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.
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.
In the conventional first-order Born approximation , the incident field [U.
Conventional dielectric profile estimation methods use Born approximation
at a preliminary stage to solve the inverse scattering problem iteratively.
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).
A detailed description of the apparatus and techniques required for these experiments is provided, and theoretical approaches to data analysis are described, including approximate methods such as the Master formula, the Born approximation
, Parratt's algorithm and the Distorted Wave Approximation.
Using this in conjunction with the Born approximation
, t = v, the optical potential then becomes
So researchers made use of the Born approximation
, a mathematical rule that can be used when the object of interest is small and transparent.
The numerical data in Tables 1 and 2 can be extended to higher incident energies by using the well known Bethe formula  for the plane-wave Born approximation
for fast (but nonrelativistic) incident electrons.
Results of systematic plane wave Born approximation
calculations with exchange for K, L, and M shell ionization cross sections over the range of electron energies used in microanalysis are presented.