## 1 Introduction  
Since [PERSON] et al. discovered in 1992 that beams with spiral structures carry OAM, it has sparked a research boom in optical OAM [1]. The mode with OAM theoretically has an infinite number of orthogonal bases, and utilizing its orthogonality as a multiplexing mechanism has great potential in expanding channel capacity. The optical field carrying OAM, a special structure, has also been widely used in scientific fields such as ultra-large capacity optical communication [2], optical imaging [3], and micromanipulation [4]. At the same time, accurately identifying orbital angular momentum states is also an important challenge facing optical communication. The effective identification of orbital angular momentum modes is key to ensuring the reliability of OAM communication systems. At present, there are two methods for identifying OAM vortex beams, namely physical optical methods and machine learning methods. In physical optics research, OAM modal detection research mainly includes diffraction methods using apertures and gratings for detection [5, 6, 7] and interference methods based on the orientation and number of interference fringes [8, 9, 10]. Both methods distinguish different topological charges by judging the stripes and orientation of the light spot. In addition, there is also the OAM shorter technique, the astigmatic mode converter, and fiber coupling methods, among which [PERSON] et al. used the cylindrical lens method to introduce an astigmatic transformation for detecting vortex beams with a maximum detectable topological charge of 100 [6]. At the same time, with the continuous development of deep learning, it has also received widespread attention and application in this field due to its ability to extract intrinsic features of light intensity distribution images. In 2014, [PERSON] et al. first used Convolutional Neural Networks (CNN) to detect OAM modes, demonstrating the feasibility of deep learning frameworks in OAM recognition [11]. In 2016, [PERSON] et al. proposed an improved deep neural network with an accuracy rate of 74% for topological load detection [12]. In 2019, [PERSON] et al. proposed a 7-layer CNN model suitable for ocean turbulent channels, which showed good tolerance to weak turbulence in turbid waters but was prone to errors in identifying larger OAM patterns [13]. In the same year, [PERSON] et al. constructed a six-layer CNN for detecting Laguerre-Gaussian (LG) beams carrying a single OAM mode, taking into account computational complexity and detection effectiveness. The number of detected OAM modes can reach 10 [14]. The scheme proposed by [PERSON] et al. in 2020, which combines the Gerchberg-Saxton Algorithm (GS) and CNN, achieves an OAM mode detection accuracy of about 95% in weak and moderate turbulence, but the recognition accuracy in strong turbulence is less than 2/3 of that in weak turbulence [15]. [PERSON] et al. proposed a six-layer CNN model for identifying 10 types of unimodal topological loads, requiring a total of 15,000 data sets. The model's recognition accuracy can reach 80% under strong turbulence [16]. The 7-layer convolutional neural network proposed by [PERSON] et al. in 2021 for ocean turbulent channels showed good recognition performance in weak turbulence, but the accuracy was less than 60% in strong turbulence strengths [17]. In 2022, [PERSON]. [PERSON] et al. proposed using densely connected convolutional networks to identify OAM unimodal and superposition states under thick smoke conditions. This approach can improve recognition accuracy under low-visibility smoke conditions, but the accuracy decreases linearly with increasing transmission distance [18]. In 2023, [PERSON] et al. proposed a residual network model that can detect turbulence strengths and OAM modes but only achieved detection of four OAM modes with topological charges of 2, 4, 6, and 8 [19]. In 2024, [PERSON] et al.