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Fractional-order vortex beams possess Fractional Orbital Angular Momentum (FOAM) modes, which theoretically have the potential to increase transmission capacity infinitely. Therefore, they have significant application prospects in the field of measurement, optical communication and microparticle manipulation. However, when fractional-order vortex beams propagate in free space, the discontinuity of the helical phase makes them susceptible to diffraction in practical applications, thereby affecting the accuracy of OAM mode recognition and severely limiting the use of FOAM-based optical communication. The problem of achieving machine learning recognition of fractional-order vortex beams under diffraction conditions is currently an urgent and unreported issue. This paper proposes a deep learning (DL) method based on ResNet for accurate recognition of the propagation distance and topological charge of fractional-order vortex beam diffraction process. Utilizing both experimental measured and theoretically simulated intensity distributions, a dataset of vortex beam diffraction intensity patterns in atmospheric turbulence environments was created. An improved 101-layer ResNet structure based on transfer learning was employed to achieve accurate and efficient recognition of the FOAM model at different propagation distances. Experimental results show that the proposed method can accurately recognize FOAM modes with a propagation distance of 100 cm, an interval of 5 cm, and a mode spacing of 0.1 under turbulent conditions, with an accuracy of 99.69%. This method considers the effect of atmospheric turbulence during spatial transmission, allowing the recognition scheme to achieve high accuracy even in special environments. It has the distinguishing capability for ultra-fine FOAM modes and propagation distances that traditional methods cannot achieve. This technology can be applied to multidimensional encoding and sensing measurements based on FOAM beam.
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Keywords:
- Fractional vortex beams /
- Machine learning /
- Atmosphere turbulence /
- ResNet
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图 2 不同拓扑荷数$\ell $和不同传播距离z的涡旋光束空间分布 (a)无湍流影响的无畸变模态的空间分布. (b)大气湍流影响的畸变模态的空间分布. 第一行和第三行是实验获得的图像, 第二和第四行是理论模拟的图像
Figure 2. The spatial profiles of vortex beams with different topological charges $\ell $ and different propagation distances z. (a) The spatial distribution of distortionless modes without turbulence. (b) The spatial distribution of distortion modes affected by atmospheric turbulence. The first and third rows are the images acquired from the experiment, and the second and fourth rows represent the theoretically simulate.
图 1 实验装置图.
Figure 1. Diagram of experimental setup.
图 3 深度学习算法. 深度学习网络由未改变的ResNet-101底层和重新设计的顶层组成.
Figure 3. The deep learning algorithm. The deep learning network consists of the unaltered ResNet-101 bottom layer and our redesigned top layer.
图 4 训练后的深度学习算法的准确率.
Figure 4. The accuracy of our trained deep learning algorithm.
图 5 训练后的深度学习算法的混淆矩阵 (a) $ \ell=3.5$时, 预测传播距离与真实传播距离之间的归一化混淆矩阵. (b) $ z=75$ cm时$\ell $的预测值和$\ell $的真实值之间的规一化混淆矩阵.
Figure 5. The confusion matrix of our trained deep learning algorithm. (a) The normalized confusion matrix between the predicted propagation distance and the true propagation distance for $ \ell=3.5$. (b) Normalized confusion matrix between predicted $\ell $ values and true $\ell $ values for z = 75 cm.
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