Backward reconstruction in acoustical holography based on iterative inversion techniques

Abstract

Reconstruction of a source surface motion from acoustic holographic data presents computational difficulties because the problem is ill-posed as is well known in the literature. In order to deal with these difficulties, a method based on a recursive algorithm was developed. In this method, the inverse problem is convened to a well-posed forward propagation problem. An initial guess regarding the source images is required to activate the iterative inversion method. Then, the tentative image is forward propagated to the hologram plane and the residue is determined. Next, a feedback operator is used to process the residue by which the image is updated. Two types of feedback operators were investigated: (1) Wiener type, suboptimal operator, and (2) dynamic, optimal operator (designed subject to minimum mean-square error optimization criteria). Both iteration methods provided satisfactory convergence. In addition, these methods were found to be relatively insensitive to the choice of the initial guess and the noise parameters used in feedback operators. The efficiency of the iteration process is greatly enhanced by 2-D FFT. Numerical and experimental results obtained by using iterative inversion techniques will be presented. The iterative inversion techniques will be compared with conventional inverse filtering methods. In addition, performance of the iterative inversion methods when used in connection with the nearfield acoustic holography technique will be discussed. [Work supported by NSF.]