Fringe projection profilometry based on a novel phase shift method

Variational image decomposition model TGV-Hilbert-BM3D for phase retrieval in FPP and its application for an on-site wall surface bulge

Mass loss from wall surface bulge deformation can be used to estimate the strength loss of reinforcement, bond reduction, and ductility degradation, so it is very important to accurately measure the three-dimensional (3D) shape of on-site wall surface bulge. In this paper, we try to solve the problem by use of fringe projection profilometry. In the fringe projection patterns of wall surface bulge, the contrast of the fringes is very weak, and there are sometimes cracks in patterns. We first present a preprocessing method to inpaint fringes if there are damaged fringes caused by cracks. Then we propose a new, to the best of our knowledge, image decomposition model, total generalized variation (TGV)-Hilbert-block-matching (BM)3D, to effectively extract the fringe component. Finally, we use Fourier transform, phase unwrapping, and carrier-removal methods to obtain the unwrapped phase. We test the proposed method on a simulated fringe projection pattern and two real fringe projection patterns of wall surface bulge. We compare our method with the advanced total variation space-generalized functions space-BM3D, TV-Hilbert-L₂, and Beppo-Levi-space-Hilbert-BM3D methods. In addition, we perform ablation experiments to prove that our preprocessing method is necessary. The experimental results demonstrate that our method can effectively measure the 3D shape of wall surface bulge from a single fringe projection pattern for the first time, to our knowledge.

High-precision 3D shape measurement of rigid moving objects based on the Hilbert transform

Phase-shifting profilometry (PSP) is a three-dimensional (3D) measurement method of point-to-point calculation. The consistency of object position is the prerequisite to ensure the successful application of PSP in moving objects. The position information of an object can be well characterized by the modulation patterns, and hence a high-quality modulation pattern is the guarantee of pixel-matching accuracy. In this paper, a generic modulation pattern enhancement method for rigid moving objects based on the Hilbert transform is proposed. First, the Hilbert transform is employed to suppress the zero-frequency components of the fringe pattern, and a hybrid digital filter window is applied to filter out the positive fundamental frequency components for a higher signal-to-noise ratio. Then the grid-based motion statistics for fast, ultra-robust feature correspondence algorithm is used to match the high-quality modulation patterns between two adjacent frames, and the object positions in the three deformed patterns are made consistent by image clipping. Finally, the three-step PSP is used to reconstruct the 3D shape of the measured object. Experimental results demonstrate that the proposed method can substantially improve the quality of the modulation pattern, achieve high-precision pixel matching, and ultimately reduce the motion-introduced phase error.

3D surface reconstruction of small height object based on thin structured light scanning

Aiming at the problem of 3D surface reconstruction of small height objects, a method based on the scanning principle with thin structured light is proposed. The laser fringe is produced by a laser light source. It scans the surface of small height object under the control of a precise motion control system, and is integrated with a stereo light microscope and two cameras to form a complete structured light profilometry system. This method is very suitable for 3D surface reconstruction of small height objects. In order to deal with the phenomenon of "cracking" and local uneven brightness in microscope fringe image, the fringe image sequence is captured under different camera exposure parameters, and the quality of fringe image is improved by image fusion. The location of pixels on the center line of laser stripes is detected by the Loess local second-order fitting method, and the positions of these pixels are smoothed and predicted by using the Lowess local linear fitting method. The deformation of the laser stripe center curve is calculated by constructing a baseline, and the 3D surface reconstruction of the object with small height is realized in the image space. Taking the small characters on the surface of Chinese coins and human hair as test samples, their 3D surfaces are constructed by using the method proposed in this paper. The reconstructed 3D surface shapes are highly consistent with the real 3D surface shapes of objects.

Flexible calibration method of an FPP system based on a geometrical model and NLSM with fewer parameters

Fringe projection profilometry (FPP) technology is an important method for 3D reconstruction. In this paper, we proposed a flexible calibration method of an FPP system based on the imaging principle and geometrical structure of the system. The target coordinates are only related to its pixel coordinates and phase. First, the fringe images are projected onto the calibration plate, and the phase can be calculated through the four-step phase-shifting method. Then, the pixel coordinates of the feature points can be located with the binarized fringe images and the centroid method. Finally, the calibration parameters are calculated by the nonlinear least-squares method (NLSM). The reconstructed experiment of 162 testing points was carried out, and the result shows that the maximum relative errors on coordinates X, Y, and h are 0.27%, 0.42%, and 0.59%, respectively. The other two surface reconstruction experiments also verify the feasibility of the calibration method.

Instability of projection light source and real-time phase error correction method for phase-shifting profilometry

The time-dependent phase error induced by the instability of projection light source (IPLS) is systematically studied for phase-shifting profilometry (PSP). The IPLS of the projection device is investigated by a specially designed experimental setup. Based on the results of the investigation, a new mathematical model to analyze the time-dependent phase error induced by IPLS is established and verified. Two real-time phase error correction methods using a new designed three-dimensional shape measurement system are proposed for the effect of IPLS. Experimental results demonstrate the two methods can effectively eliminate the induced time-dependent phase error with a good robustness and high accuracy. The two real-time correction methods for PSP will be promising for high-accuracy measurements.

Quick pre-correction of a grating fringe for phase measuring profilometry

In this paper, for a phase measuring profilometry (PMP) system based on a digital light projector, a novel method of grating fringe quick pre-correction is proposed. In the actual engineering conditions, it is impractical to strictly limit the geometry of the system. So grating fringes on the reference plane often appear as distortions of keystone and period broadening, which are difficult to completely eliminate in the traditional calibration process. A pre-correction method based on analytic spatial transform is designed to solve these problems individually. The correction process occurs before the digital micromirror device image is generated, and theoretically, it can be compatible with most existing PMP correction and calibration methods. The correction is simple and completely implicit, and does not require a special calibration target. The correction is quick, only needs to project and shoot a fringe pattern and a corner pattern, and can be completed within a few seconds. A simulation and several experiments were carried out to verify the effectiveness of this method.

Imaging quality automated measurement of image intensifier based on orthometric phase-shifting gratings

A method for automatically measuring the imaging quality parameters of an image intensifier based on orthometric phase-shifting gratings (OPSG) is proposed. Two sets of phase-shifting gratings, one with a fringe direction at 45° and the other at 135°, are successively projected onto the input port of the image intensifier, and the corresponding deformed patterns modulated by the measured image intensifier on its output port are captured with a CCD camera. Two phases are retrieved from these two sets of deformed patterns by a phase-measuring algorithm. By building the relationship between these retrieved phases, the referential fringe period can be determined accurately. Meanwhile, the distorted phase distribution introduced by the image intensifier can also be efficiently separated wherein the subtle imaging quality information can be further decomposed. Subsequently, the magnification of the image intensifier is successfully measured by fringe period self-calibration. The experimental results have shown the feasibility of the proposed method, which can automatically measure the multiple imaging quality parameters of an image intensifier without human intervention.

Flexible dynamic measurement method of three-dimensional surface profilometry based on multiple vision sensors

Single vision sensor cannot measure an entire object because of their limited field of view. Meanwhile, multiple rigidly-fixed vision sensors for the dynamic vision measurement of three-dimensional (3D) surface profilometry are complex and sensitive to strong environmental vibrations. To overcome these problems, a novel flexible dynamic measurement method for 3D surface profilometry based on multiple vision sensors is presented in this paper. A raster binocular stereo vision sensor is combined with a wide-field camera to produce a 3D optical probe. Multiple 3D optical probes are arranged around the object being measured, then many planar targets are set up. These planar targets function as the mediator to integrate the local 3D data measured by the raster binocular stereo vision sensors into the coordinate system. The proposed method is not sensitive to strong environmental vibrations, and the positions of these 3D optical probes need not be rigidly-fixed during the measurement. The validity of the proposed method is verified in a physical experiment with two 3D optical probes. When the measuring range of raster binocular stereo vision sensor is about 0.5 m × 0.38 m × 0.4 m and the size of the measured object is about 0.7 m, the accuracy of the proposed method could reach 0.12 mm. Meanwhile, the effectiveness of the proposed method in dynamic measurement is confirmed by measuring the rotating fan blades.

Real-time, high-accuracy 3D imaging and shape measurement

In spite of the recent advances in 3D shape measurement and geometry reconstruction, simultaneously achieving fast-speed and high-accuracy performance remains a big challenge in practice. In this paper, a 3D imaging and shape measurement system is presented to tackle such a challenge. The fringe-projection-profilometry-based system employs a number of advanced approaches, such as: composition of phase-shifted fringe patterns, externally triggered synchronization of system components, generalized system setup, ultrafast phase-unwrapping algorithm, flexible system calibration method, robust gamma correction scheme, multithread computation and processing, and graphics-processing-unit-based image display. Experiments have shown that the proposed system can acquire and display high-quality 3D reconstructed images and/or video stream at a speed of 45 frames per second with relative accuracy of 0.04% or at a reduced speed of 22.5 frames per second with enhanced accuracy of 0.01%. The 3D imaging and shape measurement system shows great promise of satisfying the ever-increasing demands of scientific and engineering applications.

3D shape measurement based on projection of triangular patterns of two selected frequencies

In this paper, a temporal shift unwrapping technique is presented for solving the problem of shift wrapping associated with spatial shift estimation (SSE)-based fringe pattern profilometry (FPP). Based on this technique, a novel 3D shape measurement method is proposed, where triangular patterns of two different spatial frequencies are projected. The patterns of the higher frequency are used to implement the FPP, and the one with lower frequency is utilized to achieve shift unwrapping. The proposed method is able to solve the shift unwrapping problem associated with the existing multi-step triangular pattern FPP by projection of an additional fringe pattern. The effectiveness of the proposed method is verified by experimental results, where the same accuracy as existing multi-step triangular pattern FPP can be achieved, but enabling the measurement of objects with complex surface shape and high steps.

Liquid-crystal phase-shifting lateral shearing interferometer with improved fringe contrast for 3D surface profilometry

We report the development of a common-path and nonmechanical scanning phase-shifting lateral shearing interferometer based on a homogeneous gap and wedge-shaped gap liquid-crystal (LC) cell. The modified cell consists of semi-reflecting and fully reflecting glass plates with LC material sandwiched between them so that the amount of reflected light from both the surfaces is nearly equal, thus generating high contrast interference fringes. The thickness of the LC cell was maintained at ~3 μm uniformly for a homogeneous gap and a varying wedge gap was also introduced between two glass plates. Phase-shifting linear fringe patterns of high contrast were generated. The phase-shifted interferograms were projected onto an object and the distorted interferograms were recorded by a CCD camera. The phase-shifting fringe analysis technique was used to reconstruct the 3D shape of the object. The present system is compact and low cost.