Deep learning has gained increasing attention in the field of optical metrology and demonstrated great potential in solving a variety of optical metrology tasks, such as fringe analysis and phase unwrapping. However, deep neural networks cannot always produce a provably correct solution, and the prediction error cannot be easily detected and evaluated unless the ground-truth is available. This issue is critical for optical metrology, as the reliability and repeatability of the measurement are of major importance for high-stakes scenarios. In this paper, for the first time to our knowledge, we demonstrate that a Bayesian convolutional neural network (BNN) can be trained to not only retrieve the phase from a single fringe pattern but also produce uncertainty maps depicting the pixel-wise confidence measure of the estimated phase. Experimental results show that the proposed BNN can quantify the reliability of phase predictions under conditions of various training dataset sizes and never-before-experienced inputs. Our work allows for making better decisions in deep learning solutions, paving a new way to reliable and practical learning-based optical metrology.

中文翻译：

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具有不确定性估计的基于深度学习的条纹图案分析

深度学习在光学计量领域越来越受到关注，并在解决各种光学计量任务（如条纹分析和相位展开）方面表现出巨大潜力。然而，深度神经网络并不总能产生可证明正确的解决方案，并且除非有真实可用的地面实况，否则无法轻松检测和评估预测错误。这个问题对于光学计量至关重要，因为测量的可靠性和可重复性对于高风险场景至关重要。在本文中，据我们所知，我们第一次证明了贝叶斯卷积神经网络 (BNN) 不仅可以从单个条纹图案中检索相位，还可以生成描绘像素级置信度的不确定性图估计的阶段。实验结果表明，所提出的 BNN 可以量化在各种训练数据集大小和前所未有的输入条件下相位预测的可靠性。我们的工作允许在深度学习解决方案中做出更好的决策，为可靠且实用的基于学习的光学计量学铺平了道路。