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摘要:目的
应变重构是相衬光学相干层析力学性能表征中的关键步骤，其需要准确计算出差分包裹相位的梯度分布。为了能够解决强噪声干扰下的相位梯度重构信噪比低难题，提出了一种基于贝叶斯神经网络的相位梯度计算方法。
方法首先，通过计算机模拟不同散斑噪声等级下的包裹相位图，并生成相应的理想相位梯度，以构建网络的训练集。其次，基于网络训练集采用贝叶斯推断理论学习强噪声环境下的包裹相位与相位梯度的“端到端”映射关系。最后，将相衬光学相干层析测量的差分包裹相位结果送入贝叶斯神经网络进行处理，实现高信噪比相位梯度预测。此外，通过借助贝叶斯神经网络的统计特性，以模型不确定度来定量评估相位梯度预测结果的可靠性。
结果数值实验和三点弯曲力学加载实验对比了本文方法和主流的矢量方法，实验结果表明：在噪声较小条件下，本文方法重构的相位梯度信噪比可提升8%；在噪声较强条件下，本文方法能成功恢复因相位条纹难以分辨而无法计算的相位梯度。此外，模型不确定度能够定量分析网络的相位梯度预测误差。
结论可以预见，在样品形变复杂且先验信息未知条件下，本工作为相衬光学相干层析提供了一种有效的应变重构方法，从而能实现高质量和高可靠的内部力学性能表征。
Abstract:ObjectiveStrain reconstruction is a vital component in the characterization of mechanical properties using phase-contrast optical coherence tomography (PC-OCT). It requires an accurate calculation for gradient distributions on the wrapped phase map. In order to address the challenge of low signal-to-noise ratio (SNR) in phase gradient calculation under severe noise interference, a Bayesian-neural-network-based phase gradient calculation is presented.
MethodInitially, wrapped phase maps with varying levels of speckle noise and their corresponding ideal phase gradient distributions are generated through a computer simulation. These wrapped phase maps and phase gradient distributions serve as the training datasets. Subsequently, the network learns the “end-to-end” relationship between the wrapped phase maps and phase gradient distributions in a noisy environment by utilizing a Bayesian inference theory. Finally, the Bayesian neural network (BNN), after being trained, accurately predicts the high-quality distribution of phase gradients by inputting the measured wrapped phase-difference maps into the network. Additionally, the statistical process introduced by BNN allows for the utilization of model uncertainty in the quantitative assessment of the network predictions’ reliability.
ResultComputer simulation and three-point bending mechanical loading experiment compare the performance of the BNN and the popular vector method. The results indicate that the BNN can enhance the SNR of estimated phase gradients by 8% in the presence of low noise levels. Importantly, the BNN successfully recovers the phase gradients that the vector method is unable to calculate due to the unresolved phase fringes in the presence of strong noise. Moreover, the BNN model uncertainty can be used to quantitatively analyze the prediction errors.
ConclusionIt is expected that the contribution of this work can offer effective strain estimation for PC-OCT, enabling the internal mechanical property characterization to become high-quality and high-reliability.
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图 1 用于相位梯度计算的贝叶斯深度神经网络结构
Figure 1. Bayesian deep neural network (BNN) architecture for phase gradient calculation
图 2 相位图生成过程。(a) 伪随机数；(b) 拉格朗日外推后的相位图；（c）相位梯度标签；（d）带有散斑噪声的包裹相位图
Figure 2. Phase maps generation process. (a) Pseudo-random numbers; (b) Phase maps using extrapolation;(c) Phase gradient label; (d) Wrapped phase map with speckle noise
图 3 基于贝叶斯神经网络的相位梯度预测过程
Figure 3. The prediction process of phase gradient using Bayesian neural network
图 4 不同方法估计的相位梯度结果。(a)不同噪声等级的相位图；(b)理论相位梯度结果；(c)矢量法；(d)贝叶斯神经网络；(e)贝叶斯神经网络模型不确定度；(f)网络预测结果的误差分布
Figure 4. Phase gradient estimated using different approaches. (a) Phase maps with different noise level; (b) Vector method; (c) Bayesian neural network; (d) Predicted error distributions
图 5 线扫描谱域光学相干层析测量系统。(a)原理图；(b) 实物图
Figure 5. Line-field spectral-domain OCT system. (a) Schematic diagram. (b) Photograph
图 6 硅胶薄膜样品变形实验结果。(a)差分包裹相位图；(b)矢量法估计的相位梯度；(c)贝叶斯神经网络估计的相位梯度；(d)贝叶斯神经网络的模型不确定度
Figure 6. Experimental results of silicone film deformations. (a) Wrapped phase-difference map. (b) Phase gradient estimated using vector method. (c) Phase gradient estimated using BNN. (d) BNN model uncertainty.
图 7 相位退相关实验结果。(a)-(b) 加载量分别为12 μm和14 μm对应的差分包裹相位；(c)-(d) 贝叶斯网络估计的相位梯度结果；(e)-(f) 贝叶斯网络的模型不确定度
Figure 7. Experimental results of phase decorrelation. (a)-(b) Wrapped phase-difference maps corresponding to the loading 12 μm and 14 μm, respectively. (c)-(d) Results of phase gradient estimated using BNN. (e)-(f) BNN model uncertainty.
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