Disclosed herein is a method for the optimal design of an apodization function used for non-uniform weighted periodic sparse arrays for an ultrasound imaging system. The method includes the steps of (a) setting the interval PT of a transmit sparse array and the number LT of array elements within the interval PT so that common grating lobes are not generated in the beam patterns of the transmit sparse array and a receive sparse array; (b) setting the interval PR of the receive sparse array and the number LR of array elements within the interval PR so that common grating lobes are not generated in the beam patterns of the transmit sparse array and the receive sparse array; (c) setting a transmit apodization function WT(n) configured to be applied to the beam pattern of the transmit sparse array; and (d) setting a receive apodization function WR(n) configured to be applied to the beam pattern of the receive sparse array.