Application of the Gauss–Newton optimization algorithm for phase-function reconstruction from interferometric data in flame diagnostics

Subject of study. Reconstruction of the phase structure of optical radiation in the interferometry of reacting media (flames) is studied. Aim of study. A Gauss–Newton-algorithm-based method is developed to enable automatic reconstruction of the phase profile of the investigated reacting medium, minimize ambiguity in the complex regions of the interference pattern, and determine the temperature of the diagnosed flame. Method. Detection of the phase structure of the probing radiation is based on the Gauss–Newton algorithm, which involves selecting a phase profile represented as a sum of Bézier curves, followed by calculating the interferogram and comparing it with experimental data. Agreement between the structures of the experimental and reconstructed interferograms serves as the reliability criterion. The refractive index of the flame is calculated from the reconstructed phase function and subsequently converted to temperature. The use of the Gauss–Newton algorithm is justified by its efficiency and ease of implementation. Main results. A Gauss–Newton-optimization-based method for reconstructing the phase structures of reacting media from interferometric data has been developed. The method is used to process a burner flame interferogram; the phase function is reconstructed, and the temperature distribution across a cross-section is determined. Practical significance. The results are significant for the development of a method that enables the automatic diagnostics of phase and temperature fields using interferometric data. Further application is intended for investigating the combustion of premixed CH ₄ and CH ₄ /H ₂ mixtures with air, which are promising fuels in the field of hydrogen energy.