With the advances in scientific foundations and technological implementations, optical metrology has become versatile problem-solving backbones in manufacturing, fundamental research, and engineering applications, such as quality control, nondestructive testing, experimental mechanics, and biomedicine. In recent years, deep learning, a subfield of machine learning, is emerging as a powerful tool to address problems by learning from data, largely driven by the availability of massive datasets, enhanced computational power, fast data storage, and novel training algorithms for the deep neural network. It is currently promoting increased interests and gaining extensive attention for its utilization in the field of optical metrology. Unlike the traditional “physics-based” approach, deep-learning-enabled optical metrology is a kind of “data-driven” approach, which has already provided numerous alternative solutions to many challenging problems in this field with better performances. In this review, we present an overview of the current status and the latest progress of deep-learning technologies in the field of optical metrology. We first briefly introduce both traditional image-processing algorithms in optical metrology and the basic concepts of deep learning, followed by a comprehensive review of its applications in various optical metrology tasks, such as fringe denoising, phase retrieval, phase unwrapping, subset correlation, and error compensation. The open challenges faced by the current deep-learning approach in optical metrology are then discussed. Finally, the directions for future research are outlined.

For quantitative phase imaging (QPI) based on transport-of-intensity equation (TIE), partially coherent illumination provides speckle-free imaging, compatibility with brightfield microscopy, and transverse resolution beyond coherent diffraction limit. Unfortunately, in a conventional microscope with circular illumination aperture, partial coherence tends to diminish the phase contrast, exacerbating the inherent noise-to-resolution tradeoff in TIE imaging, resulting in strong low-frequency artifacts and compromised imaging resolution. Here, we demonstrate how these issues can be effectively addressed by replacing the conventional circular illumination aperture with an annular one. The matched annular illumination not only strongly boosts the phase contrast for low spatial frequencies, but significantly improves the practical imaging resolution to near the incoherent diffraction limit. By incorporating high-numerical aperture (NA) illumination as well as high-NA objective, it is shown, for the first time, that TIE phase imaging can achieve a transverse resolution up to 208 nm, corresponding to an effective NA of 2.66. Time-lapse imaging of in vitro Hela cells revealing cellular morphology and subcellular dynamics during cells mitosis and apoptosis is exemplified. Given its capability for high-resolution QPI as well as the compatibility with widely available brightfield microscopy hardware, the proposed approach is expected to be adopted by the wider biology and medicine community.

The incremental gradient approaches, such as PIE and ePIE, are widely used in the field of ptychographic imaging due to their great flexibility and computational efficiency. Nevertheless, their stability and reconstruction quality may be significantly degraded when non-negligible noise is present in the image. Though this problem is often attributed to the non-convex nature of phase retrieval, we found the reason for this is more closely related to the choice of the step-size, which needs to be gradually diminishing for convergence even in the convex case. To this end, we introduce an adaptive step-size strategy that decreases the step-size whenever sufficient progress is not made. The synthetic and real experiments on Fourier ptychographic microscopy show that the adaptive step-size strategy significantly improves the stability and robustness of the reconstruction towards noise yet retains the fast initial convergence speed of PIE and ePIE. More importantly, the proposed approach is simple, nonparametric, and does not require any preknowledge about the noise statistics. The great performance and limited computational complexity make it a very attractive and promising technique for robust Fourier ptychographic microscopy under noisy conditions.

Optical neural network can process information in parallel by using the technology based on free-space and integrated platform. Over the last half century, the development of integrated circuits has been limited by Moore’s law. We know that neural network is based on the digital computer for successive calculation, most of which cannot be made into real-time processing system. Therefore, it is necessary to develop ONN for real-time processing and device miniaturization. In this paper, we review the progress of optical neural networks. Firstly, based on the principle of artificial neural networks, we elaborate the essence of optical matrix multiplier for linear operation. Then we introduce the optical neural network achieved by free-space optical interconnection and waveguide optical interconnection. Finally we talk about the nonlinearity in optical neural networks. With the gradual maturity of nanotechnology and the rapid advancement of silicon photonic integrated circuits, the progress of integrated photonic neural network has been promoted. Therefore, the construction of optical neural network on the future integrated photonic platform has potential application value.

Recovering the high-resolution three-dimensional (3D) surface of an object from a single frame image has been the ultimate goal long pursued in fringe projection profilometry (FPP). The color fringe projection method is one of the technologies with the most potential towards such a goal due to its three-channel multiplexing properties. However, the associated color imbalance, crosstalk problems, and compromised coding strategy remain major obstacles to overcome. Inspired by recent successes of deep learning for FPP, we propose a single-shot absolute 3D shape measurement with deep-learning-based color FPP. Through “learning” on extensive data sets, the properly trained neural network can “predict” the high-resolution, motion-artifact-free, crosstalk-free absolute phase directly from one single color fringe image. Compared with the traditional approach, our method allows for more accurate phase retrieval and more robust phase unwrapping. Experimental results demonstrate that the proposed approach can provide high-accuracy single-frame absolute 3D shape measurement for complicated objects.

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