Abstract
The transmission of an acoustical signal through a spatial arrangement consisting of a bidimensional crystal of droplets (liquid spheres) immersed into another liquid is analyzed. As a first approximation, the paraxial case is solved by considering a set of acoustical lenses which allow us to model the effect of each droplet on the signal. An expression for the Wigner distribution function that lets us evaluate the corresponding image, diffraction pattern, and even the output signal of any given paraxial input signal to that crystalline substrate is obtained, with particular emphasis on the case of an incoming plane wave. To solve the nonparaxial situation, a generalization of the concept of focal distance interpreting every sphere as a superposition of concentric rings of different radius, which permits us to find a general expression for the Wigner distribution function is proposed.
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