doi: 10.17586/2226-1494-2019-19-6-959-965


O. A. Soloviev, G. V. Vdovin, V. V. Bezzubik

Read the full article  ';
Article in English

For citation:

Soloviev O.A., Vdovin G.V., Bezzubik V.V. Сomparison of on-line and off-line Fried parameter estimation methods. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2019, vol. 19, no. 6, pp. 959–965 (in English). doi: 10.17586/2226-1494-2019-19-6-959-965


We address the problem of high-accuracy estimation of the Fried parameter r0 by comparing two approaches based on estimation of statistical properties of intensity-based wavefront measurements with parameter-fitting to the theoretically predicted values. In the first approach, the phase of the aberration-degraded field is restored from the measurements to obtain the statistical estimate for the structure function. Due to the iterative nature of the most phase retrieval methods, this approach requires significant computational time and thus cannot provide results in real time. In the second approach, the structure function of the sub-aperture wavefront slopes is directly calculated and related to the turbulence parameters in real time. We describe the equations used to obtain the estimate of the Fried parameter by both methods and check their accuracy with numerical simulations.

Keywords: wavefront aberrations, imaging through turbulence, Fried parameter, turbulence statistics

Acknowledgements. The research is carried out at ITMO University (grant 074-11-2018-004) under the financial support of the Ministry of Science and Higher Education of the Russian Federation. The authors are very grateful to F. Inochkin for his assistance in preparing the manuscript for publication.

  1. Roggemann M.C., Welsh B.Imaging through turbulence. CRC Press, 1996, 320 p.
  2. Weiss A.R., Hippler S., Kasper M.E., Wooder N.J., Quartel J.C. Simultaneous Measurements of the Fried Parameter r(0) and the Isoplanatic Angle theta(0) using SCIDAR and Adaptive Optics – First Results. Astronomical society of the pacific conference series, 2002, vol. 266, pp. 86–95.
  3. Andrade P.P., Garcia P.J.V., Correia C.M., Kolb J., Carvalho M.I. Estimation of atmospheric turbulence parameters from Shack-Hartmann wavefront sensor measurements. Monthly Notices of the Royal Astronomical Society, 2019, vol. 483, pp. 1192–1201. doi: 10.1093/mnras/sty3181
  4. Sergeyev A.V., Roggemann M.C. Monitoring the statistics of turbulence: Fried parameter estimation from the wavefront sensor measurements. Applied Optics, 2011, vol. 50, no. 20, pp. 3519–3528. doi: 10.1364/AO.50.003519
  5. Dayton D., Pierson B., Spielbusch B., Gonglewski J. Atmospheric structure function measurements with a Shack-Hartmann wave-front sensor. Optics Letters, 1991, vol. 17, no. 24, pp. 1737–1739. doi: 10.1364/OL.17.001737
  6. Silbaugh E.E., Welsh B.M., Roggemann M.C. Characterization of atmospheric turbulence phase statistics using wave-front slope measurements. Journal of the Optical Society of America A: Optics and Image Science, and Vision, 1996, vol. 13, no. 12, pp. 2453-2460. doi: 10.1364/JOSAA.13.002453
  7. Jolissaint L., Ragland S., Christou J., Wizinowich P. Determination of the optical turbulence parameters from the adaptive optics telemetry: critical analysis and on-sky validation. Applied Optics, 2018, vol. 57, no. 27, pp. 7837–7856. doi: 10.1364/AO.57.007837
  8. Wang C., Dun X., Fu Q., Heidrich W. Ultra-high resolution coded wavefront sensor. Optics Express, 2017, vol. 25, no. 12, pp. 13736–13746. doi: 10.1364/OE.25.013736
  9. Mompeán J., Aragón J.L., Prieto P.M., Artal P. GPU-based processing of Hartmann-Shack images for accurate and high-speed ocular wavefront sensing. Future Generation Computer Systems, 2019, vol. 91, pp. 177–190. doi: 10.1016/j.future.2018.09.010
  10. Wu Y., Sharma M.K., Veeraraghavan A. WISH: wavefront imaging sensor with high resolution. Light: Science and Applications, 2019, vol. 8, no. 1, pp. 44. doi: 10.1038/s41377-019-0154-x
  11. Shechtman Y., Eldar Y.C., Cohen O., Chapman H.N., Miao J., Segev M. Phase Retrieval with Application to Optical Imaging: A contemporary overview. IEEE Signal Processing Magazine, 2015, vol. 32, no. 3, pp. 87–109. doi: 10.1109/MSP.2014.2352673
  12. Lu J.-T., Lu C.-H., Fleischer J.W. Enhanced phase retrieval using nonlinear dynamics. Optics Express, 2016, vol. 24, no. 22, pp. 25091–25102. doi: 10.1364/OE.24.025091
  13. Piscaer P.J., Gupta A., Soloviev O., Verhaegen M. Modal-based phase retrieval using Gaussian radial basis functions. Journal of the Optical Society of America A: Optics and Image Science, and Vision, 2018, vol. 35, no. 7, pp. 1233–1242. doi: 10.1364/JOSAA.35.001233
  14. Polo A., Kutchoukov V., Bociort F., Pereira S., Urbach H.P. Determination of wavefront structure for a Hartmann Wavefront Sensor using a phase-retrieval method. Optics Express, 2012, vol. 20, no. 7, pp. 7822–7832. doi: 10.1364/OE.20.007822
  15. Li J., Gong Y., Chen H., Hu X. Wave-front reconstruction with Hartmann-Shack sensor using a phase-retrieval method. Optics Communications, 2015, vol. 336, pp. 127–133. doi: 10.1016/j.optcom.2014.09.086
  16. Adaptive Optics in Astronomy/ Ed. by. F. Roddier. Cambridge University Press, 1999, 411 p.
  17. Goodman J.W. Statistical Optics. New York, A Wiley-Interscience publication, 1985.
  18. Lane R.G., Glindemann A., Dainty J.C. Simulation of a Kolmogorov phase screen. Waves in Random Media, 1992, vol. 2, no. 3, pp. 209–224. doi: 10.1088/0959-7174/2/3/003
  19. Conan R., Correia C. Object-oriented Matlab adaptive optics toolbox. Proceedings of SPIE, 2014, vol. 9148, pp. 91486C. doi: 10.1117/12.2054470

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
Copyright 2001-2021 ©
Scientific and Technical Journal
of Information Technologies, Mechanics and Optics.
All rights reserved.