Optimization of wide-band linear arrays

An optimization method is proposed for linear arrays to be used in ultrasou nd systems under wide-band operation. A fast algorithm, the threshold accep ting, has been utilized to determine the element positions and weight coeff icients of a linear array that generates a desired beam pattern. To reduce the computational burden in the optimization procedure, an efficient numeri cal routine for the beam pattern evaluation has been implemented. We addres s 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 el ement weights; we compare the optimized beam pattern with that obtained wit h classical shading functions, showing that better results can be achieved with a wide-band optimization. We also consider the optimization of the lay out (positions and weights) of a sparse linear array to achieve a desired b eam pattern with a fixed or minimum number of array elements. The compariso n of the proposed method with a narrow-band optimization algorithm is prese nted, showing that better performances (about -7 dB further reduction of th e side-lobe level) can be achieved with a wide-band sparse array optimizati on. Further numerical simulations are given, showing that the proposed meth od yields better results than wideband sparse random arrays and periodic ar rays with the same aperture width.