An Exact Theory for Coherent Nondestructive Evaluation: The Application of the Bojarski Exact Inverse Scattering Theory to the Remote Probing of Inhomogenous Media

In an inverse scattering problem, the fields in the inhomogeneous wave equation are known, and it is desired to solve for the source term. N. N. Bojarski has recently derived an Exact Inverse Scattering Theory for such "inverse source" problems. The problem of determining the generalized refractive index (i.e., the complex permeability and dielectric constant for an electromagnetic problem, or the velocity and absorption for an acoustic problem) distribution of an inhomogeneous medium from measurements of the fields scattered by the medium can be treated using this theory. This solution is applicable to all remote probing problems, and in particular, to nondestructive evaluation (NDE) using coherent radiation. Although this paper uses scalar notation, all of the results have been shown to apply to the general, full vector field and tensor medium quantities. The equations applicable to the electromagnetic cases are used; however, the theory and results apply equally well to the acoustic equations.