The challenge of atmospheric turbulence measurement

Accounting for the effects of turbulence, which is characterized by multiscale complexity and stochasticity, is an important unsolved problem in classical physics and fluid mechanics¹. The widespread existence of turbulence in the atmosphere makes the quantization and measurement of turbulence strength (TS) essential in numerous engineering and theoretical fields, including aviation, meteorology, and atmospheric science². However, existing methods to measure TS usually only provide sparse point results and involve indirect measurements with expensive equipment such as high-power radars^3,4. Owing to these limitations, it is challenging to directly obtain 2D atmospheric TS fields. We therefore aimed to develop a deep learning method that can extract 2D TS fields from infrared imaging data, which is an easily accessible observation.

Inspiration and method

The inspiration of this research was generated during our previous work on neutralizing the effects of atmospheric turbulence on imaging data⁵. Atmospheric turbulence disturbs light transmission, which can have adverse effects on infrared images, including greyscale drift, geometric distortion, and blurring. Many attempts have previously been made to alleviate the effects of turbulence on imaging data⁶. However, we realised that these unfavourable turbulence effects on images could contain information about atmospheric turbulence. Therefore, we developed the idea of learning about the strength of atmospheric turbulence from turbulence-distorted infrared images.

At first, we tried to learn TS fields directly from degraded infrared images, following the most used end-to-end machine learning pipeline. Then we found it was challenging to get the machine learning model to converge. This is because the turbulence effects were submerged in the complex image background, making it difficult to capture turbulence information from the images. We then realised that turbulence effects could be captured by comparing the distorted images with restored images, and the learned TS fields could be used as a priori knowledge to guide image restoration. We thus developed a cooperative learning framework (PBCL) to combine turbulence measurement with image restoration.

PBCL is composed of two sub-networks: the turbulence measurement module (TMM) and the turbulence inhibition module (TIM). The turbulence-distorted infrared sequence is supplied as an input to both the TMM and TIM. The TMM analyses the turbulence pattern hidden in the infrared sequence to generate 2D TS fields represented by fluctuations of the atmospheric refractive index and temperature, while the TMM restores the undistorted infrared sequence. In cooperative learning, the TMM learns TS fields, which are then used to guide the spatially adaptive approach to inhibit the turbulence effects. In turn, the accuracy of the measured TS fields can be further increased by comparing the restored images with the original degraded images. To demonstrate the capability of the proposed method, we constructed a dataset of 137,336 infrared images and the corresponding 2D TS fields. This dataset included simulated data for model training and quantitative testing, as well as real-world data for performing further qualitative tests. The TMM and TIM were trained cooperatively on our constructed dataset, ultimately achieving better performance than they would achieve if they were trained separately.

Outcomes of the study

In experiments, we found that PBCL measured 2D TS fields from turbulence-distorted images with high accuracy (R² > 0.9), and the restored images were also high quality with a peak signal-to-noise ratio (PSNR) above 35 dB (2–8 dB higher than that achieved with state-of-the-art image restoration techniques). Meanwhile, we found that training TMM and TIM cooperatively increased R² of the TS measurement by 0.04 and the PSNR of the restored images by 0.33 dB. Additionally, PBCL effectively generated TS fields and restored images when tested on real-world data, indicating that PBCL successfully captures the general pattern of the effects of turbulence on images. We also used the TS fields measured with PBCL to analyse other turbulence features, such as the Reynolds stress field and power spectral density, showing the possibility of obtaining rich turbulence features from imaging data. Our research not only explored a new way for 2D strength field measurements of atmospheric turbulence, but also provided insights for imaging-based measurements of complex physical fields.

References

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2. 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. Sci.  167, 937–944 (1970).
3. Browning, K. & Watkins, C. Observations of clear air turbulence by high power radar. Nat.  227, 260–263 (1970).
4. Sathe, A., Mann & J. A review of turbulence measurements using ground-based wind lidars. Meas. Tech. 6, 3147–3167 (2013).
5. Jin, D. et al. Neutralizing the impact of atmospheric turbulence on complex scene imaging via deep learning. Nat. Mach. Intell. 3, 876–884 (2021).
6. Zhu, X. & Milanfar, P. Removing atmospheric turbulence via space-invariant deconvolution. IEEE T. Pattern. Anal. 35, 157–170 (2012).