Fringe projection profilometry (FPP) has become a more prevalently adopted technique in intelligent manufacturing, defect detection, and some other important applications. In FPP, efficiently recovering the absolute phase has always been a great challenge. The stereo phase unwrapping (SPU) technologies based on geometric constraints can eliminate phase ambiguity without projecting any additional patterns, which maximizes the efficiency of the retrieval of the absolute phase. Inspired by recent successes of deep learning for phase analysis, we demonstrate that deep learning can be an effective tool that organically unifies phase retrieval, geometric constraints, and phase unwrapping into a comprehensive framework. Driven by extensive training datasets, the neural network can gradually “learn” to transfer one high-frequency fringe pattern into the “physically meaningful” and “most likely” absolute phase, instead of “step by step” as in conventional approaches. Based on the properly trained framework, high-quality phase retrieval and robust phase ambiguity removal can be achieved only on a single-frame projection. Experimental results demonstrate that compared with traditional SPU, our method can more efficiently and stably unwrap the phase of dense fringe images in a larger measurement volume with fewer camera views. Limitations about the proposed approach are also discussed. We believe that the proposed approach represents an important step forward in high-speed, high-accuracy, motion-artifacts-free absolute 3D shape measurement for complicated objects from a single fringe pattern.

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.

Temporal phase unwrapping (TPU) is an essential algorithm in fringe projection profilometry (FPP), especially when measuring complex objects with discontinuities and isolated surfaces. Among others, the multi-frequency TPU has been proven to be the most reliable algorithm in the presence of noise. For a practical FPP system, in order to achieve an accurate, efficient, and reliable measurement, one needs to make wise choices about three key experimental parameters: the highest fringe frequency, the phase-shifting steps, and the fringe pattern sequence. However, there was very little research on how to optimize these parameters quantitatively, especially considering all three aspects from a theoretical and analytical perspective simultaneously. In this work, we propose a new scheme to determine simultaneously the optimal fringe frequency, phase-shifting steps and pattern sequence under multi-frequency TPU, robustly achieving high accuracy measurement by a minimum number of fringe frames. Firstly, noise models regarding phase-shifting algorithms as well as 3-D coordinates are established under a projector defocusing condition, which leads to the optimal highest fringe frequency for a FPP system. Then, a new concept termed frequency-to-frame ratio (FFR) that evaluates the magnitude of the contribution of each frame for TPU is defined, on which an optimal phase-shifting combination scheme is proposed. Finally, a judgment criterion is established, which can be used to judge whether the ratio between adjacent fringe frequencies is conducive to stably and efficiently unwrapping the phase. The proposed method provides a simple and effective theoretical framework to improve the accuracy, efficiency, and robustness of a practical FPP system in actual measurement conditions. The correctness of the derived models as well as the validity of the proposed schemes have been verified through extensive simulations and experiments. Based on a normal monocular 3-D FPP hardware system, our method enables high-precision unambiguous 3-D shape measurement with the highest fringe frequency up to 180 by using only 7 fringe patterns achieving a depth precision ∼ 38μm across a field of view of 400 × 300 × 400 mm.

Stereo phase unwrapping (SPU) has been increasingly applied to high-speed real-time fringe projection profilometry (FPP) because it can retrieve the absolute phase or matching points in a stereo FPP system without projecting or acquiring additional fringe patterns. Based on a pre-defined measurement volume, artificial maximum/minimum phase maps can be created solely using geometric constraints of the FPP system, permitting phase unwrapping on a pixel-by-pixel basis. However, when high-frequency fringes are used, the phase ambiguities will increase which makes SPU unreliable. Several auxiliary techniques have been proposed to enhance the robustness of SPU, but their flexibility still needs to be improved. In this paper, we proposed an adaptive depth constraint (ADC) approach for high-speed real-time 3D shape measurement, where the measurement depth volume for geometric constraints is adaptively updated according to the current reconstructed geometry. By utilizing the spatio-temporal correlation of moving objects under measurement, a customized and tighter depth constraint can be defined, which helps enhance the robustness of SPU over a large measurement volume. Besides, two complementary techniques, including simplified left-right consistency check and feedback mechanism based on valid area, are introduced to further increase the robustness and flexibility of the ADC. Experimental results demonstrate the success of our proposed SPU approach in recovering absolute 3D geometries of both simple and complicated objects with only three phase-shifted fringe images.