Modified Fresnel Approximation and Acoustical Holography

Abstract

The backward-propagation algorithm, based on the angular spectrum formulation of diffraction theory, plays a central role in acoustical holography systems. This procedure requires twice two-dimensional FFT’s to propagate the wavefront back to its origin. In contrast, the Fourier/Fresnel transformation algorithm needs only one two-dimensional FFT. This means great saving on computation time. The Fourier/Fresnel transformation algorithm, however, is seriously limited in some applications, since it does not apply in near-field region. Near field imaging is of great interest in some applications of practical reasons and offers potential improvement of the spatial resolving power of systems. Two modified approximations are discussed in this paper. They have much less error than the traditional Fresnel approximation in the near field. Simulation results show that the performance of the algorithms based on these two modified approximations may improve the performance of an acoustical holography system in the near field, even if the distance between acoustical array and object is much less than the array dimension.