Optimization of wide-band linear arrays

An optimization method is proposed for linear arrays to be used in ultrasound systems under wide-band operation. A fast algorithm, the threshold accepting, has been utilized to determine the element positions and weight coefficients of a linear array that generates a desired beam pattern. To reduce the computational burden in the optimization procedure, an efficient numerical routine for the beam pattern evaluation has been implemented. We address the optimization problem of both dense and sparse wideband arrays. In the first case, the goal is to minimize the side-lobe energy by varying the element weights; we compare the optimized beam pattern with that obtained with classical shading functions, showing that better results can be achieved with a wide-band optimization. We also consider the optimization of the layout (positions and weights) of a sparse linear array to achieve a desired beam pattern with a fixed or minimum number of array elements. The comparison of the proposed method with a narrow-band optimization algorithm is presented, showing that better performances (about -7 dB further reduction of the side-lobe level) can be achieved with a wide-band sparse array optimization. Further numerical simulations are given, showing that the proposed method yields better results than wideband sparse random arrays and periodic arrays with the same aperture width.