(45-4) 07 * << * >> * Russian * English * Content * All Issues

Optical detection of values of separate aberrations using a multi-channel filter matched with phase Zernike functions
P.A. Khorin 1, S.G. Volotovskiy 2, S.N. Khonina 1,2

IPSI RAS – Branch of the FSRC "Crystallography and Photonics" RAS,
443001, Samara, Russia, Molodogvardeyskaya 151,
Samara National Research University, 443086, Samara, Russia, Moskovskoye Shosse 34

 PDF, 1802 kB

DOI: 10.18287/2412-6179-CO-906

Pages: 525-533.

Full text of article: Russian language.

The use of a multichannel wavefront sensor matched with phase Zernike functions to determine the type and magnitude of aberration in the analyzed wavefront is investigated. The approach is based on stepwise compensation of wavefront aberrations based on a dynamically tunable spatial light modulator. As criteria for successful detection, not only the magnitude of the correlation peak, but also the maximum intensity, compactness, and orientation of the distribution in each diffraction order are considered. On the basis of numerical simulation, the efficiency of the proposed approach is shown for detecting both weak and strong (up to a wavelength) wavefront aberrations.

wavefront aberrations, Zernike functions, wavefront sensor, multichannel diffractive optical element.

Khorin PA, Volotovskiy SG, Khonina SN. Optical detection of values of separate aberrations using a multi-channel filter matched with phase Zernike functions. Computer Optics 2021; 45(4): 525-533. DOI: 10.18287/2412-6179-CO-906.

This work was supported by the Russian Foundation for Basic Research under grant No. 20-37-90129 (numerical modeling) and the Ministry of Science and Higher Education of the Russian Federation under a government project of the Federal Research Center "Crystallography and Photonics" RAS, 007-GZ/Ch3363/26 (theoretical research).
     The calculations were carried out using a hybrid supercomputer K-100, installed in the Center for Collective Use of the Institute of Applied Mathematics. M.V. Keldysh RAS.


  1. Camacho L, Mico V, Zalevsky Z, Garcia J. Quantitative phase microscopy using defocusing by means of a spatial light modulator. Opt Express 2010; 18: 6755-6766.
  2. Lombardo M, Lombardo G. Wave aberration of human eyes and new descriptors of image optical quality and visual performance. J Cataract Refract Surg 2010; 36(2): 313-320. DOI: 10.1016/j.jcrs.2009.09.026.
  3. Zhao Q, Fan H, Hu S, Zhong M, Baida L. Effect of optical aberration of telescopes to the laser radar. Proc SPIE 2010; 7656: 76565Z. DOI: 10.1117/12.867716.
  4. González-Núñez H, Prieto-Blanco X, De la Fuente R. Pupil aberrations in Offner spectrometers. J Opt Soc Am A 2011; 29: 442-449.
  5. Khonina SN, Ustinov AV, Pelevina E.A. Analysis of wave aberration influence on reducing focal spot size in a high-aperture focusing system. J Opt 2011; 13: 095702. DOI: 10.1088/2040-8978/13/9/095702.
  6. Booth M, Andrade D, Burke D, Patton B, Zurauskas M. Aberrations and adaptive optics in super-resolution microscopy. Microscopy 2015; 64(4): 251-261.
  7. Khonina SN, Kotlyar VV, Kirsh DV. Zernike phase spatial filter for measuring the aberrations of the optical structures of the eye. J-BPE 2015; 1(2): 146-153. DOI: 10.18287/jbpe-2015-1-2-146.
  8. Khorin PA, Khonina SN, Karsakov AV, Branchevskiy SL. Analysis of corneal aberration of the human eye. Computer Optics 2016; 40(6): 810-817. DOI: 10.18287/0134-2452-2016-40-6-810-817.
  9. Wilby MJ, Keller CU, Haert S, Korkiakoski V, Snik F, Pietrow AGM. Designing and testing the coronagraphic modal wavefront sensor: A fast non-common path error sensor for high-contrast imaging. Proc SPIE 2016; 9909: 990921.
  10. Klebanov IM, Karsakov AV, Khonina SN, Davydov AN, Polyakov KA. Wavefront aberration compensation of space telescopes with telescope temperature field adjustment. Computer Optics 2017; 41(1): 30-36. DOI: 10.18287/0134-2452-2017-41-1-30-36.
  11. Rastorguev AA, Kharitonov SI, Kazanskiy NL. Modeling of arrangement tolerances for the optical elements in a spaceborne Offner imaging hyperspectrometer. Computer Optics 2018; 42(3): 424-431. DOI: 10.18287/2412-6179-2018-42-3-424-431.
  12. Abramenko AA. Extrinsic calibration of stereo camera and three-dimensional laser scanner. Computer Optics 2019; 43(2): 220-230. DOI: 10.18287/2412-6179-2019-43-2-220-230.
  13. Martins AC, Vohnsen B. Measuring Ocular Aberrations Sequentially Using a Digital Micromirror Device. Micromachines 2019; 10: 117.
  14. Baum OI, Omel'chenko AI, Kasianenko EM, Skidanov RV, Kazanskiy NL, Sobol' EN, Bolshunov AV, Avetisov SE, Panchenko VYa. Control of laser-beam spatial distribution for correcting the shape and refraction of eye cornea. Quantum Electronics 2020; 50(1): 87-93. DOI: 10.1070/QEL17216.
  15. Mu Q, Cao Z, Hu L, Li D, Xuan L. Adaptive optics imaging system based on a high-resolution liquid crystal on silicon device. Opt Express 2006; 14: 8013-8018.
  16. Ellerbroek BL, Vogel CR. Inverse problems in astronomical adaptive optics. Inverse Probl 2009; 25(6): 063001.
  17. Esposito S, Riccardi A, Pinna E, Puglisi A, Quirós-Pacheco F, Arcidiacono C, Xompero M, Briguglio R, Agapito G, Busoni L, Fini L, Argomedo J, Gherardi A, Brusa G, Miller D, Guerra JC,
  18. Stefanini P, Salinari P. Large Binocular Telescope Adaptive Optics System: new achievements and perspectives in adaptive optics. Proc SPIE 2011; 8149: 814902.
  19. Luki VP. Adaptive optics in the formation of optical beams and images. Phys Usp 2014; 57: 556-592. DOI: 10.3367/UFNe.0184.201406b.0599.
  20. Ji N. Adaptive optical fluorescence microscopy. Nat Methods 2017; 14: 374-380.
  21. Bond CZ, Wizinowich P, Chun M, Mawet D, Lilley S, Cetre S, Jovanovic N, Delorme J-R, Wetherell E, Jacobson S, Lockhart C, Warmbier E, Wallace JK, Hall DN, Goebel S, Guyon O, Plantet C, Agapito G, Giordano C, Esposito S, Femenia-Castella B. Adaptive optics with an infrared pyramid wavefront sensor. Proc SPIE 2018; 10703: 107031Z.
  22. Mahajan VN. Zernike circle polynomials and optical aberration of system with circular pupils. Supp Appl Opt 1994; 33: 8121-8124.
  23. Love GD. Wavefront correction and production of Zernike modes with a Liquid crystal spatial light modulator. Appl Opt 1997; 36: 1517-1525.
  24. Khonina SN, Kotlyar VV, Soifer VA, Wang Y, Zhao D. Decomposition of a coherent light field using a phase Zernike filter. Proc SPIE 1998; 3573: 550-553. DOI: 10.1117/12.324588.
  25. Neil MAA, Booth MJ, Wilson T. New modal wave-front sensor: a theoretical analysis. J Opt Soc Am A 2000; 17: 1098-1107.
  26. Booth MJ. Direct measurement of Zernike aberration modes with a modal wavefront sensor. Proc SPIE 2003; 5162: 79-90.
  27. Sheppard CJR. Zernike expansion of pupil filters: optimization of the signal concentration factor. J Opt Soc Am A 2015; 32(5): 928-933. DOI: 10.1364/JOSAA.32.000928.
  28. Porfirev AP, Khonina SN. Experimental investigation of multi-order diffractive optical elements matched with two types of Zernike functions. Proc SPIE 2016; 9807: 98070E. DOI: 10.1117/12.2231378.
  29. Wilby MJ, Keller CU, Snik F, Korkiakoski V, Pietrow AGM. The coronagraphic Modal Wavefront Sensor: a hybrid focal-plane sensor for the high-contrast imaging of circumstellar environments. A&A 2017; 597: A112.
  30. Degtyarev SA, Porfirev AP, Khonina SN. Zernike basis-matched multi-order diffractive optical elements for wavefront weak aberrations analysis. Proc SPIE 2017; 10337: 103370Q. DOI: 10.1117/12.2269218.
    Khonina SN, Karpeev SV, Porfirev AP. Wavefront aberration sensor based on a multichannel diffractive optical element. Sensors 2020; 20: 3850. DOI: 10.3390/s20143850.
  31. Gerchberg R, Saxton W. Phase determination for image and diffraction plane pictures in the electron microscope. Optik 1971; 34: 275-284.
  32. Fienup JR. Reconstruction of an object from the modulus of its Fourier transform. Opt Lett 1978; 3(1): 27-29.
  33. Elser V. Phase retrieval by iterated projections. J Opt Soc Am A 2003; 20(1): 40-55. DOI: 10.1364/JOSAA.20.000040.
  34. Marchesini S. A unified evaluation of iterative projection algorithms for phase retrieval. Rev Sci Instrum 2007; 78(1): 011301. DOI: 10.1063/1.2403783.
  35. Zhang C, Wang M, Chen Q, Wang D, Wei S. Two-step phase retrieval algorithm using single-intensity measure-ment. Int J Op; 2018: 8643819. DOI:10.1155/2018/8643819.
  36. Tokovinin A, Heathcote S. DONUT: measuring optical aberrations from a single extrafocal image. Publications of the Astronomical Society of the Pacific 2006; 118(846): 1165-1175. DOI: 10.1086/506972.
  37. Guo H, Korablinova N, Ren Q, Bille J. Wavefront recon-struction with artificial neural networks. Opt Express 2006; 14(14): 6456-6462. DOI: 10.1364/OE.14.006456.
  38. Paine SW, Fienup JR. Machine learning for improved im-age-based wavefront sensing. Opt Lett 2018; 43(6): 1235-1238. DOI: 10.1364/OL.43.001235.
  39. Rivenson Y, Zhang Y, Günaydın H, Teng D, Ozcan A. Phase recovery and holographic image reconstruction using deep learning in neural networks. Light Sci Appl 2018; 7(2): 17141. DOI: 10.1038/lsa.2017.141.
  40. Dzyuba AP. Optical phase retrieval with the image of intensity in the focal plane based on the convolutional neural networks. J Phys Conf Ser 2019; 1368(2): 022055. DOI: 10.1088/1742-6596/1368/2/022055.
  41. Nishizaki Y, Valdivia M, Horisaki R, Kitaguchi K, Saito M, Tanida J, Vera E. Deep learning wavefront sensing. Opt Express 2019; 27(1): 240-251. DOI: 10.1364/OE.27.000240.
  42. Rodin IA, Khonina SN, Serafimovich PG, Popov SB. Recognition of wavefront aberrations types corresponding to single Zernike functions from the pattern of the point spread function in the focal plane using neural networks. Computer Optics 2020; 44(6): 923-930. DOI: 10.18287/2412-6179-CO-810.

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