Diffraction Tomographic Imaging With A Circular Array

Abstract

In the conventional diffraction tomography a linear array is used to receive forward scattered field. Then a standard algorithm like back propagation or Fourier domain interpolation is used for reconstruction of the object. A circular array which captures both forward and backward scattered field has been proposed. A new theorem is proposed, which states that the scattered field measured with a large circular array surrounding the object is proportional to the Fourier transform of the object profile taken on the circumference of a circle of radius equa1 to the wave number and centered at (-k0 cosZO, -k0 sin Z0). The circular array outperforms in two counts. Firstly, a larger bandwidth of Fourier transform is used for reconstruction. Secondly, in circular array since the scattered field itself is related to the object Fourier transform, the reconstruction is free from the errors induced by finite array size. The effect of broad band illumination has been studied. A fewer number of illuminations appear to produce a reconstruction which is possible only with a large number of illuminations but narrow band illumination. Thus a trade off between the number of illumination angles and the bandwidth of the source exists.