Predistorting Projected Fringes for High-Accuracy 3-D Phase Mapping in Fringe Projection Profilometry

Fringe projection profilometry (FPP) is a three-dimensional (3D) shape measurement method that involves projecting fringe patterns onto the object. A phase map retrieved from these fringe images is used for reconstructing the 3D surface of the object. Fourier transform and phase-shifting are two of the widely used fringe analysis techniques for performing 3D shape measurement using FPP. Fourier transform profilometry (FTP) has the advantage of performing high-speed measurement due to its single-shot nature. However, the reconstructed 3D surface has artifacts and high noise, specifically on the edges. On the other hand, phase-shifting profilometry (PSP) has the advantage of higher accuracy (relatively less noise level) but compromises on measurement speed. In this research, we propose a deep learning method to enhance the quality of the FTP phase maps using an efficient deep learning model called phase map enhancement net (PMENet). PMENet takes an FTP phase map as input and predicts a high-quality phase map in a supervised manner by using the phase maps obtained from 18-step PSP as ground truth. The training dataset was generated using a virtual FPP system. Validations were conducted on both the simulated data (generated by virtual FPP system) and the real-world data. The experimental results demonstrate that the trained neural network model can successfully improve the quality of the 3D geometric reconstruction with FTP and reduced the mean and root-mean-square error by 66% and 43%, respectively.

In fringe projection profilometry, by taking the projector as a camera, depth measurement has the similar principle with binocular vision. The matching of feature points carrying depth information plays an important role in measurement. Due to the existence of difficultly-corrected projector errors, the measurement results of using a fixed point in camera corresponding to the points in the projector or of conversely using a fixed point in projector corresponding to the points in the camera is not exactly same. According to fringe projection system, a function representing the relationship between the depths and the corresponding fringe phases is introduced for measurement. This traditional method usually requires three or more known reference planes to calibrate parameters determined by the measurement system. However, another way is also feasible. Based on the measurement system, a generic function representing the relationship between the depths and the corresponding pixel shifts are also presented in this paper. Using these two functions allows us to recover the depth information of the object. Theoretical analyses are carried out to investigate the performances of these two methods. Comparative experiments are implemented, and their results demonstrate that the depth measurement method from pixel shifts is immune to the influence of high order harmonics as a little expense of efficiency, being better than the method from fringe phases having high measurement efficiency regardless of the low accuracy.

In-situ areal inspection of powder bed for electron beam fusion system based on fringe projection profilometry

A spatial algorithm to reduce phase wraps from two dimensional signals in fringe projection profilometry

In fringe projection profilometry, system calibration is crucial for guaranteeing the measurement accuracies. Its difficulty lies in calibrating projector parameters, especially when the projector lens has distortions, since the projector, unlike a camera, cannot capture images, leading to an obstacle to knowing the correspondences between its pixels and object points. For solving this issue, this paper, exploiting the fact that the fringe phases on a plane board theoretically have a distribution of rational function, proposes an iterative calibration method based on phase measuring. Projecting fringes onto the calibration board and fitting the measured phases with a rational function allow us to determine projector pixels corresponding to the featured points on the calibration board. Using these correspondences, the projector parameters are easy to estimate. Noting that the projector lens distortions may deform the fitted phase map thus inducing errors in the estimates of the projector parameters, this paper suggests an iterative strategy to overcome this problem. By implementing the phase fitting and the parameter estimating alternately, the intrinsic and extrinsic parameters of the projector, as well as its lens distortion coefficients, are determined accurately. For compensating for the effects of the lens distortions on measurement, this paper gives two solutions. The pre-compensation actively curves the fringes in computer when generating them; whereas when using the post-compensation, the lens distortion correction is performed in the data processing stage. Both methods are experimentally verified to be effective in improving the measurement accuracies.

In fringe projection profilometry, system calibration serves as a critical prerequisite for ensuring measurement precision. During calibration procedures, the elimination of specular reflection-induced saturated image poses significant challenges due to inherent surface reflectance variations. Therefore, a calibration technique utilizing adaptive polarization fringe projection is proposed in this paper. The proposed method analyzes gray-level information model from the polarization camera and employs a dichotomizing search strategy to determine optimal polarization projection intensity for saturated pixels. Furthermore, precise correspondence between image pixels and projection pixels is established. Then, adaptive polarization projection fringe patterns are generated. The proposed method enables the acquisition of high-quality calibration images, effectively enhancing system calibration accuracy. Compared with conventional calibration methods under natural conditions, the proposed method improves calibration accuracy while achieving a 9.6% improvement in measurement precision.

In the task of 3-D topography measurement by fringe projection profilometry (FPP), it is crucial to establish mapping from the phase map to the 3-D coordinates, known as 3-D calibration. The traditional methods are prone to select some specific functions to fit the phase-to-coordinates’ relationship, which needs to make a compromise between measurement accuracy and efficiency. This article proposes a novel calibration method based on the Gaussian process (GP) regression to solve this problem. In this work, according to the geometric and other systemic constraints, a pixel-dependent semiparameterized calibration model is derived to guarantee the efficiency of computation and data storage. Based on the spatial correlations of the calibration data, the GP regression method is applied to enhance the fitting ability and flexibility of the calibration model without any specific functions and parameters. The GP regression method is also applied to remove random noise from the phase map, which further improves the accuracy of 3-D coordinates. The experimental results of measuring a whiteboard and a double ball bar demonstrate the superiority of the proposed GP-based calibration model in terms of accuracy and robustness when compared with the traditional models.

Three-dimensional (3D) shape measurement of fringe projection profilometry (FPP) with high speed and accuracy is required in many applications. The measurement speed of FPP system is mainly limited by the low frame rate of pattern projection. Although defocusing binary patterns can be used to increase the measurement speed greatly, it will decrease the measurement depth. To this end, a novel triangular pattern generation method is proposed in this paper. By designing and projecting binary strip patterns with focused projector, images of triangular patterns can be then acquired with high frame rate. Fast and accurate 3D shape measurement can be finally obtained by using phase-shifting triangular patterns. Compared with the traditional sinusoidal patterns, the proposed method can improve the projection rate more than 4 times. Moreover, the proposed method will not decrease the measurement depth. Experimental results are given to confirm the validity of the proposed method.

Fringe projection profilometry (FPP) is a widely employed technique owing to its rapid speed and high accuracy. However, when FPP is utilized to measure shiny surfaces, the fringes tend to be saturated or too dark, which significantly compromises the accuracy of the 3D measurement. To overcome this challenge, this paper proposes an efficient method for the 3D measurement of shiny surfaces based on FPP. Firstly, polarizers are employed to alleviate fringe saturation by leveraging the polarization property of specular reflection. Although polarizers reduce fringe intensity, a deep learning method is utilized to enhance the quality of fringes, especially in low-contrast regions, thereby improving measurement accuracy. Furthermore, to accelerate measurement efficiency, a dual-frequency complementary decoding method is introduced, requiring only two auxiliary fringes for accurate fringe order determination, thereby achieving high-efficiency and high-dynamic-range 3D measurement. The effectiveness and feasibility of the proposed method are validated through a series of experimental results.

A phase unwrapping method suitable for high frequency fringe based on edge feature

Fringe projection profilometry (FPP) has been one of the most popular non-contact methods for 3D surface measurement in recent years. In FPP, the quality of the fringe pattern determines the measurement accuracy and measurement range to a great extent. In this paper, we proposed a high-quality fringe projection method using a biaxial MEMS scanning mirror and a laser diode (LD). The fringe pattern is produced by a very low NA (numerical aperture) scanning laser beam. Compared with pixel array based fringe pattern generation method, such as DLP and LCOS, the generation method can produce higher performance fringe pattern, which is high contrast, narrow pitch and long depth. In this paper, we also did a contrast between different fringe pattern generation methods.

Single-shot fringe projection profilometry (FPP) is essential for retrieving the absolute depth information of the objects in high-speed dynamic scenes. High-precision 3D reconstruction using only one single pattern has become the ultimate goal in FPP. The frequency-multiplexing (FM) method is a promising strategy for realizing single-shot absolute 3D measurement by compounding multi-frequency fringe information for phase unwrapping. In order to solve the problem of serious spectrum aliasing caused by multiplexing schemes that cannot be removed by traditional spectrum analysis algorithms, we apply deep learning to frequency multiplexing composite fringe projection and propose a composite fringe projection deep learning profilometry (CDLP). By combining physical model and data-driven approaches, we demonstrate that the model generated by training an improved deep convolutional neural network can directly perform high-precision and unambiguous phase retrieval on a single-shot spatial frequency multiplexing composite fringe image. Experiments on both static and dynamic scenes demonstrate that our method can retrieve robust and unambiguous phases information while avoiding spectrum aliasing and reconstruct high-quality absolute 3D surfaces of objects only by projecting a single composite fringe image.

Aiming at the problem of the low accuracy of projector calibration in a structured light system, an improved projector calibration method is proposed in this paper. One of the key ideas is to estimate the sub-pixel coordinates in the projector image plane using local random sample consensus (RANSAC). A bundle adjustment (BA) algorithm is adopted to optimize the calibration parameters to further improve the accuracy and robustness of the projector calibration. After system calibration and epipolar rectification, the mapping relationship between the pixel coordinates and the absolute phase in the projector image plane is established by using cubic polynomial fitting, and the disparity is rapidly solved by using the mapping relationship, which not only ensures the measurement accuracy, but also improves the measurement efficiency. The experimental results demonstrated that the average re-projection error after optimization is reduced to 0.03 pixels, and the proposed method is suitable for high-speed 3D reconstruction without the time-consuming homogenous point searching.

Profilometry by fringe projection is an optical metrology technique implemented projecting a sinusoidal grating onto a three-dimensional surface, where the resulting deformed grating image represents the object's height dis- tribution modulated in phase. Fringe projection can be implemented as a phase shifting process or as a one-frame method. In this work, both approaches are compared using a correlation and a Fourier transform based algorithm for phase extraction. As a first step of the surface recovering process, a wrapped phase image is obtained. Therefore, a correction is applied by means of a phase un- wrapping algorithm, obtaining a continuous phase distribution. The results show that the phase shifting approach returns a phase distribution with higher resolution and less noise than the one-frame approach.

Blade is the key component of the aero-engine. In generally, it requires precise size and accurate shape, so the three-dimensional shape measurement of the blade is very important. Fringe projection profilometry is generally used to measure the 3D shape of an object, because of the advantages of non-contact operation, full-field acquisition, high resolution, and fast data processing. In this paper, 3D shape measurement method based on surface structured light that combination of gray-code and phase-shift projection is proposed. The wrapped phase of the blade is got by the four-step phase-shift method. In the projection process of the gray-code, due to the ambient light, different surface reflectance and surface physical discontinuous, the edge of gray-code becomes smooth, leading to decode error, so that the gray-code pattern must be binaried before decode. Through the accurate binarization of the blade gray-code pattern, the decoding cycle of the blade is achieved, and the unwrapped phase is achieved by phase unwrapping. Then the unwrapped phase difference between the blade and reference plane is got, the height of the blade can be obtained by the relationship between the phase difference and the height. The experimental and simulation results show that the proposed method can achieve a high precision, high speed and low cost 3D shape measurement of the blade. The measurement accuracy reaches 0.03 mm. The proposed method extends the reliability and practicality of the fringe projection profilometry.