Fringe projection profilometry (FPP) is a non-contact, high-precision technique for measuring three-dimensional (3D) shapes. An essential step of FPP is to recover the phase distribution from the deformed fringe patterns. In real applications, the captured fringe patterns often suffer from noises, which results in degradation of the performance of phase retrieval and shape reconstruction. Fringe denoising can be applied to suppress the influence of noise in FPP. This paper introduces a novel fringe denoising method based on robust principal component analysis (RPCA). The proposed method makes use of the low-rankness of the clean fringe patterns and the sparsity of the strong impulsive fringe noise. RPCA is then applied to effectively mitigate the strong impulsive fringe noise and suppress the random additive noise. The proposed method features 2D processing of the fringe patterns and is easy to implement. Its effectiveness is demonstrated via numerical simulations.
Phase unwrapping is an essential step for 3D shape measurement based on fringe projection. Temporal phase unwrapping methods can be implemented by analyzing the multiple patterns that encode the fringe order information. They can retrieve the fringe orders on a pixel-by-pixel basis and are less prone to error propagation compared with spatial methods. However, fringe orders errors may still occur due to noise, reflectivity fluctuation and discontinuity of the object surface. Such errors may exhibit an impulsive nature and result in significant error to the recovered absolute phase map. This has been exploited by several methods to correct the fringe order errors, e.g., by filtering the fringe order sequences in a line-by-line manner. In this paper, a new method is proposed to correct the errors associated with fringe orders for the temporal phase unwrapping. The scheme first makes use of the low-rankness property of the fringe order map and sparse nature of the impulsive fringe order errors to more effectively remove the impulsive errors by applying robust principal component analysis (RPCA) algorithm. Then the smoothness of the two-dimensional unwrapped phase map is examined and the residual fringe order errors are detected based on a discontinuity measure of the phase map and corrected by comparing phase difference between two adjacent pixels in the unwrapped phase. The effectiveness of the proposed method is demonstrated via numerical experiments.
Phase shifting profilometry (PSP) is considered as an effective method for 3D shape measurement based on fringe projection. However, PSP is not suitable for dynamic measurement, as it requires that the object be kept still. Movement of the object during the cause of projection of multiple fringe patterns may lead to significant error in the measurement of the 3D shape. A number of approaches were proposed to combat this problem consisting of two steps: Capturing of the movement and then compensation (or correction) of fringe patterns. However, such compensation is only valid for the cases where the object moves or rotates in the way that all points on the object surface change by the same amount. In other words, there is still not a method effective for measuring objects moving in a free 3D space. In this paper, a new method is proposed to combat the problem. Firstly, movement of the object is capturing by means of existing methods, yielding rotation matrix and translation vector, able to characterize arbitrary movement in a 3D space. Secondly, variation of the fringe patterns by the movement is analyzed and formulated, leading to the expressions of phase maps. Based on these expressions, a new method is proposed to compensate the variance on height map, with which PSP can be used to yield improved measurement performance. Computer simulations is carried out to verify the effectiveness of the proposed method.
Fringe projection profilometry (FPP) has attracted considerable interests for addressing the challenge of measuring three-dimension (3D) shapes of moving objects. Compared with phase shift profilometry (PSP) which requires the capture of multiple fringe patterns and is thus only suitable for static objects, Fourier transform profilometry (FTP) is less sensitive to motion-induced errors. However, FTP is prone to the influence of background lights and variations of the surface reflectivity, which may result in less accurate measurements. There are studies aimed to reduce the measurement errors with FTP using more sophisticated processing of the fringe patterns. However, existing works focus on schemes based on single images and the correlation of the dynamic 3D shapes is largely unexplored. In this work, we present a new method that refines FTP-based dynamic shape measurements. Assuming 3D rigid movements of the targets, we propose to utilize knowledge of the motion parameters and combine the multiple height maps obtained from several FTP measurements after compensating the motion effect. Approaches for automatically combining the height information are studied. It is observed that the measurement accuracy can be improved using the proposed method and the influence due to ambient lights and reflectivity variations can be suppressed. Computer simulations are performed to verify the effectiveness of the proposed method. The proposed method can also be integrated into other FPP systems to improve the performance for dynamic object measurements.
KEYWORDS: Fringe analysis, Speckle pattern, Speckle, Principal component analysis, 3D metrology, Composites, Error analysis, Shape analysis, Superposition, Signal to noise ratio
Phase unwrapping is one of the key steps for fringe projection profilometry (FPP)-based 3D shape measurements. Conventional spatial phase unwrapping schemes are sensitive to noise and discontinuities, which may suffer from low accuracies. Temporal phase unwrapping is able to improve the reliability but often requires the acquisition of additional patterns, increasing the measurement time or hardware costs. This paper introduces a novel phase unwrapping scheme that utilizes composite patterns consisting of the superposition of standard sinusoidal patterns and randomly generated speckles. The low-rankness of the deformed sinusoidal patterns is studied. This is exploited together with the sparse nature of the speckle patterns and a robust principal component analysis (RPCA) framework is then deployed to separate the deformed fringe and speckle patterns. The cleaned fringe patterns are used for generating the wrapped phase maps using the standard procedures of phase shift profilometry (PSP) or Fourier Transform profilometry (FTP). Phase unwrapping is then achieved by matching the deformed speckle patterns that encode the phase order information. In order to correct the impulsive fringe order errors, a recently proposed postprocessing step is integrated into the proposed scheme to refine the phase unwrapping results. The analysis and simulation results demonstrate that the proposed scheme can improve the accuracy of FPP-based 3D shape measurements by effectively separating the fringe and speckle patterns.
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