Vortex beam with fractional orbital angular momentum (FOAM) is the excellent candidate for improving the capacity of free-space optical (FSO) communication system due to its infinite modes. Therefore, the recognition of FOAM modes with higher resolution is always of great concern. In this work, through an improved EfficientNetV2 based convolutional neural network (CNN), we experimentally achieve the implementation of the recognition of FOAM modes with a resolution as high as 0.001. To the best of our knowledge, it is the first time this high resolution has been achieved. Under the strong atmospheric turbulence (AT) \((C_n^2 = {10^{ - 15}}\,{{\rm{m}}^{ - 2/3}})\), the recognition accuracy of FOAM modes at 0.1 and 0.01 resolution with our model is up to 99.12% and 92.24% for a long transmission distance of 2000 m. Even for the resolution at 0.001, the recognition accuracy can still remain at 78.77%. This work provides an effective method for the recognition of FOAM modes, which may largely improve the channel capacity of the free-space optical communication.

分数轨道角动量涡旋光束（FOAM）由于其无限模式而成为提高自由空间光学（FSO）通信系统容量的绝佳候选者。因此，对更高分辨率的FOAM模式的识别一直备受关注。在这项工作中，通过改进的基于EfficientNetV2的卷积神经网络（CNN），我们实验性地实现了分辨率高达0.001的FOAM模式的识别。据我们所知，这是第一次实现如此高分辨率。强大气湍流(AT)下\((C_n^2 = {10^{ - 15}}\,{{\rm{m}}^{ - 2/3}})\) FOAM的识别精度对于 2000 m 的长传输距离，我们的模型在 0.1 和 0.01 分辨率下的模式分别高达 99.12% 和 92.24%。即使分辨率为0.001，识别准确率仍能保持在78.77%。这项工作为FOAM模式的识别提供了一种有效的方法，可大大提高自由空间光通信的信道容量。