ABSTRACT
As previously discussed in Section 4 .3, the Born approximation seems to generally perform well when the target is a “weak” scatterer, since one can replace the total field inside the target by the known incident field, and this leads naturally to the Fourier transform relationship described earlier . However, as the permittivity of the target increases, the performance of “Born” algorithm tends to decrease . This is not unexpected due to the fact that less of the incident wave might be penetrating and propagating through the target, but is reflected off the surface of the target as well as being scattered multiple times from inhomogeneities that exist inside the target . The reflected wave emerging from more highly structured scattered field components needs to be interpreted as carrying information about V(r) (see Equations 4 .7 and 4 .28) or, depending on how the scattered field is processed, as noise-like terms arising from strong scattering that one might be able to remove . In the latter case, if the noise-like terms can be identified and removed or attenuated, then this can ideally reduce a strongly scattering target to one that can be imaged more like a weakly scattering one . In the cepstral method, the total field estimated within the target volume is regarded as a form of spatial noise to be removed . When this is justified, the reconstructed image of the target based on assuming the first Born approximation can be expressed as
V VBA inc
( ) , ( )
( , ) ,
r r r r r r r
≈
Ψ Ψ
(8 .1)
where 〈 〉Ψ Ψ( , )/ ( , )r r r r inc inc inc is a symbolic representation for a complex and noise-like term with a characteristic range of spatial frequencies dominated by the average local wavelength of the source . The problem is now reduced to a complex filtering problem in which the multiplicative term 〈 〉Ψ Ψ( , )/ ( , )r r r r inc inc inc needs to be filtered out of the data .
