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图1为基于点衍射干涉的三维坐标定位系统示意图。从稳频激光器发出的激光经过偏振片(P)和半波片(HWP1)后转换为线偏振光[9],然后由偏振分光棱镜(PBS)分成两部分线偏振光,即p光和s光。p光经过第二块半波片(HWP2),并由耦合器耦合进单模光纤(SF2)中。s光两次经过四分之一波片(QWP)后,再次通过PBS,并经由耦合器耦合进另一根单模光纤(SF1)中。两根光纤(SF1和SF2)的出射端集成到测量探头上,并产生点衍射球面波(W1与W2),进而叠加形成点衍射干涉场。将相机放置于干涉场中获取干涉条纹图,通过移相、解包裹等算法进行相位信息提取,利用基于深度学习的点衍射干涉三维坐标定位方法得到最优的被测对象的空间三维坐标值。
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根据点衍射干涉场的相位分布与点衍射源的光程差之间的一一对应关系,可以建立两个点衍射源与相机探测平面之间的数学模型,如图2所示。
图2中,相机探测平面原点为O,两个点衍射源(SF1和SF2)和相机探测平面上的任意一点像素点P之间的光程分别为
${r_1}$ 、${r_2}$ ,SF1和SF2的间距为d,即两根光纤的出射端距离为d,中点为O',则可得像素点P处的相位差信息为:$$ \varphi (x,y,z) = \dfrac{{2\pi }}{\lambda }({r_1} - {r_2}) $$ (1) 由像素点P处的相位差信息与两个点衍射源三维坐标值之间的关系,可得出非线性方程。根据非线性方程建立超定方程组并转化如下:
$$ \psi \left( \varOmega \right) = \dfrac{1}{2}f{\left( \varOmega \right)^{\rm{T}}}f\left( \varOmega \right) $$ (2) 式中:有关相位差信息的非线性方程为
$f(\varOmega ) = \left[ {\varphi (x,y,z) - {\varphi _0}} \right] - \left[ {{\varphi _{{\rm{CCD}}}}(x,y,z) - \zeta } \right]$ ,向量$ \varOmega \text{=} ({x}_{1},{y}_{1},{z}_{1},{x}_{2}, {y}_{2},{z}_{2}) $ 表示点O'与O位置之间的相互关系,$ {\varphi _0} $ 为通过计算得到点O的相位差值,$ {\varphi _{{\text{CCD}}}}(x,y,z) $ 和$\zeta $ 分别为测量得到的点P、O的相位差信息[18]。对于两个点衍射源SF1和SF2的三维坐标值,可通过求解方程
$\psi (\varOmega )$ 的全局最优解${\varOmega ^ * }$ 获得。利用基于深度学习的点衍射干涉三维坐标定位方法可对目标方程进行求解,从而可以实现最终的高精度三维坐标定位。为了实现三维坐标的高精度和良好鲁棒性的定位,文中所提方法主要包含两个步骤来获取全局最优解
${\varOmega ^ * }$ 。在第一步中,文中采用深度学习算法获取初始点衍射源坐标。通过光线追迹点衍射干涉系统模型,获得大量数据集,包括不同位置的点衍射源坐标${\varOmega _{true}}$ 和相应的相位差信息${\varPhi _{train}}$ 。相位差信息${\varPhi _{train}}$ 被投入进搭建好的神经网络模型中,经过前向传播之后,输出两个点衍射源坐标${\varOmega _{predict}}$ 。文中通过损失函数$ {L_{RMSE}} $ 来评估神经网络的训练结果:$$ \begin{split} {L_{RMSE}} =& {\text{RMSE}}\left( {{\varOmega _{predict}} - {\varOmega _{true}}} \right) =\\ & \sqrt {\frac{1}{m}\sum\limits_{i = 1}^m {{{\left( {{{\omega '}_i} - {\omega _i}} \right)}^2}} } \\ \end{split} $$ (3) 式中:RMSE表示均方根误差;m为神经网络的输出数据个数;
$ {\omega '_i} $ 和$ {\omega _i} $ 分别表示模型的输出结果和对应的真值。在反向传播中,神经网络的神经元会根据损失函数的结果进行更新优化。$ {L_{RMSE}} $ 逐步迭代减小直至收敛,神经网络的输出值逐步逼近真值。将实测的相位差信息${\varPhi _{test}}$ 投入训练好的神经网络模型中,获得输出的点衍射源坐标$\varOmega '$ 。在第二步中,将第一步所得的初始坐标$\varOmega '$ 设为初始粒子,采用粒子群算法进行迭代优化,进一步提高坐标重构精度。最终通过以上两个步骤,可以获得高精度的三维坐标值${\varOmega ^ * }$ 。
Deep-learning-based point-diffraction interferometer for 3D coordinate positioning
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摘要: 为了提高现有的三维坐标定位技术的测量精度、稳定性和测量效率,提出了基于深度学习的点衍射干涉三维坐标定位方法。该方法设计了一个深度神经网络用于点衍射干涉场的坐标重构,将相位差矩阵作为输入,构建训练数据集,将点衍射源坐标作为输出,训练神经网络模型。利用训练有素的神经网络对测量到的相位分布进行初步处理,将相位信息转换为点衍射源坐标,根据得到的点衍射源坐标进一步修改粒子群算法的初始粒子,进而重构出高精度的三维坐标值。该神经网络为建立干涉场相位分布与点衍射源坐标之间的非线性关系提供了一种可行的方法,显著提高了三维坐标定位的精度、稳定性和测量效率。为验证所提方法的可行性,进行了数值仿真和实验验证,采用不同的方法进行反复对比与分析。结果表明:所提方法的单次测量时间均在0.05 s左右,其实验精度能够达到亚微米量级,重复性实验的均值和RMS值分别为0.05 μm和0.05 μm,充分证明了该方法的可行性,并证明了其良好的测量精度和可重复性,为三维坐标定位提供了一种有效可行的方法。Abstract: In order to improve the measurement accuracy, stability and efficiency of the existing 3D coordinate positioning technology, a deep-learning-based point-diffraction interferometer for 3D coordinate measurement method was proposed. A deep neural network was designed for coordinate reconstruction of the point-diffraction interference field. The phase difference matrix was used as the input to construct the training dataset, and the coordinates of point-diffraction sources were used as the output to train the neural network model. The well-trained neural network was used to process the measured phase distribution initially and the phase information was converted to the coordinates of point-diffraction sources. According to the obtained coordinates of point-diffraction sources, the initial particles of the particle swarm optimization algorithm were further modified, and then the high-precision three-dimensional coordinate was reconstructed. This neural network provides a feasible method to establish the nonlinear relationship between the phase distribution of the interference field and the coordinates of the point-diffraction sources, and significantly improves the accuracy, stability and measurement efficiency of the 3D coordinate positioning. In order to verify the feasibility of the proposed method, numerical simulation and experimental verification were carried out, and different methods were used for repeated comparison and analysis. The results show that the single measurement time of the proposed method is about 0.05 s, and the experimental accuracy can reach the submicron magnitude. The mean and RMS values of the repeatability experiments are 0.05 μm and 0.05 μm, respectively, which proves the feasibility of the proposed method and its good measurement accuracy and stability. It provides an effective and feasible method for 3D coordinate positioning.
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