Measurement of transverse phase space based on machine learning
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摘要: 理论上，使用断层扫描技术可以得到真实的横向相空间分布。但是想要更加精确地了解分布的细节，需要解决旋转角度范围受限和投影数目不足的问题。针对这两个问题，提出了在混合域处理的神经网络模型，即组合地在正弦域和断层域分别使用插值和去除伪影神经网络。在简单地测量束线以及投影数目比较少（7个）的情况下，该网络模型也能高质量地重建束团横向相空间分布。并且，由于选择旋转角度的方式和归一化相空间无关，因此，无需测量Twiss参数。采用该方法测量束团横向相空间，一定程度提升了重建质量，简化了测量的方式。Abstract: Accurate measurement of the transverse phase space distribution of electron beams is of great importance in the design and optimization of accelerators. The computerized tomography theoretically provides the true transverse phase space distribution. However, to understand the details of the distribution more accurately, it is necessary to solve the problems of limited range of rotation angle and insufficient number of projections. In this paper, a neural network model is proposed to address these two problems in the hybrid domains, which combines interpolation and artifact removal neural networks in the sinogram and tomogram domains, respectively. Even with a simple diagnostic beamline and a small number of projections (7), the network model can reconstruct the transverse phase space distribution of beams with high quality. Moreover, since the selection of angles is independent of the normalized phase space, Twiss parameters do not need to be measured. Using the proposed method to measure the transverse phase space improves reconstruction quality to a certain extent and simplifies the measurement process.
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Key words:
- transverse phase space /
- computerized tomography /
- machine learning /
- neural network
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图 5 某一个相空间分布和它的归一化相空间分布
Figure 5. A TPS distribution and its normalized TPS distribution
图 6 不同采样方式对应的旋转角度
Figure 6. Rotation angles corresponding to different sampling methods
图 9 插值网络的结果正弦图举例
Figure 9. An example of the interpolation network results in the form of sinogram
图 10 插值网路结果断层图举例
Figure 10. An example of the interpolation network results in the form of tomography
表 1 Residual U-Net 网络参数
Table 1. Residual U-Net network parameter settings
name parameters output Conv_block_1 1 $ \times $1 conv, 64 200 $ \times $57, 64 3 $ \times $3 conv, 64 Conv_block_2 2 $ \times $3 conv, s=2, p=0, 64 100 $ \times $28, 64 [3 $ \times $3 conv, 64] $ \times $2 Conv_block_3 2 $ \times $2 conv, s=2, p=0, 64 50 $ \times $14, 64 [3 $ \times $3 conv, 64] $ \times $2 Conv_block_4 2 $ \times $2 conv, s=2, p=0, 64 25 $ \times $7, 64 [3 $ \times $3 conv, 64] $ \times $2 ConvT_block_1 $2 \times 2$ convT, s=2, p=0, 64 50 $ \times $14, 64 ConvT_block_2 Conv_block_3, concatenation 100 $ \times $28, 64 [ $3 \times 3$ conv,64] $ \times $2 $2 \times 2$ convT, s=2, p=0, 64 ConvT_block_3 Conv_block_2, concatenation 200 $ \times $57, 64 [ $3 \times 3$ conv, 64] $ \times $2 $2 \times 3$ convT, s=2, p=0, 64 Conv_block_5 Conv_block_1, concatenation 200 $ \times $57, 1 $3 \times 3$ conv,16 $3 \times 3$ conv, 1 shortcut connection 
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表 2 RED-CNN 网络参数
Table 2. RED-CNN network parameter settings
name parameters output Conv_1 [5, Conv, 16] $ \times $2 192 $ \times $192, 16 Conv_2 [5, Conv, 16] $ \times $2 184 $ \times $184, 16 Conv_3 [5, Conv, 16] $ \times $2 176 $ \times $176, 16 ConvT_1 [5, ConvT, 16] $ \times $2 184 $ \times $184, 16 ConvT_2 Conv_2, addition 192 $ \times $192, 16 [5, convT, 16] $ \times $2 ConvT_3 Conv_1, addition 200 $ \times $200, 1 [5, convT1, 1] $ \times $2 shortcut connection
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