Multifrequency backscattering tomography for constant and vertically varying backgrounds

Abstract

AbstractTo improve the resolution and image quality of the SFDT (Sigle‐Frequency Diffraction Tomography), a special fast multi‐frequency imaging method: Multi‐Frequency Backscattering Tomography (MFBT) is introduced in this paper. The method uses only the backscattered waves (after plane wave decomposition) while maintaining the merit of multi‐frequency method. The method is formulated for both the constant and vertically varying backgrounds. For the latter case the WKBJ approximation is used for the background Green's function. Formulas are derived both for volume scattering using the Born approximation and for boundary scattering using the physical optics approximation. Two reconstruction methods are presented. The backpropagation method can be used and has the same computation speed for both the constant and vertically varying backgrounds. Meanwhile the direct FT method is only formulated for the constant background, in which the backpropagation in z‐direction is implemented by FFT and therefore the computation speed is significantly increased. Compared with the SFDT using backpropagation reconstruction, the MFBT is nearly Nz/log2Nz faster, where Nz is the number of grid points in z‐direction, and at the same time has a much better resolution and image quality. When Nz is big, the time saving is remarkable. Compared with other multi‐frequency methods such as the multi‐frequency holography (prestack migration), the speeding factor becomes NfNz/log2Nz, where Nf, is the number of frequencies used. Numerical simulations for both constant and vertically varying backgrounds are performed to demonstrate the feasibility of the method and the quality of reconstructed images for different situations. Examples are also given to show that when the reconstruction procedure of constant background is applied to the case of vertically varying background, the image quality will be greatly deteriorated.©1994 John Wiley & Sons Inc