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 algorithm, 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 development of the method and its applications is associated with the application of the algorithm to the processing of experimental results.

Cite: Arbuzov E.V. , Zolotukhina O.S.
Gauss-Newton method application in the problem of phase function reconstructing from hilbertograms
Eurasian Journal of Mathematical and Computer Applications. 2023. V.11. N4. P.4 - 13. DOI: 10.32523/2306-6172-2023-11-4-4-13 WOS Scopus РИНЦ OpenAlex

Dates:

Submitted:	Sep 30, 2023
Accepted:	Oct 6, 2023
Published print:	Nov 27, 2023
Published online:	Nov 27, 2023

Identifiers:

Web of science:	WOS:001110697200009
Scopus:	2-s2.0-85178415486
Elibrary:	65442630
OpenAlex:	W4389518824

Citing: Пока нет цитирований

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