Fringe Projection System Research Articles

Surface profile measurement of metal objects by use of a fringe projection system with polarized dual projectors

When measuring surface profiles of metal objects by use of the fringe projection technique, a “high dynamic range” issue usually occurs and affects measurement accuracy and efficiency. To alleviate this problem, this paper suggests a fringe projection measurement system that consists of dual projectors having orthogonal polarization directions and a polarization camera with four polarized channels. The projectors simultaneously cast fringe patterns with opposite phases onto the measured metal objects, and the camera grabs four composite patterns at a single shot. By analyzing these composite patterns, two separate fringe patterns that correspond to the projected fringe patterns can be reconstructed. In this procedure, because redundant fringe patterns have been collected, the oversaturated areas that are caused by the “high dynamic range” issue and appear in some of the four composite patterns can be excluded and will not affect the reconstructed fringes. As a result, the reconstructed fringe patterns can have a larger dynamic range over the camera capacity, thus helping to alleviate the effects of the “high dynamic range” issue. By using the phase-shifting technique, the fringe phases and, further, the depth map of the measured object, are calculated. Additionally, this method has an improved measurement efficiency in comparison with others using a single projector because we reconstruct two phase-shifted fringe patterns from a single shot. The validity of this method is demonstrated by using experimental results.

Extrinsic parameters optimization for fringe projection system based on standard components

Fringe projection profilometry (FPP) is a wildly used three-dimension reconstruction method, where the reconstruction accuracy is closely related to the calibration precision. However, various sources of error in the calibration process can result in inaccurate calibration results. In particular, the calibration results of extrinsic parameters are more likely to deviate from the true values, which in turn leads to low-frequency errors in the reconstruction results. In order to obtain the extrinsic parameters closer to the true values, a simple but effective method is proposed in this paper. The proposed method utilizes the standard plane and the dumbbell bat, which are commonly used in measurements, to optimize the extrinsic parameters. First, the standard plane and dumbbell bat are reconstructed using the initial calibration results to transfer the errors in the extrinsic parameters to the plane fitting residuals, as well as to the fitting residuals for the radius and the center distance of dumbbell bat. The residuals and errors are then minimized using nonlinear optimization, resulting in the more accurate extrinsic parameters. Experimental results demonstrate that the proposed method can effectively compensate the calibration error of the extrinsic parameters. The root mean square (RMS) error of planar reconstruction is reduced from 0.0291 mm to 0.0106 mm, which is reduced by about 63.6 %. The RMS error of spherical reconstruction is reduced from 0.0358 mm to 0.0166 mm, which is about 53.6 %. The measurement accuracy of the FPP system is further improved.

In-situ monitoring of laser-based powder bed fusion using fringe projection

The implementation of in-situ sensing solutions to monitor additive manufacturing processes has seen a significant surge in recent years, notably in processes where localised heating is used. These technologies, however, have not always yielded accurate information about final part quality, due to differences between the irregularities observed in-process and the anomalies present in the finished part. One way of investigating such differences is to establish correlations between in-process layer properties and the final condition of the part. In this work, we put forward a solution based on a bespoke fringe projection system designed to monitor layers within the build chamber of a PBF-LB machine. Through the computation of quantitative indicators on fringe projection data and the use of statistical control charts for their monitoring and analysis, we are able to predict local reductions in part density, detrimental to the quality of the final build, which are typically only visible after part manufacture. Principally, this article describes the developed fringe projection system utilised for data collection and the custom indicators used to examine layer topographical characteristics and which are correlated with local final densities. We design an experimental campaign to produce parts with different local densities and show how the proposed indicators, combined with statistical control charts, can predict in-process drops in density. The monitoring performance is validated via X-ray computed tomography (XCT) measurements performed on the as-built samples.

Fast high-precision 3D shape measurement using linear phase encoding with geometry constraints

A three-dimensional (3D) profile measurement method based on geometric constraints combined with linear phase encoding (GCPE) is proposed. This method encodes the wrapped phase and the linear signal in the same phase domain, achieves the elimination of the phase ambiguity within the local fringe period, and obtains an unambiguous absolute phase within the entire period through geometric constraints. Compared with the traditional phase encoding method, this method solves the problem of period sequence errors caused by a large number of codewords by encoding linear signals in the phase domain and using a period order correction method to deal with the period jump phenomenon caused by noise. At the same time, the measurement range of the fringe projection system under geometric constraints is significantly improved. Experimentally, 3D profiles of standard planes, complex statues, and separated objects were measured by the use of the GCPE. The results show that the GCPE has the advantage of fast speed and high accuracy in measuring the 3D profile of objects.

Motion-Induced Error Reduction for Motorized Digital Fringe Projection System

Motion-Induced Error Reduction for Motorized Digital Fringe Projection System

Residue-guided phase unwrapping in fringe projection measurements using second differences

This paper presents an innovative algorithm for unwrapping 2D phase maps with discontinuities. The method employs residue detection for identifying affected areas at a coarse scale. Unlike traditional techniques relying on subjective assessment, this algorithm automates threshold determination, ensuring precision without manual intervention. At the pixel level, it utilizes a bitmap mask based on second differences and the geometric mean formula to locate inconsistencies within the wrapped map precisely. This coarse-to-fine process establishes an optimal threshold for the second difference mask, resulting in highly accurate unwrapped outcomes while maintaining computational efficiency. Compared to conventional methods, this approach delivers superior unwrapped results, making it suitable for diverse applications. Experimental validation includes computer-simulated surfaces and practical fringe projection systems, accompanied by a thorough error analysis.

Suppression for Phase Error of Fringe Projection Profilometry Using Outlier-Detection Model: Development of an Easy and Accurate Method for Measurement

Fringe projection is an important technology in three-dimensional measurement and target recognition. The measurement accuracy depends heavily on the calibration of the absolute phase and projector pixels. An easy-to-implement calibration method based on the Random Sample Consensus (RANSAC) algorithm is proposed to exterminate the phase error data and elevate the measurement accuracy in a fringe projection system. The reconstruction experiments of a double-sphere standard demonstrate that the uncertainties in radius and sphere-distance measurement are reduced to one thousandth of the measured value or even less, and the standard deviation in multiple measurements is restricted to within 50 μm. The measurement accuracy provided by the proposed RANSAC method can be improved by up to 44% compared with that provided by traditional least squared method (LSM). The proposed calibration method is easy and simple to implement, and it does not need additional hardware, but rather a calibration board.

Fringe projector with submillimeter fringe spacing at a meter-scale field of view.

State-of-the-art fringe projection systems generate fringe patterns using digital light projectors (DLP). The axial uncertainty is limited by the smallest fringe period and is directly related to the pixel count. This results in limited accuracy of current DLP systems that affect applications such as in situ measurements for laser powder bed fusion systems, where a submillimeter fringe period is needed for field-of views larger than 500m m×500m m. This work presents a scalable fringe projection technique that enables the generation of stable fringe patterns over a large field of view spanning several meters while maintaining submillimeter fringe periods. This system uses geometric phase gratings to enable variable fringe spacing and fringe orientation capabilities. The system shears a coherent beam in the Fourier plane using a pair of geometric polarization gratings. The separation between the gratings directly affects the fringe spacing, and the orientation of the gratings affects the fringe orientation. The depth of focus is only limited by the coherence of the light source, enabling high fringe periods even on tilted planes. The system is designed with a single path configuration, making the system more robust to environmental noise. With a rotating linear polarizer, we demonstrate that phase-shifting methods could be employed to acquire phase information about the object. This paper employs a single-shot Fourier transform phase estimation technique to process the intensity maps acquired using projected fringe patterns. Further, we demonstrate the capabilities of the system to produce submillimeter fringe spacing and the ability to project fringes on larger scales for measurements.

Wide field 3D optical profilometry using a diffraction Lloyd's mirror interferometer.

Interference fringe projection is used as a non-contact optical profilometry method for accurate 3D measurements. In interferometric fringe projection schemes, the maximum measurable size of the test object is limited by the optics of the interferometer. In this work, we report the application of a diffraction Lloyd's mirror interferometer (DLMI) as a wide-field sinusoidal fringe projection system for 3D shape measurement. The DLMI works on diffracted light and therefore generates interference fringes over a large area. This enables measurement of large objects using DLMI as compared to a conventional Lloyd's mirror interferometer. The performance of the proposed system is evaluated in terms of its stability and reproducibility of the results through measurement of the standard deviation in the phase values.

Adequate phase unwrapping based on 2[formula omitted] cycle invariant between shifted phase maps

To obtain an adequate unwrapping solution for reliable phase measurement under noisy circumstances, a novel unwrapping algorithm is proposed. This algorithm extracts abundant valid pixels and rejects noise based upon revealing a property of 2π invariant, which is implied between wrapped phase maps with shifted fringe patterns. Distinct from conventional algorithms that use residues or minimum norm solution to attenuate the impacts of noise affected areas, this technique is free from the uncertainties arising from inadequate resources or over-smoothing effects during the unwrapping process. The performance of the proposed algorithm is demonstrated and confirmed through both computer simulations and practical experiments carried out using a fringe projection system. Superior capability in handling noise affected phase images is then achieved.

Sub-regional phase error compensation based ona probability distribution function and gammaprecoding.

In this paper, a phase error compensation method based on a probability distribution function (PDF) is proposed to improve the accuracy of phase extraction, which is helpful for three-dimensional (3D) reconstruction. First, the relationship between the gamma and the gray values is established to segment the projection regions. Then a new method based on a PDF is designed to represent the variation degree of phase error, which fits the precoded gamma value in the minimum range of the phase error. After that, the error compensation method is applied to the self-built system and packaged independently from the 3D reconstruction system to unwrap phases with high precision. The experimental results show that the proposed method can reduce the standard deviation of the phaseerror by 46.9% compared without phase error compensation, and decrease the standard deviation of thephase error by 30% compared with the whole precoding. Generally, our method can effectively avoid overcompensation or under-compensation caused by single global gamma precoding correction, and better reduce the phase error and improve the 3D reconstruction accuracy in the fringe projection system.

CF3DNet: A learning-based approach for single-shot 3D reconstruction from circular fringes

3D reconstruction by fringe projection is an ill-posed problem that is of significance in many practical applications. Conventional algorithms employ multiple steps like fringe analysis, phase unwrapping, and calibration to reconstruct the 3D profile. Recent deep learning (DL) methods circumvent this multi-step approach by directly mapping the deformations in linear fringes caused by objects to the absolute phase shifts. However, this mapping is not one-to-one for the discontinuous objects due to 2π periodicity of linear fringes, and hence it is impossible to reconstruct using a single deformed fringe. In this work, we propose Circular Fringe-to-3D reconstruction Network (CF3DNet), a learning-based approach for 3D reconstruction from circular fringes, that can establish a one-to-one mapping between the phase deformations and the absolute phase shifts. This is viable because the radially symmetric circular fringes can distinctly record the lateral shifts caused by objects, and the learning-based approach can uniquely map them to absolute phase shifts. Thus, the proposed CF3DNet can reconstruct discontinuous object profiles, which is infeasible with linear fringe-based methods. Further, to evade the tedious process of real data collection and to bring generalization, the model is trained with synthetically generated smooth, discontinuous and Computer-Aided Design (CAD) object profiles. The results demonstrate that the proposed method led to tenfold improved performance over linear fringe-based methods in 3D reconstruction of various synthetic objects, and accurately estimate the real object profile compared to the other state-of-art methods. The extensive analysis presented in this work shows that the proposed method can work with carrier frequencies as low as 10 cycles/row to reconstruct dynamic ranges up to 100 radians under high noise, paving a way for the development of a cost-effective fringe projection system.

Local-to-global structure prior guided high-precision point cloud registration framework based on FPP

As one of the popular point cloud reconstruction technologies, fringe projection profilometry (FPP) has great application prospects in point cloud registration from different viewing angles. While the existing point cloud registration algorithm that focuses on FPP is limited to high-speed fringe projection system. Besides, the deep learning methods based on the global feature retrieval mechanism can hardly mine the multi-modal data features of FPP, and are difficult to meet the accuracy requirements of FPP. To address the above issue, we design a local–global structure prior guided high-precision registration framework that focuses on the FPP data characteristics. Specifically, the consistent clustering matching (CCM) module is proposed firstly to obtain the structure priors of cluster correspondences in the overlap regions by analyzing the FPP multi-modal data. Then the local-cluster interaction network (LCINet) guided by the structure priors is introduced for feature extraction and interaction. Finally, the spatial alignment module based on cluster voting(SACV) is proposed to select cluster correspondences with high confidence to calculate the transformation matrix and align point clouds. Experiments show that our method achieves state-of-the-art performance on the dataset collected by FPP, and our framework can also greatly improve the training efficiency and performance of other deep learning models.

Gamma estimation method based on phase error coefficients vector in digital fringe projection system

For phase-measuring profilometry systems, gamma effect is important to the accuracy while its gamma factor cannot be measured goodly when there are a few images. To tackle the problem, this paper proposes a novel idea: calculate the phase errors coefficients vector (PECV) of a series of heuristic gamma values, and measure the distances from the PECV of the current measurement to those, respectively; then, the gamma corresponding to minimal distance is the measured gamma factor. The idea does not measure the gamma factor straightforwardly and novelly measures the phase error distances. The technique is fast and robust, and only needs at least six images. Experimental results demonstrate the feasibility and performance.

In vitro and in vivo validation of a new three-dimensional fringe projection-based device (AEVA-HE) dedicated to skin surface mapping.

Aging signs are much visible on the surface of the skin that presents different changes: cheeks start to sag, more and deeper wrinkles appear, and pigmentation spotsincrease.Face diagnostic torecommend products includes assessingcutaneous micro-reliefor themicro-depressive networkon the face.Furthermore,there is anincreasing demand for clinical and instrumental methods to provetheefficacy ofanti-agingtreatments.As a result,very accurate and sensitive three-dimensional (3D) devicesare developedand validatedto measure and quantify aging skin andto catch fine anti-aging productsacting on wrinklesand fine lines. AEVA-HE,anon-invasive3Dmethodbased onfringe projectiontechnology, is used to robustly characterize theskinmicro-relieffrom afull-faceacquisitionandfrommultipleextractedzonesof interest.In vitro and in vivo studiesare conductedtoassessthe reproducibility of this systemandits precision towarda standard fringe projection system,DermaTOP. TheAEVA-HEsuccessfully measuredmicro-relief and wrinklesand demonstrated the reproducibility of measurements. AEVA-HEparameters were found highly correlated toDermaTOP. The present work illustrates theperformance of theAEVA-HEdevice and its dedicatedsoftwarekitasa precious tool for quantifying themajor characteristics ofwrinklesappearingwith ageandthus offersa high potential forassessing the effect of anti-wrinkling products.

In-motion 3D reconstruction of high dynamic range surfaces.

Efficient and refined three-dimensional (3D) reconstruction of industrial parts has become an urgent need in the field of advanced manufacturing, and it's a great challenge when facing in-motion and online inspection requirements of high dynamic range (HDR) surfaces that have large reflectivity variations. This paper proposes a method using RGB line-scan cameras to realize in-motion multiple-shot 3D shape measurements with RGB channel fusion to increase the measurement dynamic range. First, multi-channel one-dimensional background-normalized Fourier transform profilometry (MC-1DBNFTP) is proposed as an effective in-motion HDR method. Second, for HDR surfaces with strongly overexposed areas, we propose a solution that obtains 6 results of different dynamic ranges for fusion with only 5 projected patterns, which further extends the measurement dynamic range while ensuring the small projection period. Third, we develop a fusion method based on reliability evaluation, which is more reliable than the existing methods in fringe projection systems. In addition, colored textures can be mapped to the reconstructed surfaces. Experimental results prove that the proposed method realizes accurate and reliable in-motion 3D reconstruction of HDR surfaces.

Model-independent nonlinearity rectification algorithm using a phase-probability-equalization-based look-up table.

In the fringe projection system, nonlinearities often result in severe artifacts, such as the gamma effect and the phase-shifting error. Most previous methods can only eliminate the nonlinearity of a particular model. Additionally, the problems of coupling nonlinearities are difficult to solve. Therefore, this paper proposes a model-independent nonlinear rectification algorithm. By applying phase probability equalization (PPE) on several complete periods of a flat area, we built a look-up table (LUT) between the phase error and the wrapped phase, and retrieved an accurate phase with the subtraction of a searched phase error. The simulation and experimental results show that, compared with the traditional full-field PPE algorithm, the proposed algorithm is more robust to the object height distributions and has better rectification on incomplete fringe periods. Besides, the proposed algorithm also has higher efficiency because of the characteristics of local processing and noniterative characteristics.

High-flexibility and high-accuracy phase delay calibration method for MEMS-based fringe projection systems.

Microelectromechanical system (MEMS) mirror based laser beam scanning (LBS) projectors for fringe projection profilometry (FPP) are becoming increasingly popular attributing to their small size and low cost. However, the initial phase of the scanning MEMS mirror employed in an LBS projector may vary over time, resulting in unstable and distorted fringe patterns. The distorted fringe patterns will largely decrease the accuracy of the three-dimensional (3D) topographic reconstruction. In this paper, an efficient phase delay calibration method based on a unique fringe projection sequence and a corresponding image processing algorithm is proposed. The proposed method can compensate the phase uncertainty and variation with no need to add any extra components. One LBS projector has been constructed using a uniaxial electrostatic MEMS mirror that has a mirror size of 2.5 mm × 2.5 mm and a scanning field of view of 60 ∘ at its resonance of 1523 Hz. 3D reconstruction experiments are conducted to study how the 3D reconstruction results are affected by the phase delay. The standard deviation of a sphere reconstruction is improved from 2.05 mm to 0.20 mm after the positive phase delay deviation of 5 μs is compensated using this new calibration method.

Pixel-Wise Phase Unwrapping With Adaptive Reference Phase Estimation for 3-D Shape Measurement

Phase unwrapping plays an important role in phase-based three-dimensional (3D) shape measurement. This paper proposes an effective pixel-wise phase unwrapping method without requiring additional fringe patterns. Firstly, compared with the geometric constraint-based (GCB) method which needs calibrate the fringe projection system and create a reference phase at the closest plane <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z_min</i> within the measurement volume, the proposed method can adaptively and directly estimate the reference phase from the wrapped phase without system calibration and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z_min</i> estimation. Secondly, based on the finding that the slope angle of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z_min</i> plane ignored by the GCB method has significant impact on the measurement range, thus the phase gradients that highly correlates with the optimal slope angle are involved into reference phase estimation. The wrapped phase can be pixel-by-pixel unwrapped by comparing with the reference phase. Both simulations and experiments have been conducted to demonstrate the efficiency of the proposed method. Compared with traditional two-frequency method and phase-coding method, the proposed method can improve the measuring speed by 2 times. Experiment results show that the proposed method can effectively remove the phase unwrapping errors and achieve the mean absolute phase error of 0.0137 rad, which has obvious advantages relative to traditional methods.

A rapid and accurate gamma compensation method based on double response curve fitting for high-quality fringe pattern generation

The gamma effect of structured light illumination devices and camera will yield undesired nonlinear phase errors both in fringe projection system and fringe reflection system. The existing nonlinear correction methods can be classified into two categories: actively modifying the fringe patterns before their projection, or passively compensating the phase error after the fringe patterns are captured. The former needs to capture lots of fringe patterns in advance, while the latter occupies measurement time. In this paper, a rapid and robust active gamma compensation method based on double response curve fitting is proposed for the first time. In the proposed method, the appropriate pre-coding gamma value is determined jointly by the two constructed response curves, so the correction results will not get worse when the number of projected grayscale images decreases and no more than 4 frames of grayscale images are required. Experimental results verified that this method is fast, accurate and easy to implement. With the proposed technique, high-accuracy measurement can be achieved with the conventional 3-step phase-shifting algorithm.