamforming.