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

Abstract

A method for reconstructing phase disturbances of a probing light field using the iterative Gauss-Newton algorithm is discussed as part of the Hilbert diagnostics development of gaseous, condensed and reacting media. In this case, the need to determine second derivatives is eliminated, which simplifies the calculations. The method consists of selecting a phase profile, which is specified by a Bezier curve, and hilbertogram calculating. The coincidence of the reference and reconstructed hilbertograms serves as a criterion for the results reliability. The Jacobian matrix for the nonlinear integral operator of Hilbert visualization is obtained. The algorithm is analyzed using a test function. The method development is associated with the algorithm application to the processing of experimental results, including the reconstruction of complex structures in which the phase function is described by several Bezier polynomials.