GAUSS-NEWTON METHOD APPLICATION IN THE PROBLEM OF PHASE FUNCTION RECONSTRUCTING FROM HILBERTOGRAMS

Abstract

The problem of phase function reconstructing in Hilbert diagnostics of gaseous, condensed and reacting media is discussed in the work. The method for reconstructing the phase disturbances structure of a probing light field, based on the iterative Gauss-Newton al- gorithm, is proposed.This method does not require the second derivatives determination and greatly reduces the number of calculations.It consists in the sequential selection of a complex phase profile, which is specified by the sum of third degree Bezier curves, and the hilbertogram calculation in order to minimize the root-mean-square error between the experimental and reconstructed hilbertograms. The Jacobi matrix for the nonlinear integral operator of Hilbert visualization is calculated. The proposed algorithm was tested on test functions.The devel- opment of the method and its applications is associated with the application of the algorithm to the processing of experimental results.