vestifmИзвестия Национальной академии наук Беларуси. Серия физико-математических наукProceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series1561-24302524-2415The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"10.29235/1561-2430-2026-62-1-59-72vestifm-876Research ArticleФИЗИКАPHYSICSСтруктурный подход к решению томографической задачи адаптивной оптики: реконструкция турбулентности в объемеStructural approach to the Adaptive Optics tomography problem: the volume turbulence reconstructionhttps://orcid.org/0000-0001-9215-3570ПетровП. К.PiatrouP. K.

Петров Петр Казимирович – кандидат физико-математических наук, ведущий научный сотрудник

пр. Независимости, 68-2, 220072, Минск

Piotr K. Piatrou – Ph. D. (Physics and Mathematics), Leading Researcher

68-2, Nezavisimosti Ave., 220072, Minsk

p.piatrou@dragon.bas-net.byИнститут физики имени Б. И. Степанова Национальной академии наук БеларусиБеларусьB. I. Stepanov Institute of Physics of the National Academy of Sciences of BelarusBelarus2026310320266215972Copyright © Петров П.К., 20262026Петров П.К.Piatrou P.K.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestifm.belnauka.by/jour/article/view/876

Адаптивная оптика как относительно новое направление развития современных оптических систем позволяет корректировать искажения, связанные с распространением света в турбулентной атмосфере и получать изображения дифракционного качества. Поскольку это требует компьютерной обработки больших потоков информации в реальном времени, ключевой проблемой является снижение вычислительной сложности соответствующих математических алгоритмов. В статье предложен подход, учитывающий структурные свойства как атмосферной турбулентности, так и самой активной оптической системы. Продемонстрирована возможность одновременного учета разреженной и сверточной (теплицевой) структуры адаптивной коррекции в одном алгоритме. Дан анализ многосопряженной адаптивной оптической системы и сравнение естественной сложности алгоритма, индуцированного его структурой, со сложностью разреженного алгоритма. Показано применение структурного подхода к достаточно трудоемкому алгоритму томографической объемной реконструкции турбулентной фазы с получением благодаря этому существенного ускорения вычислений.

Adaptive Optics as a relatively new trend in the modern optical systems allows correcting the perturbations related to light propagation in the turbulent atmosphere obtaining the diffraction-limited images. Because it requires computer processing of large information flow in real time, a key problem lays in finding the mathematical algorithms with reduced computational complexity. The paper proposes the approach, which takes into account structural properties of both atmospheric turbulence and the most active optical system. The possibility was demonstrated of one-dimensional accounting of sparse and convolution-like (Toeplitz) structure of adaptive correction in one algorithm. The analysis is made of Multi-Conjucate Adaptive Optics and the comparison was conducted of the nature complexity of the algorithm induced by this strucute with the complexity of sparse algorithm. It was demonstrated how the structural approach can be applied to the quite laborious tomographic turbulence volume reconstruction phase with obtaining due to this a significant computational speed-up.

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The authors declare that there are no conflicts of interest present.