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This study aims at a sound field calculation for the spherical-section phased array and an optimization algorithm for the focus patterns of phased array ultrasound surgery. An efficient field calculation formula represented as an explicit expression is derived by the strategies of projection and binomial expansion. An optimization algorithm based on genetic algorithm is constructed by the suitable fitness function and the selection strategies. The simulation results of 256-element spherical-section phased array show the capability of controlling focus accurately and effectively with the combined method made up of the explicit expression method and the genetic optimization algorithm. The simulation results of single focus, multiple foci, on-axial focus, and off-axial focus further convince the feasibility of three-dimensional (3-D) focus steering with excellent acoustic performances. A single focus with the focus dimension of 1.25 mm /spl times/ 1.25 mm /spl times/ 7 mm and with the intensity of 6080 W/cm/sup 2/ is formed. The multiple-focus pattern can enlarge the treatment volume 22 times larger than that of single focus with a sonication. In addition, a comparison between the explicit expression approach and the point source approach testifies to the applicability of the explicit expression approach. The experiment and simulation results of 16-element array actually confirm the feasibility of the combined method.