A Unified Theory for Acoustical Holography and Diffraction Tomography

Abstract

In optical holography, the object is assumed to be such that a considerable part of the wave penetrates undisturbed through it, a diffraction pattern called hologram which is formed by the interference of the secondary waves arising from the presence of the object scattering with the strong background wave, is recorded on a photographic plate. This means that, if the wave is expressed as the sum of the incident wave and a diffracted secondary wave, the scattering of the secondary wave and interaction within the object is neglected. This negligence represents what is usually known as Born’s first approximation. In acoustical holography, where the sound wavelength is about the same order as the obstacle in the medium that causes the scattering, diffraction takes place and the scattering of the secondary wave and the interaction within the object can no longer be neglected. This is what is done in diffraction tomography (DT), but is neglected in acoustical holography (AH), sofar. So one has to combine DT and AH. Hence a unified theory for AH and DT is proposed.