Laser self-mixing interference micro displacement reconstruction based on convolutional neural network
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摘要: 提出了一种基于卷积神经网络CNN）的半导体激光自混合干涉（SMI）微位移重构方法，将SMI信号分段并以窗口平均位移作为标签输入卷积神经网络，实现了物体微米量级位移的直接重构，避免了位移重构过程中复杂的SMI信号相位解包裹计算过程。所使用的卷积神经网络由三组卷积层、池化层和线性整流函数组成，其中卷积层用于提取SMI信号中的局部位移特征，池化层用于压缩SMI信号中的特征信息并增强抗干扰能力，线性整流函数有助于突出SMI信号中的关键位移特征。在理论仿真中，将具有10 dB噪声的SMI信号输入至已训练完成的卷积神经网络中，直接输出物体重构微位移的均方根误差为
$ 5.3\times {10}^{-8} $ ；在实验中，将包含系统噪声的SMI信号输入已训练完成的卷积神经网络中，直接输出物体重构微位移的均方根误差为$ 2.1\times {10}^{-7} $ 。理论仿真与实际实验结果均表明，卷积神经网络通过分析SMI信号的时序片段，能够实现半导体激光自混合干涉信号的微米量级位移重构。Abstract:Background Laser self-mixing interferometry (SMI) is a highly sensitive and non-contact technique widely used for micro-displacement measurement. However, traditional displacement reconstruction methods typically involve complex phase unwrapping calculations, which increases computational difficulty and limits the efficiency of signal processing in practical applications.Purpose This study aims to propose a novel micro-displacement reconstruction method for semiconductor laser SMI based on convolutional neural networks (CNN). The objective is to achieve direct and accurate reconstruction of micron-scale displacement while bypassing the tedious phase unwrapping process.Methods The proposed method involves segmenting the SMI signal and using the window-averaged displacement as the label for training the CNN. The architecture of the network consists of three sets of convolutional layers, pooling layers, and Rectified Linear Unit (ReLU) functions. Specifically, the convolutional layers are utilized to extract local displacement features from the SMI signal, the pooling layers are designed to compress feature information and enhance noise immunity, and the ReLU functions help highlight critical displacement features within the signal.Results In theoretical simulations, SMI signals with 10 dB noise were input into the trained CNN, resulting in a displacement reconstruction RMSE of 5.3 × 10−8. In experimental tests, SMI signals containing system noise were processed by the network, yielding a reconstructed displacement RMSE of 2.1 × 10−7. The simulation and experimental results demonstrate consistent performance.Conclusions Both theoretical and experimental results indicate that the convolutional neural network can effectively achieve micron-level displacement reconstruction by analyzing the temporal segments of SMI signals. This method provides an efficient alternative for semiconductor laser self-mixing interference systems by eliminating the need for complex phase-based algorithms. -
图 1 卷积神经网络的网络架构(SMI(Self-Mixing Interferometry): 激光自混合干涉；ReLU(Rectified Linear Unit): 线性整流函数)
Figure 1. Convolutional neural network architecture :(SMI) laser Self-Mixing Interferometry; Rectified Linear Unit (ReLU)
图 4 模拟物体的振动位移和对应的SMI信号
Figure 4. Simulated vibration displacement of the object and corresponding SMI signals
图 5 卷积神经网络训练集的SMI模拟信号与重构结果
Figure 5. Simulated SMI signals and reconstructed displacement results of the CNN training set
图 6 卷积神经网络测试集的SMI模拟信号与重构结果
Figure 6. Simulated SMI signals and reconstructed displacement results of the CNN testing set
图 7 卷积神经网络的回归拟合效果散点图
Figure 7. Scatter plots of regression fitting results of the convolutional neural network
图 8 激光自混合干涉实验结构示意图
Figure 8. Schematic diagram of the experimental structure for laser self-mixing interference
图 10 压电陶瓷的调制电压和实验SMI信号
Figure 10. Modulation voltage of PZT and experimental SMI signal
图 11 卷积神经网络训练集的SMI实验信号与归一化位移重构结果
Figure 11. Experimental SMI signals and normalized displacement reconstruction results of the CNN training set
图 12 卷积神经网络测试集的SMI实验信号与归一化位移重构结果
Figure 12. Experimental SMI signals and normalized displacement reconstruction results of the CNN testing set
图 13 卷积神经网络的回归拟合效果散点图
Figure 13. Scatter plots of regression fitting results of the convolutional neural network
表 1 数值模拟中使用的参数
Table 1. Parameters used in numerical simulation
$ {\boldsymbol{L}}_{\boldsymbol{e}\boldsymbol{x}\boldsymbol{t}} $ (distance from the laser
to the object)/mm$ \boldsymbol{L} $ (cavity length of diode
laser)/mmt (simulation
time)/sA (vibration amplitude of
external object)/$ \mu \mathrm{m} $49.43 0.5 0.2 2 f (external object vibration
frequency)/$ \mathrm{Hz} $$ \boldsymbol{\alpha } $ (linewidth enhancement
factor)/C (feedback
parameter)/$ \lambda $ (wavelength of the laser
diode)/nm10 4.15 0.8 635 
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