  We study the acoustic scattering properties of a phononic crystal designed to
behave as a gradient index lens in water, both experimentally and
theoretically. The gradient index lens is designed using a square lattice of
stainless-steel cylinders based on a multiple scattering approach in the
homogenization limit. We experimentally demonstrate that the lens follows the
graded index equations derived for optics by mapping the pressure intensity
generated from a spherical source at 20 kHz. We find good agreement between the
experimental result and theoretical modeling based on multiple scattering
theory.
