Recently, deep learning has yielded transformative success across optics and photonics, especially in optical metrology. Deep neural networks (DNNs) with a fully convolutional architecture (e.g., U-Net and its derivatives) have been widely implemented in an end-to-end manner to accomplish various optical metrology tasks, such as fringe denoising, phase unwrapping, and fringe analysis. However, the task of training a DNN to accurately identify an image-to-image transform from massive input and output data pairs seems at best na?ve, as the physical laws governing the image formation or other domain expertise pertaining to the measurement have not yet been fully exploited in current deep learning practice. To this end, we introduce a physics-informed deep learning method for fringe pattern analysis (PI-FPA) to overcome this limit by integrating a lightweight DNN with a learning-enhanced Fourier transform profilometry (LeFTP) module. By parameterizing conventional phase retrieval methods, the LeFTP module embeds the prior knowledge in the network structure and the loss function to directly provide reliable phase results for new types of samples, while circumventing the requirement of collecting a large amount of high-quality data in supervised learning methods. Guided by the initial phase from LeFTP, the phase recovery ability of the lightweight DNN is enhanced to further improve the phase accuracy at a low computational cost compared with existing end-to-end networks. Experimental results demonstrate that PI-FPA enables more accurate and computationally efficient single-shot phase retrieval, exhibiting its excellent generalization to various unseen objects during training. The proposed PI-FPA presents that challenging issues in optical metrology can be potentially overcome through the synergy of physics-priors-based traditional tools and data-driven learning approaches, opening new avenues to achieve fast and accurate single-shot 3D imaging.

We propose a high-accuracy artifacts-free single-frame digital holographic phase demodulation scheme for relatively low-carrier frequency holograms—deep learning assisted variational Hilbert quantitative phase imaging (DL-VHQPI). The method, incorporating a conventional deep neural network into a complete physical model utilizing the idea of residual compensation, reliably and robustly recovers the quantitative phase information of the test objects. It can significantly alleviate spectrum-overlapping-caused phase artifacts under the slightly off-axis digital holographic system. Compared to the conventional end-to-end networks (without a physical model), the proposed method can reduce the dataset size dramatically while maintaining the imaging quality and model generalization. The DL-VHQPI is quantitatively studied by numerical simulation. The live-cell experiment is designed to demonstrate the method's practicality in biological research. The proposed idea of the deep learning-assisted physical model might be extended to diverse computational imaging techniques.

三维形貌测量在先进制造、航空航天、生物医学等领域发挥着重要的应用。凭借高精度、全视场、非接触等优点，条纹投影轮廓术是目前使用最广泛的一种光学三维测量手段。为了获得物体全局三维信息，通常需要将待测物置于转台之上，通过不断地扫描和拼接来获得物体的全局信息。然而，传统的扫描和拼接是以离线的方式进行的，导致整个三维模型的重建速度缓慢。现有的实时点云配准方法虽然能够有效提高点云扫描与拼接的速度，但实时点云拼接的精度依然受待测物的运动状态影响。本文针对上述问题进行优化改进，提出一种基于全局优化的实时高精度模型重建方法。首先，介绍了一种由粗配准到精配准的快速点云配准算法并提出了基于点云法向量约束的点云初始化算法，能够提升粗配准过程中点云初始位姿计算的稳定性与精度。其次，在精配准阶段引入了图优化算法以获得全局点云位姿的最优解，进一步提升了全局点云配准的精度。实验结果表明，所提方法相比于现有实时模型重建方法，能够实现更高精度且稳定的全局点云配准。特别地，针对动态场景中由于抖动等因素引起的被测物体速度突变等情况，本方法依然能够鲁棒地完成三维模型重建，全方位模型重建的精度达84 μm。

In recent years, there has been tremendous progress in the development of deep-learning-based approaches for optical metrology, which introduce various deep neural networks (DNNs) for many optical metrology tasks, such as fringe analysis, phase unwrapping, and digital image correlation. However, since different DNN models have their own strengths and limitations, it is difficult for a single DNN to make reliable predictions under all possible scenarios. In this work, we introduce ensemble learning into optical metrology, which combines the predictions of multiple DNNs to significantly enhance the accuracy and reduce the generalization error for the task of fringe-pattern analysis. First, several state-of-the-art base models of different architectures are selected. A K-fold average ensemble strategy is developed to train each base model multiple times with different data and calculate the mean prediction within each base model. Next, an adaptive ensemble strategy is presented to further combine the base models by building an extra DNN to fuse the features extracted from these mean predictions in an adaptive and fully automatic way. Experimental results demonstrate that ensemble learning could attain superior performance over state-of-the-art solutions, including both classic and conventional single-DNN-based methods. Our work suggests that by resorting to collective wisdom, ensemble learning offers a simple and effective solution for overcoming generalization challenges and boosts the performance of data-driven optical metrology methods.