Another approach is proposed here to invert a boundary-value problem for the Riccati equation. Its main point is that the variation of unkown permittivity profile at each iteration step is represented in terms of reflection coefficient (which is unknown, too) rather than in terms of any standard system of orthogonal functions. Then a set of differential equations is solved for the reflection coefficient distribution and partial variations of the permittivity profile are calculated with subsequent integration over the frequency band of operation. Such representation of the profile reflects adequately interaction of the electromagnetic wave with the inhomogeneous medium resulting in fast convergence of the iterative procedure.

The method was applied to two important NDT schemes: a guided wave case, when the propagation constants of a set of eigenmodes in the inhomogeneous slab are used as input data for the reconstruction, and usual reflectometry of stratified half-space. Computer simulations performed for different kinds of profiles showed good convergence of the solution retaining even for such a strong discontinuity as air gap inside the slab of high permittivity value. The method is in principle exact, since no approximations are used in the derivation. However, the accuracy of reconstruction of the discontinuous profile depends on the highest frequency in the input data. An addition of uniformly distributed random error to the input data demonstrated also good robustness of the algorithm. REFERENCES

1. P. V. Frangos and D. L. Jaggard, "The reconstruction of stratified dielectric profiles using successive approximations", IEEE Trans. on Antennas and Propagation, Vol. AP-35, No. 11, pp. 1267-1272, 1987 [2]
2. D. L. Jaggard and Y. Kim, "Accurate one-dimensional inverse scattering using a nonlinear renormalization technique", J. Opt. Soc. Am. A, vol. 2 No. 11, pp. 1922-1930, 1985