Shape and topology optimization of acoustic lens system using phase field method

A layout optimization method for a two-dimensional acoustic lens system used in underwater imaging is presented. To this end, a shape and topology optimization is formulated for the design problem of a lens system for the first time. The layout of a lens system to be optimized includes the number of lenses, shape of lens surfaces, distances between lenses, and lens materials. A phase field function is employed to implicitly parameterize the boundaries of the lenses, which move according to design sensitivities during optimization. Multiple lenses with different materials are optimized using a single phase field function. Because the ratio of the acoustic wavelength with respect to lens dimensions is large, diffraction effects should be taken into account. Accordingly, the performance of a lens system should be analyzed using wave acoustics and not the ray tracing method. The optimization problem is formulated to remove the aberrations of coma and field curvature. The validity of the proposed optimization method is demonstrated by solving benchmark design problems including a lens system with a large field of view.