The Gauss-Newton Method in the Problems of Optimizing the Phase Function Calculation Based on the Hilbert Diagnostic Data

Abstract

The problem of reconstructing the phase function in the Hilbert diagnostics of gaseous, condensed and reacting media is discussed in the paper. The method for restoring the phase disturbances structure of a probing light field based on the iterative Gauss-Newton algorithm is proposed. It does not require the definition of second derivatives and significantly reduces the number of computes. The method consists in successive selection of the phase profile given by the Bezier curve and calculation of the hilbertogram. The reliability of the results is the coincidence of the reference and reconstructed hilbertograms local extrema. The Jacobian matrix of the nonlinear integral operator of the Hilbert visualization is calculated. The proposed algorithm has been certified on test functions. The development of the method and its applications is associated with the processing of experimental results, including complex structures, where the phase function is represented by several Bezier polynomials.