Broadband array transducers are widely used in medical imaging systems, and their beam patterns determine the imaging quality. The characteristics of the beam patterns such as mainlobe beamwidth and sidelobe levels are the major criteria for designing and optimizing sparse array systems. The spatial impulse response approach can be used to calculate the beam patterns rigorously in both near field and far field. However, it is time consuming due to the high sampling frequency required, and thus not suitable for array optimization. On the other hand, assuming the array elements to be omnidirectional point sources the field calculation can be much simplified and fast but at the expense of poor accuracy. This paper presents a modified model that has the accuracy comparable to that from the impulse response model while keeping the efficiency close to that of the simple point source model. The developed algorithm is particularly suitable for stochastic methods for two-dimensional (2D) sparse arrays design and optimization such as genetic algorithms (GA), in which the iterative beam pattern calculation dominates the optimization program running time.