High-order extended Born approximations for EM scattering by buried dielectric objects

Finding fast solutions for the electromagnetic (EM) scattering by dielectric objects buried in lossy earth is very important in near-surface geophysical exploration and landmine detection. Although conjugate gradient fast Fourier transform (CG-FFT) algorithms are much more efficient than the conventional method of moments (MoM), they are still not fast enough because many iterations are required. Consequently, some approximate methods, like the Born approximation and the extended Born (ExBorn) approximation, are usually used in the detection of buried objects. The ExBorn approximation is the more accurate, but it requires O(N/sup 2/) computational complexity (N is the number of unknowns). Recently, we proposed a fast ExBorn method using the FFT technique (Cui, T.J. et al., IEEE APS Int. Symp., vol.II, p.570-3, 2002), where the computational complexity is proportional to CN log N with a small coefficient C. Hence, ExBorn is much more efficient than the CG-FFT algorithm. However, the ExBorn approximation is less accurate when the target contrast is high. We derive high-order ExBorn approximations, all of which have closed-form expressions. Using the FFT technique, these approximations can be evaluated at a cost of O(N log N). Compared with full-wave analysis, high-order ExBorn approximations are more accurate than ExBorn.