Synthetic Aperture Diffraction Tomography and Its Interpolation-Free Computer Implementation

Abstract

A new tomographic imaging technique is presented that requires only two rotational positions of an object. Although ideally the angle between the two rotational positions should be 90°, theory predicts that valid results should be obtainable, albeit with reduced spatial resolution, even when this condition is not satisfied. For each rotational position of the object, the data is collected most efficiently by using arrays on both the transmit and the receive sides; the elements of the transmit array are fired sequentially, and for each such firing the received field is measured over all the elements of the receive array. It is shown that this measurement strategy fills up the Fourier space, from which the object can be recovered by simple Fourier inversion. This imaging strategy was derived from the equations of propagation in an inhomogeneous medium with Born and Rytov approximations. A digital implementation is also presented of the proposed algorithm that requires no interpolations in either the frequency or the space domain, and can be carried out with only 2N FFT's for reconstructing an N X N image. Since no interpolations are carried out whatsoever, no computational errors are introduced by the algorithm itself. The total computational complexity of the procedure is of the order of O(N3) as compared to 0(N4) for a filtered-backpropagation algorithm and O(N2log N) for procedures based on interpolation in the frequency domain. Some computer simulation results have been included to demonstrate the numerical accuracy of the algorithm. © 1984 IEEE