Reconstruction of one-dimensional dielectric profiles
Giuseppe Mazzarella, Gaetano Panariello · Journal of the Optical Society of America A · 1991
The problem of the reconstruction of one-dimensional profiles from frequency-domain reflection measurements is examined. A new reconstruction strategy, able to give accurate reconstructions for continuous as well as for discontinuous profiles, was developed and tested. First a Volterra series expansion of the functional relation between the reflection coefficient and the refractive-index profile was established and recast as a Padeé approximant. Then a spectral-line-estimation method, the Prony method, was employed, instead of the usual numerical integration, to compute the Fourier transform of the reflection coefficient. Finally, for a further improvement of the reconstruction, a Newton-like iterative scheme was devised. The examples presented show the feasibility of the proposed strategy.