(43-4) 10 * << * >> * Russian * English * Content * All Issues

Reconstruction of wavefront distorted by atmospheric turbulence using a Shack-Hartman sensor

V.V. Lavrinov1, L.N. Lavrinova1

V.E. Zuev Institute of Atmospheric Optics SB RAS, 1, Academician Zuev Square, 634055, Tomsk, Russia

 PDF, 1467 kB

DOI: 10.18287/2412-6179-2019-43-4-586-595

Pages: 586-595.

Full text of article: Russian language.

The reconstruction of a wave front containing random phase distortions of the light field is considered. The reconstruction is performed by a Hartmann method based on the approximation of the wave function by Zernike polynomials using estimates of local slopes. The slope values depend on the algorithms by which they are determined. The number of slopes is proportional to the number of focal spots recorded in the plane of the receiving device, which varies depending not only on the raster dimension, but also on the parameters of turbulence, design features of the receiving devices, as well as being restricted by the orthogonality of Zernike polynomials. Results of numerical experiments are given, which will be taken into account when creating adaptive optics systems for correcting strong turbulent distortions of the optical radiation.

adaptive optics system, atmospheric turbulence, phase fluctuations, lenslet

Lavrinov VV, Lavrinova LN. Reconstruction of wavefront distorted by atmospheric turbulence using a Shack-Hartman sensor. Computer Optics 2019; 43(4): 586-595. DOI: 10.18287/2412-6179-2019-43-4-586-595.


  1. Razgulin AV, Kuzhamaliyev YZh, Goncharov AS, Larichev AV. A variational method for wavefront reconstruction from Shack–Hartman sensor measurements [In Russian]. Atmospheric and Oceanic Optics 2017; 30(1): 104-108. DOI: 10.15372/AOO20170114.
  2. Thomas S, Fusco T, Tokovinin A, Nicolle M, Michau V, Rousset G. Comparison of centroid computation algorithms in a Shack–Hartmann sensor. Mon Not Royal Astron Soc 2006; 371(1): 323-336. DOI: 10.1111/j.1365-2966.2006.10661.x.
  3. Thomas S. Optimized centroid computing in a Shack-Hartmann sensor. Proc SPIE 2004; 5490: 1232-1246.
  4. Vargas J, Restrepo R, Estrada JC, Sorzano COS, Du Y-Z, Carazo JM. Shack–Hartmann centroid detection using the spiral phase transform. Appl Opt 2012; 51(30): 7362-7367. DOI: 10.1364/AO.51.007362.
  5. Kong F, Polo MC, Lambert A. Centroid estimation for a Shack-Hartmann wavefront sensor based on stream processing. Appl Opt 2017; 56(23): 6466-6475. DOI: 10.1364/AO.56.006466.
  6. Wang Y, Chen X, Cao Z, Zhang X, Liu C, Mu Q. Gradient cross-correlation algorithm for scene-based Shack–Hartmann wave-front sensing. Opt Express 2018; 26(13): 17549-17562. DOI: 10.1364/OE.26.017549.
  7. Li Z, Li X. Centroid computation for Shack–Hartmann wavefront sensor in extreme situations based on artificial neural networks. Opt Express 2018; 2(24): 31675-31692. DOI: 10.1364/OE.26.031675.
  8. Shack RV, Platt BC. Production and use of a lenticular Hartmann screen. J Opt Soc Am 1971; 61: 656-660.
  9. Taranenko VG, Shanin OI. Adaptive optics in instruments and devices [In Russian]. Moscow: "CNIIatominform" Publisher; 2005. ISBN: 5-87911-123-7.
  10. Cui M, Hovenier JN, Ren Y, Polo A, Gao JR. Terahertz wavefronts measured using the Hartmann sensor principle. Opt Express 2012; 20(13): 14380-14391. DOI: 10.1364/OE.20.014380.
  11. Richter H, Greiner-Byor M, Desmann N, Pfund J, Wienold M, Schrottke L, Hey R, Grahn HT, Hyubers H-W. Terahertz wave-front measurement with a Hartmann sensor. Appl Phys Lett 2012; 101: 031103. DOI: 10.1063/1.4737164.
  12. Tokovinin А. Adaptive optics lectures. Source: <http://www.ctio.noao.edu/~atokovin/tutorial/>.
  13. Poleshchuk AG, Sedukhin AG, Trunov VI, Maksimov VG. Hartmann wavefront sensor based on multielement amplitude masks with apodized apertures [In Russian]. Computer Optics 2014; 38(4): 695-703.
  14. Lukin VP, Botygina NN, Emaleev ON, Korol'kov VP, Lavrinova LN, Nasyrov RK, Poleshchuk AG, Cherkashin VV. Shack-Hartmann sensor based on a low-aperture off-axis diffraction lens array. Optoelectronics, Instrumentation and Data Processing 2009; 45(2): 161-170. DOI: 10.3103/S8756699009020101.
  15. Antoshkin LV, Botygina NN, Bol'basova LA, Emaleev ON, Konyaev PA, Kopylov EA, Kovadlo PG, Kolobov DYu, Kudryashov AV, Lavrinov VV, Lavrinova LN, Lukin VP, Chuprakov SA, Selin AA, Shikhovtsev AYu. Adaptive optics system for solar telescope operating under strong atmospheric turbulence [In Russian]. Atmospheric and oceanic optics 2016; 29(11): 895-904. DOI: 10.15372/AOO20161101.
  16. Shlenov SA, Vasiltsov VV, Kandidov VP. Energy parameters of CO2 laser radiation focused in a turbulent atmosphere under wind-dominated thermal blooming [In Russian]. Atmospheric and Oceanic Optics 2016; 29(4); 324-330. DOI: 10.15372/AOO20160302.
  17. Lukin VP, Fortes BV. Adaptive formation of beams and images in the atmosphere [In Russian]. Novosibirsk: Publishing House of the Institute of Atmospheric Optics SB RAS; 1999.
  18. Shanin OI. Adaptive optics systems for correction of slopes. Resonant adaptive optics [In Russian]. Moscow: "Tehnosphera" Publisher; 2013.
  19. Rukosuev AL, Kudryashov AV, Lylova AN, Samarkin VV, Sheldakova YuV. Adaptive optics system for real-time wavefront correction [In Russian]. Atmospheric and oceanic optics 2015; 28(2): 189-195.
  20. Fried DL. Statistics of a geometric representation of wavefront distortion. J Opt Soc Am 1965; 55(11): 1427-1435.
  21. Noll RJ. Zernike polynomials and atmosphere turbulence. J Opt Soc Am 1976; 66(3): 207-211.
  22. Robbins M, Solomitsky D. Registration of single photons using a CCD with electron multiplication [In Russian]. Source: <http://www.npkphotonica.ru/images/single_photon_imaging_using_a_ccd_and_electron_multiplication_rus.pdf>.
  23. Artyshchenko SV, Golovinski PA, Chernov RA. Reconstruction of the wavefront phase with the use of a complex neural network [In Russian]. Atmospheric and Oceanic Optics 2014; 27(10): 932-936.
  24. Botygina NN, Emaleev ON, Konyaev PA, Kopylov EA, Lukin VP. The development of components for creation of adaptive optics system for the solar telescope [In Russian]. Atmospheric and Oceanic Optics 2017; 30(11): 990-997. DOI: 10.15372/AOO20171113.
  25. Yagnyatinskiу DA, Lyakhov DM, Borshevnikov AN, Fedoseev VN. The control algorithm for adaptive optics system based on the focal spot radius minimizing [In Russian]. Atmospheric and Oceanic Optics 2016; 29(11): 949-953. DOI: 10.15372/AOO20161108.
  26. Lavrinov VV. Dynamic control of adaptive optics correction of turbulent distortions in laser [In Russian]. Atmospheric and Oceanic Optics 2016; 30(10): 893-901. DOI: 10.15372/AOO20171013.
  27. Antoshkin LV, Lavrinov VV, Lavrinova LN. Advanced adaptive correction of turbulent distortions based on a Shack–Hartmann wavefront sensor measurements. Optoelectronics, Instrumentation and Data Processing 2012; 48(2): 188-196. DOI: 10.3103/S8756699012020124.
  28. Antoshkin LV, Lavrinov VV, Lavrinova LN, Lukin VP. Using photodetectors in Shack–Hartmann wavefront sensors measurements. Optoelectronics, Instrumentation and Data Processing 2012; 48(2): 146-152. DOI: 10.3103/S8756699012020069.
  29. Lavrinov VV, Lavrinova LN, Tuev MV. Wavefront reconstruction based on the results of light-field conversion by a Shack-Hartmann sensor. Optoelectronics, Instrumentation and Data Processing 2013; 49(3): 305-312. DOI: 10.3103/S8756699013030138.
  30. Klebanov YaM, Karsakov АV, Honina SN, Davydov AN, Polyakov KA. Wave front aberration compensation of spacecraft telescopes with telescope temperature field adjustment [In Russian]. Computer Optics 2017; 41(1): 30-36. DOI: 10.18287/0134-2452-2017-41-1-30-36.
  31. Reddy AK, Martinez-Corral M, Khonina SN, Karpeev SV. Focusing of light beams with the phase apodization of the optical system [In Russian]. Computer Optics 2018; 42(4): 620-626. DOI: 10.18287/2412-6179-2018-42-4-620-626.
  32. Mahajan VN. Zernike annular polynomials for imaging systems with annular pupils. J Opt Soc Am 1981; 71: 75-85.
  33. Tolstoba ND. Gram-Schmidt technique for aberration analysis in telescope mirror testing. Proc SPIE 1991; 3785: 140-151.

© 2009, IPSI RAS
151, Molodogvardeiskaya str., Samara, 443001, Russia; E-mail: ko@smr.ru ; Tel: +7 (846) 242-41-24 (Executive secretary), +7 (846) 332-56-22 (Issuing editor), Fax: +7 (846) 332-56-20