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

被引：0

作者：

Arbuzov E.V. ^{[1
,2
]}

Arbuzov V.A. ^{[1
]}

Dubnishchev Yu.N. ^{[1
]}

Zolotukhina O.S. ^{[1
]}

机构：

[1] Kutateladze Institute of Thermophysics, Siberian Branch of the Russian Academy of Sciences

[2] Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

来源：

Scientific Visualization | 2023年 / 15卷 / 04期

关键词：

Gauss-Newton method; Hilbert optics; optimization; phase function;

D O I：

10.26583/sv.15.4.05

中图分类号：

学科分类号：

摘要：

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. © 2023 National Research Nuclear University. All rights reserved.

引用

页码：56 / 67

页数：11

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