Optimization techniques and inverse problems: Reconstruction of conductivity profiles in the time domain

The iterative probing of an inhomogeneous lossy dielectric slab, whose conductivity is unknown, is discussed. The probing is done in the time domain from the measurements of the field on the interface when this slab is illuminated by a known field. An exact integral formulation is used. Minimization of a cost function, characteristic of the discrepancy between the measured field and the field which would be scattered by a known slab, is specified by the optimization theory. The notion of the adjoint state of the field is introduced. The influence of some parameters of this minimization is studied. Great importance is given to the sensitivity of the probing as function of the amplitude of errors in the data. Such an iterative probing appears fast, accurate, and efficient, even in the case of large errors.