关键词: 大气湍流, 卷积网络, 激光光斑图像, 光强分布, 平均光强

Abstract: Objective　The atmospheric refractive index structure constant, Cn 2, is a key physical parameter for quantifying the intensity of atmospheric optical turbulence. Traditional measurement methods, including the two-point temperature-fluctuation and scintillation methods, are limited by bulky and costly equipment, complex operation, and inadequate real-time performance. With the rapid development of convolutional neural networks (CNNs) in image processing, retrieving turbulence intensity from laser spot images has emerged as a promising research direction. However, accurately mapping complex spot morphology and intensity variations to turbulence levels remains challenging. This study proposes a novel atmospheric turbulence detection method based on an improved ConvNeXt-t model. By analyzing the morphological and intensity characteristics of turbulence-distorted Gaussian beam spot images, the method achieves accurate classification of turbulence intensity levels, offering an efficient and low-cost approach for both laboratory and field atmospheric turbulence detection. Methods　The study was conducted in three sequential stages: experimental system development, dataset preparation, and model development and training. Firstly, a laboratory-based turbulence simulation system was established using a transmissive spatial light modulator (SLM). A 632.8 nm He-Ne laser was used to generate a Gaussian beam, which was subsequently phase-modulated by the SLM (HOLOEYE LC2012; 768 × 1024 pixels) to simulate atmospheric turbulence. The distorted beam spot images were captured using a CCD camera (Thorlabs BC207VIS/M), and the central 1073 × 868- pixel region was extracted for subsequent analysis. And then, the dataset was constructed. In this stage, phase screens corresponding to 9 turbulence intensities (with Cn 2 values ranging from 2 × 10−15 m−2/3 to 7 × 10−13 m−2/3) were generated in Matlab based on the modified Von Kármán turbulence spectrum model. And a third harmonic scheme was employed to compensate for low-frequency components of phase screens. For each turbulence intensity level, 380 instantaneous spot images were acquired, resulting in a total of 3420 images. Furthermore, by randomly selecting 100 instantaneous images from the 380 instantaneous images of each turbulence intensity level and performing average processing, an averaged spot image for this turbulence intensity level was obtained, and a total of 3600 averaged spot images were finally generated by repeating this process 400 times for each turbulence intensity level. All images were resized to 256 × 256 pixels and divided into training and validation subsets at a 4:1 ratio. Finally, the lightweight ConvNeXt-t architecture was modified in two ways: 3 × 3 and 5 × 5 multi-scale convolutional kernels were incorporated into the residual blocks to improve feature representation, while the original 4 × 4 stem layer was replaced with a 16 × 16 large-kernel design to enhance global feature extraction. And training was performed for 100 epochs using the AdamW optimizer, with a base learning rate of 5 × 10−4 and a loss function that combines sparse categorical cross-entropy loss with L2 regularization. Results and discussion　Using the experimental dataset, the performance of the improved ConvNeXt-t model was systematically evaluated, with particular emphasis on the factors affecting turbulence detection accuracy. The main findings are summarized as follows: (1) For instantaneous spot images, the improved ConvNeXt-t model achieved a validation accuracy of 92.7% in the six-class turbulence intensity classification task, outperforming both the original ConvNeXt-t and the Swin-Transformer models. The model also demonstrated a stable improvement in accuracy during training. (2) With a single instantaneous spot image as the input, the model could accurately distinguish turbulence intensity classes separated by a Cn 2 difference of 2 × 10−14 m−2/3. For the three classes corresponding to Cn 2 values of 2 × 10−14, 4 × 10−14, and 7 × 10−14 m−2/3, the mean recognition accuracy reached 87.0%. However, the model showed limited capability to discriminate between classes separated by smaller Cn 2 differences of 1 × 10−14 m−2/3. This limitation may primarily result from the small differences in phase distortion between adjacent turbulence intensity classes and the limited information contained in a single instantaneous spot image. (3) When averaged spot images, generated by combining multiple instantaneous spot images, were used as input, the model could correctly classify all 9 turbulence intensity classes only within 10 training epochs, enabling it to distinguish Cn 2 differences as small as 1 × 10−14 m−2/3. This demonstrates that averaging multiple instantaneous spot images can effectively integrate more turbulence information and significantly improve the fine-grained classification capability of the model. Conclusions　The improved ConvNeXt-t-based atmospheric turbulence detection method proposed in this study can extract turbulence-related features from laser spot images and accurately classify atmospheric turbulence intensity over the investigated Cn 2 over a certain range. By using averaged spot images, the proposed method overcomes the limited finegrained classification capability associated with individual instantaneous spot images. The laboratory results obtained using SLM-simulated turbulence demonstrate the feasibility of the proposed approach and provide a basis for subsequent field experiments. Future work will focus on further optimizing the network architecture, expanding the dataset to improve detection accuracy and robustness, and validating the method under practical scenarios such as laser communication, astronomical observation, and civil aviation flight safety assurance.

Key words: atmospheric turbulence, convolutional networks, laser spot image, light intensity distribution, average intensity