Optical vortex beam (OVB) is characterized by orbital angular momentum (OAM), a helical phase front, and a dark core, demonstrating promising applications in quantum entanglement, optical imaging, nonlinear optics, and optical communication. The ring-like intensity distribution of an OVB can be described by exp(imθ), where m, the topological charge, is proportional to the photon’s OAM. OVB signals employing different coding modes demonstrate resistance to interference and improve data transmission rate and communication capacity. However, atmospheric turbulence and aberrations significantly degrade the performance of OVB in practical applications. Spherical aberration, a common coaxial aberration typically represented by the coefficient kC₄, significantly affects beam spreading and energy dispersion. Atmospheric turbulence significantly affects the propagation of beams with spherical aberration. Studies have shown that positive spherical aberration beams exhibit a comparatively smaller divergence effect, whereas negative spherical aberration beams are more susceptible to turbulent conditions, leading to increased beam spreading and energy dispersion. Moreover, the effect of spherical aberration on beam drift intensifies with increasing transmission distance. Consequently, a network model based on depthwise separable convolutions is proposed for the concurrent identification of topological charges and spherical aberration coefficient of spherical aberration vortex beams transmitted through atmospheric turbulence.

We developed a neural network model, SepNet, based on depthwise separable convolutions, to simultaneously identify the topological charge and spherical aberration coefficient from spot images. The SepNet architecture comprises an input layer, an initial convolutional module, depthwise separable convolutional modules, a final convolutional module, an adaptive global pooling layer, and a fully connected layer. The model took a single-channel spot image and associated parameters as input. The initial convolutional module utilized two convolutional layers, incorporating batch normalization (BN) and a rectified linear unit (ReLU) activation function, for feature extraction and spatial downsampling. The depthwise separable convolutional modules consist of three repeated blocks, each with a similar internal structure and progressively increasing number of channels, so as to enhance representational capacity. Skip connections were integrated into these blocks to mitigate gradient vanishing. The final convolutional module consists of two layers designed to extract high-level semantic features. An adaptive global pooling layer transformed the feature map into a feature vector, which was then flattened and input to the fully connected layer, consisting of two independent dense layers. To enhance model generalization and prevent overfitting, a dropout mechanism was implemented before the fully connected layer, effectively reducing reliance on specific input features and enhancing robustness. The topological charge and spherical aberration coefficient changed within the range of [1.1, 5.0], with an interval of 0.1. We utilized the SepNet model to investigate the influence of different turbulence intensities and transmission distances on the identification of topological charges and spherical aberration coefficient in vortex beams carrying spherical aberration phases and propagating through turbulent media.

The results of the study demonstrate that the SepNet model achieves optimal recognition performance for turbulence intensity values of 2000 m, 3000 m, and 4000 m, respectively, and that all three evaluation metrics (including Precision, Recall, and F1-score) are at 100%, as shown in Fig. 4(a). At the transmission distance of 3000 m and turbulence intensities of 10-16m-2/3 and 10-15m-2/3, the model maintains optimal performance with all metrics at 100%. Increasing the turbulence intensity to 10-14m-2/3 results in good recognition performance for the topological charge, with corresponding metrics reaching 100%, while the spherical aberration coefficient metrics decrease to 99.61%, 99.52%, and 99.56% [Fig. 4(b)]. In the comparative study of the performance of the two groups of models, all models exhibit high proficiency in identifying topological charges. However, when the identification of the spherical aberration coefficient kC₄ is identified, the SepNet model demonstrates superior performance, achieving success rates exceeding 99.50% across all three evaluation metrics and indicating a notable improvement over Resnet 18, Resnet 34, and Xception models (Table 1). The topological charge range is expanded to [1.1, 7.0] (with an interval of 0.1), while the spherical aberration coefficient range remains at [1.1, 5.0] (with an interval of 0.1). The SepNet model’s combined performance in identifying topological charges and spherical aberration coefficient outperforms Resnet 18, Resnet 34, and Xception models (Table 2). The experimental results demonstrate the superiority of SepNet in terms of network performance. Moreover, an evaluation of the generalization ability and robustness of the SepNet model is conducted. It is demonstrated that the model can maintain a high level of accuracy in scenarios where the turbulence intensity is unknown (Fig. 5?7).

We propose a neural network model, SepNet, based on depthwise separable convolution and investigate its performance under atmospheric turbulence conditions. We examine the influence of varying atmospheric turbulence intensities and transmission distances on the model’s recognition accuracy. The results demonstrate that SepNet demonstrates high performance in the recognition of topological charges and spherical aberration coefficient, exhibiting high stability. Notably, under strong turbulence conditions (Cn2=10-14m-2/3), at a transmission distance of 3000 m, SepNet exhibits the best overall performance compared to Resnet 18, Resnet 34, and Xception. Moreover, the SepNet model has shown good generalization capabilities and robustness, retaining high accuracy in scenarios even where the turbulence intensity is unknown. These research findings have important implications for the design of OAM encoding approaches used in free-space optical communication systems. Although this paper has investigated the combined effects of spherical aberration and atmospheric turbulence on topological charge identification, practical applications are often confronted with complex and variable atmospheric conditions. Beyond turbulent effects, phenomena such as gas absorption and scattering are also frequently encountered. Therefore, to enhance the practicality and performance of the SepNet model, multi-scenario testing is essential, along with the integration of advanced architectures such as attention mechanisms and inverted residual structures to improve its adaptability and robustness in complex atmospheric environments.