Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Revelation of hidden 2D atmospheric turbulence strength fields from turbulence effects in infrared imaging

Nature Computational Science volume 3, pages 687–699 (2023)Cite this article

Subjects

Abstract

Turbulence exists widely in the natural atmosphere and in industrial fluids. Strong randomness, anisotropy and mixing of multiple-scale eddies complicate the analysis and measurement of atmospheric turbulence. Although the spatially integrated strength of atmospheric turbulence can be roughly measured indirectly by Doppler radar or laser, direct measurement of two-dimensional (2D) strength fields of atmospheric turbulence is challenging. Here we attempt to solve this problem through infrared imaging. Specifically, we propose a physically boosted cooperative learning framework, termed the PBCL, to quantify 2D turbulence strength from infrared images. To demonstrate the capability of the PBCL, we constructed a dataset with 137,336 infrared images and corresponding 2D turbulence strength fields. The experimental results show that cooperative learning brings performance improvements, enabling the PBCL to simultaneously learn turbulence strength fields and inhibit adverse turbulence effects in images. Our work demonstrates the potential of imaging in measuring physical quantity fields.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Learning the hidden TS fields through the proposed framework.
Fig. 2: Visual presentation of some test results.
Fig. 3: Experimental results on real-world data.
Fig. 4: Comparison of turbulence effects inhibition.
Fig. 5: Fluctuations and pre-multiplied turbulence power spectra.
Fig. 6: Fields of kinetic energy dissipation rate and Reynolds stress derived from the PBCL results.

Similar content being viewed by others

Data availability

Our data include real data and simulated data. The real data were recorded by a infrared camera in outdoor atmospheric turbulence environment. The simulation data were synthesized by simulating the atmospheric turbulence effects on infrared images. The real data used in this paper and the full simulated data are publicly available in a Zenodo repository at https://doi.org/10.5281/zenodo.8002688 ref. 43. Source data are provided with this paper.

Code availability

The code presented in this article is publicly available through a Code Ocean compute capsule at https://doi.org/10.24433/CO.9167814.v1 ref. 44.

References

  1. Qi, Y. et al. Fragmentation in turbulence by small eddies. Nat. Commun. 13, 1–8 (2022).

  2. Iyer, K. P., Bonaccorso, F., Biferale, L. & Toschi, F. Multiscale anisotropic fluctuations in sheared turbulence with multiple states. Phys. Rev. Fluids 2, 052602 (2017).

    Article  Google Scholar 

  3. Nakayama, Y. Introduction to Fluid Mechanics (Butterworth-Heinemann, 2018).

  4. Eames, I. & Flor, J.-B. New developments in understanding interfacial processes in turbulent flows. Phil. Trans. R. Soc. A 369, 702–705 (2011).

    Article  Google Scholar 

  5. Dutton, J. A. & Panofsky, H. A. Clear air turbulence: a mystery may be unfolding: high altitude turbulence poses serious problems for aviation and atmospheric science. Science 167, 937–944 (1970).

    Article  Google Scholar 

  6. Sathe, A. & Mann, J. A review of turbulence measurements using ground-based wind lidars. Atmos. Meas. Tech. 6, 3147–3167 (2013).

    Article  Google Scholar 

  7. Toselli, I., Andrews, L. C., Phillips, R. L. & Ferrero, V. Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence. Opt. Eng. 47, 026003 (2008).

    Article  Google Scholar 

  8. Ramlau, R. & Rosensteiner, M. An efficient solution to the atmospheric turbulence tomography problem using Kaczmarz iteration. Inverse Probl. 28, 095004 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  9. Alterman, M., Schechner, Y. Y., Vo, M. & Narasimhan, S. G. Passive tomography of turbulence strength. In European Conference on Computer Vision 47–60 (Springer, 2014).

  10. Kolmogorov, A. N. Dissipation of energy in the locally isotropic turbulence. Proc. R. Soc. Lond. Ser. A 434, 15–17 (1991).

    Article  MathSciNet  MATH  Google Scholar 

  11. Moore, R. L. & Krishnamurti, T. N. Atmospheric clear air turbulence. Nature 209, 462–463 (1966).

    Article  Google Scholar 

  12. Engelmann, R. et al. Lidar observations of the vertical aerosol flux in the planetary boundary layer. J. Atmos. Ocean. Technol. 25, 1296–1306 (2008).

    Article  Google Scholar 

  13. Zhu, X. & Kahn, J. M. Free-space optical communication through atmospheric turbulence channels. IEEE Trans. Commun. 50, 1293–1300 (2002).

    Article  Google Scholar 

  14. Pipinato, A. Innovative Bridge Design Handbook: Construction, Rehabilitation and Maintenance (Elsevier, 2021).

  15. Wu, S. et al. Measurement and analysis of atmospheric optical turbulence in Lhasa based on thermosonde. J. Atmos. Sol. Terr. Phys. 201, 105241 (2020).

    Article  Google Scholar 

  16. Jaiswal, A., Phanikumar, D., Bhattacharjee, S. & Naja, M. Estimation of turbulence parameters using ARIES ST radar and GPS radiosonde measurements: first results from the central Himalayan region. Radio Sci. 55, 1–18 (2020).

  17. Clark, T. L. et al. Origins of aircraft-damaging clear-air turbulence during the 9 December 1992 Colorado downslope windstorm: numerical simulations and comparison with observations. J. Atmos. Sci. 57, 1105–1131 (2000).

    Article  Google Scholar 

  18. Frehlich, R. Simulation of laser propagation in a turbulent atmosphere. Appl. Opt. 39, 393–397 (2000).

    Article  Google Scholar 

  19. Browning, K. & Watkins, C. Observations of clear air turbulence by high power radar. Nature 227, 260–263 (1970).

    Article  Google Scholar 

  20. Qiang, X. et al. Measurement of the inner scale of laboratory-simulated atmospheric turbulence. In Asia Communications and Photonics Conference and Exhibition 1–2 (IEEE, 2009).

  21. Megaw, E. Scattering of electromagnetic waves by atmospheric turbulence: stellar scintillation and the spectrum of turbulence in the free atmosphere. Nature 166, 1100–1101 (1950).

    Article  Google Scholar 

  22. Lohse, D. & Xia, K.-Q. Small-scale properties of turbulent Rayleigh–Bénard convection. Annu. Rev. Fluid Mech. 42, 335–364 (2010).

    Article  MATH  Google Scholar 

  23. Cui, L., Xue, B. & Zhou, F. Atmospheric turbulence MTF for infrared optical waves’ propagation through marine atmospheric turbulence. Infrared Phys. Technol. 65, 24–29 (2014).

    Article  Google Scholar 

  24. Datcu, S., Ibos, L., Candau, Y. & Matteϊ, S. Improvement of building wall surface temperature measurements by infrared thermography. Infrared Phys. Technol. 46, 451–467 (2005).

    Article  Google Scholar 

  25. Xue, B. et al. Analysis of non-Kolmogorov weak turbulence effects on infrared imaging by atmospheric turbulence MTF. Opt. Commun. 300, 114–118 (2013).

    Article  Google Scholar 

  26. Rigaut, F. & Neichel, B. Multiconjugate adaptive optics for astronomy. Annu. Rev. Astron. Astrophys. 56, 277–314 (2018).

    Article  Google Scholar 

  27. Shimizu, M., Yoshimura, S., Tanaka, M. & Okutomi, M. Super-resolution from image sequence under influence of hot-air optical turbulence. In IEEE Conference on Computer Vision and Pattern Recognition 1–8 (IEEE, 2008).

  28. Hirsch, M., Sra, S., Schölkopf, B. & Harmeling, S. Efficient filter flow for space-variant multiframe blind deconvolution. In IEEE Conference on Computer Vision and Pattern Recognition 607–614 (IEEE, 2010).

  29. Zhu, X. & Milanfar, P. Removing atmospheric turbulence via space-invariant deconvolution. IEEE Trans. Pattern Anal. Mach. Intell. 35, 157–170 (2012).

    Article  Google Scholar 

  30. Anantrasirichai, N., Achim, A., Kingsbury, N. G. & Bull, D. R. Atmospheric turbulence mitigation using complex wavelet-based fusion. IEEE Trans. Image Process. 22, 2398–2408 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  31. Wang, F. et al. Phase imaging with an untrained neural network. Light Sci. Appl. 9, 1–7 (2020).

  32. Chen, G., Gao, Z., Wang, Q. & Luo, Q. Blind de-convolution of images degraded by atmospheric turbulence. Appl. Soft Comput. 89, 106131 (2020).

    Article  Google Scholar 

  33. Jin, D. et al. Neutralizing the impact of atmospheric turbulence on complex scene imaging via deep learning. Nat. Mach. Intell. 3, 876–884 (2021).

    Article  Google Scholar 

  34. Andrews, L. C. & Phillips, R. L. Laser Beam Propagation Through Random Media 2nd edn 66-72 (SPIE, 2005).

  35. Hocking, W. K. Measurement of turbulent energy dissipation rates in the middle atmosphere by radar techniques: a review. Radio Sci. 20, 1403–1422 (1985).

    Article  Google Scholar 

  36. Luce, H., Kantha, L., Hashiguchi, H., Lawrence, D. & Doddi, A. Turbulence kinetic energy dissipation rates estimated from concurrent UAV and MU radar measurements. Earth Planets Space 70, 207 (2018).

    Article  Google Scholar 

  37. Meilă, M. Comparing clusterings—an information based distance. J. Multivar. Anal. 98, 873–895 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  38. Garratt, J. R. The atmospheric boundary layer. Earth Sci. Rev. 37, 89–134 (1994).

    Article  Google Scholar 

  39. Rasouli, S. & Tavassoly, M. T. Measurement of the refractive-index structure constant, Cn2, and its profile in the ground level atmosphere by moiré technique. In Optics in Atmospheric Propagation and Adaptive Systems IX 101–111 (SPIE, 2006).

  40. Du, W. et al. Angle-of-arrival fluctuations for wave propagation through non-Kolmogorov turbulence. Opt. Commun. 282, 705–708 (2009).

    Article  Google Scholar 

  41. Hou, Q., Zhou, D. & Feng, J. Coordinate attention for efficient mobile network design. In IEEE Conference on Computer Vision and Pattern Recognition 13713–13722 (IEEE, 2021).

  42. Raissi, M., Yazdani, A. & Karniadakis, G. E. Hidden fluid mechanics: learning velocity and pressure fields from flow visualizations. Science 367, 1026–1030 (2020).

    Article  MathSciNet  MATH  Google Scholar 

  43. Wang, Y. et al. Turbulence-distorted infrared imaging dataset. Zenodo https://doi.org/10.5281/zenodo.8002688 (2023).

  44. Wang, Y. et al. PBCL (physically boosted cooperative learning framework). Code Ocean https://doi.org/10.24433/CO.9167814.v1 (2023).

  45. Chan, S. H., Khoshabeh, R., Gibson, K. B., Gill, P. E. & Nguyen, T. Q. An augmented Lagrangian method for total variation video restoration. IEEE Trans. Image Process. 20, 3097–3111 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  46. Lou, Y., Kang, S. H., Soatto, S. & Bertozzi, A. L. Video stabilization of atmospheric turbulence distortion. Inverse Probl. Imaging 7, 839 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  47. Nah, S., Son, S. & Lee, K. M. Recurrent neural networks with intra-frame iterations for video deblurring. In IEEE Conference on Computer Vision and Pattern Recognition 8094–8103 (IEEE, 2019).

  48. Zhong, Z., Gao, Y., Zheng, Y. & Zheng, B. Efficient spatio-temporal recurrent neural network for video deblurring. In European Conference on Computer Vision 191–207 (Springer, 2020).

  49. Zamir, S. W. et al. Learning enriched features for real image restoration and enhancement. In European Conference on Computer Vision 492–511 (Springer, 2020).

  50. Chan, K. C., Wang, X., Yu, K., Dong, C. & Loy, C. C. BasicVSR: the search for essential components in video super-resolution and beyond. In IEEE Conference on Computer Vision and Pattern Recognition 4947–4956 (IEEE, 2021).

Download references

Acknowledgements

X.B. acknowledges the support by the National Natural Science Foundation of China under Grant 62271016, the Beijing Natural Science Foundation under Grant 4222007, and the Fundamental Research Funds for the Central Universities. The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript. X. Jiang and Y. Hu, with the Image Processing Center of Beihang University, provided suggestions for the analysis of fluid mechanics.

Author information

Authors and Affiliations

  1. Image Processing Center, Beihang University, Beijing, China

    Yadong Wang, Darui Jin, Junzhang Chen & Xiangzhi Bai

  2. State Key Laboratory of Virtual Reality Technology and Systems, Beihang University, Beijing, China

    Xiangzhi Bai

  3. Advanced Innovation Center for Biomedical Engineering, Beihang University, Beijing, China

    Xiangzhi Bai

Authors
  1. Yadong Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Darui Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Junzhang Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xiangzhi Bai
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

X.B. and Y.W. conceived and designed the experiments. Y.W. and D.J. performed the experiments. Y.W. and X.B. analyzed the data. X.B., Y.W. and J.C. contributed analysis tools. Y.W. and X.B. wrote the paper.

Corresponding author

Correspondence to Xiangzhi Bai.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Computational Science thanks Kozo Fujii and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Jie Pan, in collaboration with the Nature Computational Science team.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Sections 1 and 2, Figs. 1–8 and Tables 1–6.

Supplementary Video 1

Visual comparison of the proposed method and comparison methods on inhibiting turbulence effects.

Supplementary Video 2

The results of the proposed method on real data.

Source data

Source Data Fig. 1

Source data of the turbulence strength fields and source PSNR indicators on the whole test dataset, along with the code to conduct statistical analysis.

Source Data Fig. 2

Source data of the turbulence strength fields.

Source Data Fig. 3

Source data of the turbulence strength fields, input video and output video, along with the data processing code.

Source Data Fig. 4

Source data of the comparison videos, along with the data processing code.

Source Data Fig. 5

Source data of the turbulence strength fields, input video and output video, along with the data processing code.

Source Data Fig. 6

Source data of the turbulence strength fields and the data processing code.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Y., Jin, D., Chen, J. et al. Revelation of hidden 2D atmospheric turbulence strength fields from turbulence effects in infrared imaging. Nat Comput Sci 3, 687–699 (2023). https://doi.org/10.1038/s43588-023-00498-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s43588-023-00498-z

Search

Advanced search

Quick links

Nature Briefing AI and Robotics

Sign up for the Nature Briefing: AI and Robotics newsletter — what matters in AI and robotics research, free to your inbox weekly.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing: AI and Robotics