The Born approximation
(single scattering theory) uses the perturbation theory to describe the field itself, and in the Rytov approximation, the perturbation theory is employed to derive the complex phase associated with the field logarithm.
Hence, we must find the Born approximation
for V(x)-[m.sup.2.sub.L] rather than the one for the pseudopotential [V.sub.P](x) (see (19)).
Such VPRT reformulation also enables an interesting interpretation in terms of internal field approximation, which is consistent with the gently rough assumption, thus providing an additional insight into the first-order approximation (which is slightly different from the usual Born approximation
It is worth remarking that since the approximated virtual total field is tailored to the target (in an implicit fashion) via the FM preprocessing, the adopted linearization is deeply different from the Born approximation
wherein the target is instead neglected.
Among his topics are characterizing the host medium, the two-dimensional scattering equations for dielectric and magnetic targets, the Born approximation
, diffraction tomography, three-dimensional scattering equations, the singular value decomposition, and numerical and experimental examples.
These methods include Born approximation
, neural-networks , and Levenberg-Marquardt method .
We obtain an analytical expression in the first-order Born approximation
, which can be easily used to calculate the diffraction field of MDECBFZP in the Fresnel diffraction region.
Conventional dielectric profile estimation methods use Born approximation
at a preliminary stage to solve the inverse scattering problem iteratively.
The differential ionisation cross-section of the S-shell of the atom of the target (S = K, L, M, ...) in the Born approximation
of planar waves (PWBA) : is.
(The parameter b is equal to zero for the standard vector--axial vector type of weak interactions, and the parameter D is related to time-odd correlations of spin and momenta, therefore in the first Born approximation
, it is defined by a time reversal violating process.)
In this framework, the adoption of the simplified linear model provided by the Distorted Born Approximation
(DBA) (7) allows effective algorithms to be generated, which are needed if the investigation domains are electrically large (which is often the case for subsurface prospecting applications).
To solve this problem, under conventional methods such as the Born approximation
, we use the principles of linear scattering to determine a linear relationship between measured returns and target shape.