Methods for Efficient Computation of the Image Field of Holographic Lenses for Sound Waves

Abstract

Methods for efficient computation of the image field of acoustical holographic lenses are presented. The methods are valid for large field angles and large relative apertures and apply at short as well as at long wavelengths. Some of the techniques are based on the Kirchhoff diffraction integral, others on the boundary-diffraction-wave integral. For rapid computation of these integrals we employ three different techniques for different positions of the object and observation points: In the case in which the integrand has small variations we employ the technique of phase and amplitude approximations; in shadow boundary regions we use a uniform asymptotic technique; and in other regions we use a second order asymptotic method.