Algorithm for correcting star image jitter in a ground-based optical telescope using an artificial reference source

Publication in Journal of Optical Technology

For Russian citation (Opticheskii Zhurnal):

Клеймёнов В.В., Новикова Е.В. Алгоритм коррекции дрожания изображения звезды в наземном оптическом телескопе с помощью искусственного опорного источника // Оптический журнал. 2024. Т. 91. № 1. С. 25–32. http://doi.org/10.17586/1023-5086-2024-91-01-25-32

Kleymionov V.V., Novikova E.V. Algorithm for correcting star image jitter in a ground-based optical telescope using an artificial reference source [in Russian] // Opticheskii Zhurnal. 2024. V. 91. № 1. P. 25–32. http://doi.org/10.17586/1023-5086-2024-91-01-25-32

For citation (Journal of Optical Technology):

Viktor V. Kleymionov and Elena V. Novikova, "Algorithm for correcting star image jitter in a ground-based optical telescope using an artificial reference source," Journal of Optical Technology. 91(1), 14-18 (2024). https://doi.org/10.1364/JOT.91.000014

Abstract:

Subject of study. Analytical correlation dependence between random vectors characterizing the positions of the predicted (calculated) image of an inconspicuous star and the measured image of an artificial reference source — a laser reference star in the focal plane of a ground-based adaptive optical telescope. The aim of this work is to develop, based on the correlation theory, an algorithm for correcting the jitter of the predicted image of an inconspicuous natural star in the focal plane of the telescope based on the recorded image of the laser reference star. Method. The algorithm is based on the provisions of the correlation theory for determining the vector of the predicted position of the image of an inconspicuous star during a short exposure, taking into account the measured position of the image of an artificial reference source (in the form of linear regression). Main results. Analytical expressions are obtained for the modulus of the vector of the predicted position of the image of an inconspicuous star and its inclination relative to the vector of the measured position of the image of the laser reference star. On their basis, an algorithm for correcting the image jitter of an inconspicuous star in a ground-based optical telescope using an artificial reference source was developed. For monostatic and bistatic schemes of laser guide star formation, the module of the star image vector and its inclination relative to the laser guide star image vector are calculated for various ratios of the aperture diameters of the telescope and the probing laser. Practical significance. The results obtained in this article can be used in the synthesis of ground-based adaptive optical telescopes when observing small-sized space objects of natural and artificial origin, taking into account the astroclimatic features in their geographic locations.

Keywords:

adaptive optics, laser reference star, monostatic and bistatic schemes, image jitter, correlation coefficient

OCIS codes: 010.1080, 110.1085, 010.3310, 010.1330, 010.1300

References:

Lukin V.P. Adaptive optics in the formation of optical beams and images // Physics Uspekhi. 2014. V. 57. № 6. С. 556–592. http://dx.doi.org/10.3367/UFNe.0184.201406b.0599

2. Bolbasova L.A., Lukin V.P. Adaptive correction of atmospheric distortions of optical images based on an artificial reference source [in Russian]. Moscow: ''Fizmatlit'' Publ., 2012. 125 p.

3. Hardy J.W. Adaptive optics for astronomical telescopes. Oxford: University Press, 1998. 437 p.

4. Tyson R.K. Principles of adaptive optics, 3ded. N.Y.: CRC Press, 2010. 350 p.

5. Sviridov K.N. Technologies for achieving high angular resolution of optical atmospheric vision systems [in Russian]. Moscow: 'Znanie'' Publ., 2005. 452 p.

6. Lukin V.P. Atmospheric adaptive optics [in Russian]. Novosibirsk: ''Nauka'' Publ., 1986. 250 p.

7. Foy R., Foy F.C. Laser guide star: Principle, cone effect and tilt measurement // Optics in Astrophysics / Springer, 2006. P. 249–273. http://dx.doi.org/10.1007/1-4020-3437-7_15

8. Kleymionov V.V., Novikova E.V. Extremely large ground-based optical telescopes [in Russian] // News of Universities. Instrumentation. 2021. № 1. P. 5–20. https://doi.org/10.17586/0021-3454-2021-64-1-5-20

9. Rigaut F. On practical aspects of laser guide star // C.R. Physique. 2005. V. 6. P. 1089–1098. http://dx.doi.org/10.1016/j.crhy.2005.11.014

10. Bolbasova L.A., Lukin V.P. Possibilities of adaptive optical correction of wavefront tilts when using signals from traditional and polychromatic laser guide stars [in Russian] // Atmosphere and Ocean Optics. 2022. V. 35. № 10. P. 1–7. https://doi.org/10.15372/AOO20221011

11. Lukin V.P., Fortes B.V. Comparison of the maximum efficiency of various schemes for the formation of laser guide stars [in Russian] // Atmosphere and Ocean Optics. 1997. V. 10. № 1. P. 56–65.

12. Lukin V.P., Fortes B.V. Adaptive formation of beams and images in the atmosphere [in Russian]. Novosibirsk: Publishing house SO RAN, 1999. 314 р.

13. Fried D.L. Statistics of a geometric representation of wavefront distortion // JOSA. 1965. V. 55. № 11. P. 1427–1435. http://dx.doi.org/10.1364/JOSA.56.000410

14. Kleymionov V.V., Vozmishchev I.Yu., Novikova E.V. Efficiency of using monostatic and bistatic schemes for the formation of laser guide stars [in Russian] // Journal of Optical Technology. 2022. V. 89. № 11. P. 656–660. https://doi.org/10.1364/JOT.89.000656

15. Kleymionov V.V., Novikova E.V. Analysis of the effectiveness of monostatic and bistatic schemes for the formation of LOCs based on correlation theory [in Russian] // Atmosphere and Ocean Optics. 2023. № 4. P. 331–336. https://ao.iao.ru/ru/content/vol.36-2023/iss.04/10

16. Korenny A.V., Kuleshov S.A. Fundamentals of statistical theory of radio engineering systems [in Russian]. Moscow: ''Radiotehnika'' Publ., 2021. 240 p.

17. Ventzel E.S. Probability theory [in Russian]. Moscow: ''Vysshaya Shkola'' Publ., 2006. 575 p.

18. Tikhonov V.I. Statistical radio engineering [in Russian]. Moscow: ''Radio i Svyaz'' Publ., 1982. 624 p.