Vol. 36, issue 04, article # 10

Abstract:

The efficiency of monostatic and bistatic schemes of the formation of a laser guide staris is analyzed on the basis of the correlation theory of Gaussian random processes. In the focal plane of a ground-based optical telescope, the position of a natural star relative to the measured instantaneous position of a laser guide star is calculated based on Pearson's linear regression. An expression is derived for the correlation coefficient of random angular displacements of images of a natural star and a laser guide star. Based on this expression, the normalized dispersion of uncompensated (residual) angular errors is determined. The results of calculations for monostatic and bistatic schemes of the formation of a laser guide star are presented, which make it possible to estimate and compare their efficiency.
 

Keywords:

adaptive optics, atmospheric turbulence, laser guide star, monostatic and bistatic schemes, image jitter, angle correlation coefficient

References:

1. Lukin V.P. Formirovanie opticheskikh puchkov i izobrazhenij na osnove primeneniya sistem adaptivnoj optiki // Uspekhi fiz. nauk. 2014. V. 184, N 6. P. 599–640.
2. Bol'basova L.A., Lukin V.P. Adaptivnaya korrektsiya atmosfernykh iskazhenij opticheskikh izobrazhenij na osnove iskusstvennogo opornogo istochnika. M.: Fizmatlit, 2012. 125 p.
3. Hardy J.W. Adaptive Optics for Astronomical Telescopes. Oxford: Oxford University Press, 1998. 437 p.
4. Tyson R.K. Principles of Adaptive Optics. New York: CRCPress, 2010. 350 p.
5. Foy R., Foy F.C. Laser guide star: Principle, cone effect and tilt measurement // Optics in Astrophysics. England: Springer, 2006. P. 249–273.
6. Quirrenbach A. The Effects of atmospheric turbulence on astronomical observations // Adaptive Optics for Vision Science and Astronomy ASP. Conf. Ser. 2005. P. 129–144.
7. Rigaut F. On practical aspects of laser guide star // C.R. Phys. 2005. V. 6. P. 1089–1098.
8. Bol'basova L.A., Lukin V.P. Vozmozhnosti adaptivnoj opticheskoj korrektsii naklonov volnovogo fronta pri ispol'zovanii signalov ot traditsionnoj i polikhromaticheskoj lazernoj opornykh zvezd // Optika atmosf. i okeana. 2022. V. 35, N 10. P. 1–7.
9. Kleymionov V.V., Novikova E.V. Ekstremal'no bol'shie nazemnye opticheskie teleskopy // Izv. vuzov. Priborostroenie. 2021. N 1. P. 5–19.
10. Lukin V.P., Fortes B.V. Sopostavlenie predel'noy effektivnosti razlichnykh skhem formirovaniya lazernykh opornykh zvezd // Optika atmosf. i okeana. 1997. V. 10, N 1. P. 56–65.
11. Lukin V.P., Fortes B.V. Adaptivnoe formirovanie puchkov i izobrazheniy v atmosfere. Novosibirsk: Izd-vo SO RAN, 1999. 314 p.
12. Korennoy A.V., Kuleshov S.A. Osnovy statisticheskoy teorii radiotekhnicheskikh sistem. M.: Radiotekhnika, 2021. 240 p.
13. Lukin V.P. Ostatochnye iskazheniya, obuslovlennye razmerom opornogo istochnika // Optika atmosf. i okeana. 2014. V. 27, N 11. P. 949–956; Lukin V.P. Residual distortions caused by the size of a reference source // Atmos. Ocean. Opt. 2015. V. 28, N 2. P. 107–114.
14. Lukin V.P. Atmosfernaya adaptivnaya optika. Novosibirsk: Nauka, 1986. 250 p.
15. Fried D.L. Statistics of a geometric representation of wavefront distortion // J. Opt. Soc. Am. 1965. V. 55, N 11. P. 1427–1435.
16. Sovremennye problemy atmosfernoy optiki / pod red. akad. V.E. Zueva. L.: Gidrometeoizdat, 1999. V. 5. 371 p.
17. Fried D.L. Anisoplanatism in adaptive optics // J. Opt. Soc. Am. 1982. V. 72, N 1. P. 52–61.