Inverse problem of the theory of laser radiation scattering in a 2D irregular integrated-optical waveguide in the presence of noise

The linear inverse problem of laser-light scattering in a 2D integrated-optical waveguide with statistical irregularities is analyzed in detail in the presence of noise (imperfect input data). An approximately correct solution to the formulated inverse problem of the waveguide scattering of laser radiation is derived upon natural physical and mathematical limitations imposed on the measured scattering pattern. The uniqueness of the solution to the inverse problem and its stability against small variations in the input data are provided by a complex algorithm for the reconstruction of the autocorrelation function of the waveguide irregularities. The algorithm is based on a combination of classical regularization and quasi-optimal filtering on the interval of the variable length that permits achieving a certain super resolution. English Translation Copyright © 2005 by MAIK "Nauka Interperiodica" (Russia)