Nearfield acoustic holography (NAH) II. Holographic reconstruction algorithms and computer implementation

The basic theory treating steady-state acoustic radiation problems in the nearfield has been presented in several articles on nearfield acoustic holography. In this article, the approximations and assumptions necessary to reduce the infinite and continuous convolution integrals encountered in these problems to a finite and discrete form, suitable for high-speed numerical processing, are illuminated theoretically and tested numerically. To evaluate the convolution integrals two assumptions are made: First, the boundary field may be replaced with a patchwise constant field for reasonably small patches; and, second, the field is negligible outside of a finite region. With these two assumptions, the problem reduces to one of representing the Green’s functions. Six methods of sampling or representing the Green’s functions are developed, and these are compared theoretically and numerically.