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.

二维材料由于其独特的物理化学性质，对纳米光子学及光电子学的应用与发展具有重要研究价值。特别是二维材料中声子与光子耦合激发产生的声子极化激元高度局域在纳米尺度，在片上光子学的光学操控和能量传输等前沿研究领域具有极大的应用潜力。同时，光电器件制造进入纳米节点，器件应用对材料表征精度具有纳米级的要求。然而目前对声子极化激元特性分析的关键之一在于测量其干涉条纹周期，测量结果准确性依赖于仪器设备校准。因此，为实现对声子极化激元干涉条纹的精确测量，文中提出构建铬原子自溯源型光栅与二维材料的复合结构，分析金属光栅结构周期性变化对二维材料的声子极化激元耦合增强与调制作用，以及基于该原理实现对声子极化激元干涉条纹周期的精密测量。研究实现了测量干涉条纹周期为(261.01±0.34) nm的亚纳米级高精度测量，相比具有不确定度为4 nm的传统拟合测量方式具有可溯源的计量精度，同时实现了对测量仪器的亚纳米级精密校准。自溯源光栅天然溯源至基本自然常数的特性使得测量结果具备极好的准确性和可靠性，为二维材料在微纳光子学器件领域的应用提供了保障。