Fringe projection profilometry method with high efficiency, precision, and convenience: theoretical analysis and development

Abstract

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.

An optical non-contact flow-meter of conveyor belt based on FPGA

“…In formula (13), h j and w j can be obtained by the mathematical relationship between the two-dimensional coordinates of the light bar in the image coordinate system and the threedimensional coordinates in the world coordinate system.…”

“…Given the limitations of ultrasonic belt scales, some noncontact measurement methods based on the principle of optical projection have been proposed. In article [13], the authors proposed a new method for edge projector profile measurement and demonstrated the perpendicular relationship between the epipolar line and the optimal fringe angle and reconstructed the three-dimensional model of the object by using three equations. In article [14], Huang designed an optical belt scale.…”

High-Efficiency Dynamic Three-Dimensional Topography Measurement Using the Phase Shift Generation Method

“…In contrast, the transform-based methods [17][18][19][20][21][22] (e.g., FT, window Fourier transform, and wavelet transform) just need one single fringe for phase calculation by spatial or frequency domain analysis. The FT [17,18] method is the most representative transform method, which is well-suited for high-speed 3D measurement. Nevertheless, the FT method has the inherent problem of spectrum leakage that will influence its precision in dynamic scenes.…”

Use of Phase-Angle Model for Full-Field 3D Reconstruction under Efficient Local Calibration

“…Fringe projection profilometry (FPP) has emerged as a powerful and versatile technique in the field of optical metrology and surface profilometry. Over the years, it has gained significant attention due to its high-accuracy [ 1 , 2 ], high-speed [ 3 , 4 ], and high-resolution [ 5 , 6 ] capabilities, enabling the accurate measurement of 3D shapes and surface topography. This technology has been widely applied in industrial measurement [ 7 ], cultural relic protection [ 8 ], surgical medicine [ 9 ], artificial intelligence [ 10 ], and other fields [ 11 , 12 ].…”