Broadband acoustic lens design using the principle of reciprocity and gradient-based optimization

In this work, we will present a gradient-based optimization method for the design of an acoustic lens. This design is based on an optimization process using the semi-analytical optimization approach and applying the principle of reciprocity. Here, we will illustrate the use of acoustic reciprocity to define the pressure at the focal point due to a source located in a far-field. The reciprocity enables us to relate the response by configuration of scatterers for an incident plane wave in terms of the far-field Green's function. The idea differs from earlier inverse designs that use topology optimization tools and generic algorithms. The gradient-based optimization algorithm maximizes the sound amplification at the focal point by evaluating pressure derivative with respect to the cylinder positions and then perturbatively optimizing the position of each cylinder in the lens while taking into account acoustic the multiple scattering between the cylinders. Computations are performed on MATLAB using “fmincon” function with a MultiStart optimization solver, and supplying the gradient of pressure at the focus. The reciprocal formulation of inverse design of acoustic lens leads to the closed-form solution that takes lesser time to compute the absolute pressure and it gradients at the focal point. The numerical results for the optimization of the broadband acoustic lens will be illustrated for configurations of uniform rigid cylinders.