From beamforming to diffraction tomography

Recent progress in sensor array technology has boosted the use of beamforming (BF) in a number of applications. The same progress has generated interest in other imaging modalities such as diffraction tomography (DT). This paper demonstrates the existence of a linear mapping between BF and DT, which is represented by a linear filter in the spatial frequency domain. The filter is used to study and compare the information content of images obtained with the two imaging modalities. In particular, it is demonstrated that a BF image is a distorted version of the corresponding DT image. Moreover, the analytical expression of the filter is derived leading to an algorithm for DT which, in contrast to currently available algorithms, does not require the use of data interpolation techniques.