基于卷积神经网络的偏振器多图像退化模式分解
Convolution Neural Network based Mode Decomposition for Degenerated Modes via Multiple Images from Polarizers
摘要：
本文研究了退化模态的模态分解方法。卷积神经网络（CNN）已被用于图像训练和预测模式系数。四重简并的$LP_{11}$系列是被分解的目标。多幅图像被视为一个输入分解的退化模式。总共七个不同的图像，包括完整的原始近场图像、四个方向的线性偏振器（0 $^\circ$、45 $^\circ$、90 $^\circ$和135 $^\circ$）之后的图像以及两个圆偏振器（右旋和左旋）之后的图像，已被考虑用于训练、验证和测试。模型的输出标签被选择为模式系数的实部和虚部，并且损失函数被选择为标签的均方根（RMS）。已选择实际值和预测值之间的标记、强度、相位和场相关性的RMS和平均绝对误差（MAE）作为评估CNN模型的度量。CNN模型已经用10万张深度为3、4和7的三维图像进行了训练。训练模型的性能通过10，000个测试样本进行评估，这些测试样本具有四组图像-三个线性偏振器之后的图像（0 $^\circ$，45 $^\circ$，90 $^\circ$）和在右旋圆偏振器之后的图像-显示0.0634的标记RMS，0.0292的强度RMS，0.1867 rad的相位MAE，平均场相关系数为0.9978。4个图像集的性能表现出至少50.68%的性能增强模型相比，只考虑图像后的线性偏振器。
英文摘要：
In this paper, a mode decomposition (MD) method for degenerated modes has been studied. Convolution neural network (CNN) has been applied for image training and predicting the mode coefficients. Four-fold degenerated $LP_{11}$ series has been the target to be decomposed. Multiple images are regarded as an input to decompose the degenerate modes. Total of seven different images, including the full original near-field image, and images after linear polarizers of four directions (0$^\circ$, 45$^\circ$, 90$^\circ$, and 135$^\circ$), and images after two circular polarizers (right-handed and left-handed) has been considered for training, validation, and test. The output label of the model has been chosen as the real and imaginary components of the mode coefficient, and the loss function has been selected to be the root-mean-square (RMS) of the labels. The RMS and mean-absolute-error (MAE) of the label, intensity, phase, and field correlation between the actual and predicted values have been selected to be the metrics to evaluate the CNN model. The CNN model has been trained with 100,000 three-dimensional images with depths of three, four, and seven. The performance of the trained model was evaluated via 10,000 test samples with four sets of images - images after three linear polarizers (0$^\circ$, 45$^\circ$, 90$^\circ$) and image after right-handed circular polarizer - showed 0.0634 of label RMS, 0.0292 of intensity RMS, 0.1867 rad of phase MAE, and 0.9978 of average field correlation. The performance of 4 image sets showed at least 50.68\% of performance enhancement compared to models considering only images after linear polarizers.
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