Fringe projector profilometry (FPP) is an important three-dimensional (3D) measurement technique, especially when high precision and speed are required. Thus, theoretical interrogation is critical to provide deep understanding and possible improvement of FPP. By dividing an FPP measurement process into four steps (system calibration, phase measurement, pixel correspondence, and 3D reconstruction), we give theoretical analysis on the entire process except for the extensively studied calibration step. Our study indeed reveals a series of important system properties, to the best of our knowledge, for the first time: (i) in phase measurement, the optimal and worst fringe angles are proven perpendicular and parallel to epipolar line, respectively, and can be considered as system parameters and can be directly made available during traditional calibration, highlighting the significance of the epipolar line; (ii) in correspondence, when two sets of fringes with different fringe orientations are projected, the highest correspondence precision can be achieved with arbitrary orientations as long as these two orientations are perpendicular to each other; (iii) in reconstruction, a higher reconstruction precision is given by the 4-equation methods, while we notice that the 3-equation methods are almost dominatingly used in literature. Based on these theoretical results, we propose a novel FPP measurement method which (i) only projects one set of fringes with optimal fringe angle to explicitly work together with the epipolar line for precise pixel correspondence; (ii) for the first time, the optimal fringe angle is determined directly from the calibration parameters, instead of being measured; (iii) uses 4 equations for precise 3D reconstruction but we can remove one equation which is equivalent to an epipolar line, making it the first algorithm that can use 3-equation solution to achieve 4-equation precision. Our method is efficient (only one set of fringe patterns is required in projection and the speed is doubled in reconstruction), precise (in both pixel correspondence and 3D reconstruction), and convenient (the computable optimal fringe angle and a closed-form 3-equation solution). We also believe that our work is insightful in revealing fundamental FPP properties, provides a more reasonable measurement for practice, and thus is beneficial to further FPP studies.
In a structured-light system, lens distortion of the camera and projector is the main source of 3D measurement error. In this Letter, a new approach, to the best of our knowledge, of using deep neural networks to address this problem is proposed. The neural network consists of one input layer, five densely connected hidden layers, and one output layer. A ceramic plate with flatness less than 0.005 mm is used to acquire the training, validation, and test data sets for the network. It is shown that the measurement accuracy can be enhanced to 0.0165 mm in the RMS value by this technique, which is an improvement of 93.52%. It is also verified that the constructed neural network is with satisfactory repeatability.
The monotonicity of depth in a geometric constraint based absolute phase unwrapping is analyzed and a monotonic discriminant of Δ(uc,vc) is presented in this paper. The sign of the discriminant determines the distance selection for the virtual plane to create the artificial absolute phase map for a given structured light system. As Δ(uc,vc) ≥ 0 at an arbitrary point on the CCD pixel coordinates the minimum depth distance is selected for the virtual plane, and the maximum depth distance is selected as Δ(uc,vc) ≤ 0. Two structured light systems with different signs of the monotonic discriminant are developed and the validity of the theoretical analysis is experimentally demonstrated.
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