Shape Measurement Method Research Articles

Accuracy assessment of fringe projection profilometry and digital image correlation techniques for three-dimensional shape measurements

With ever-increasing demand for three-dimensional (3D) imaging and shape measurements in a variety of fields, measurement accuracy has become of vital importance to numerous scientific and engineering applications. This paper presents an experimental investigation into the accuracy comparison of two prevalent 3D imaging and shape measurement methods: fringe projection profilometry (FPP) and 3D digital image correlation (3D-DIC) techniques. A detailed description of their principles reveals their inherent similarities and fundamental differences. A measurement system composed of both techniques is employed in the study, and a test target with speckle checkerboard patterns on its surface is adopted to allow simultaneous FPP and 3D-DIC measurements. The evaluation puts emphasis on how the geometric angles between key hardware components affect the 3D measurement accuracy. Experiments show that the depth and height measurements of both techniques can reach sub-micron accuracy, and the relative accuracy of the 3D shape or position measurements can reach 1/600 000.

Self-registration shape measurement based on fringe projection and structure from motion.

As an accurate and efficient shape measurement method, fringe-projection-based three-dimensional (3D) reconstruction has been extensively studied. However, patchwise point cloud registration without extra assistance is still a challenging task. We present a flexible and robust self-registration shape measurement method based on fringe projection and structure from motion (SfM). Other than ordinary structured-light measurement devices in which the camera and the projector are rigidly connected together, the camera and the projector in our method can be moved independently. An image-capturing scheme and underlying image-matching strategy are proposed. By selectively utilizing some sparse correspondence points across the fringe images as virtual markers, the global positions of the camera and the projector corresponding to each image are calculated and optimized under the framework of SfM. Dense global 3D points all over the object surface are finally calculated via forward intersection. Experimental results on different objects demonstrate that the proposed method can obtain a self-registered 3D point cloud with comparable accuracy to the state-of-the-art techniques by using only one camera and one projector, requiring no post-registration procedures and no assistant markers.

Observation of micro-characters using three-dimensional shape measurement method based on speckle interferometry

Speckle interferometry has long been used to measure the deformation of an object with a rough surface. Currently, it can be used to measure the shape of a three-dimensional microstructure by intentionally applying a lateral shift to the measured object and analysing the change in phase due to the shift. Furthermore, the validity of this measurement method has been verified in terms of the measurement of microstructures, such as micro-silica spheres and diffraction gratings. In this study, the validity of the measurement of an object possessing an artificial shape by this method in the micro-region is analysed using micro-characters drawn by an electron-beam lithography system. It is confirmed that this method can perform the shape measurement of three-dimensional microstructures that are artificially produced. This was achieved by observing the letter ‘U’, illustrated with a line width beyond the diffraction limit of the objective lens.

A fast and precise three-dimensional measurement system based on multiple parallel line lasers

This paper conducts a trade-off between efficiency and accuracy of three-dimensional (3D) shape measurement based on the triangulation principle, and introduces a flying and precise 3D shape measurement method based on multiple parallel line lasers. Firstly, we establish the measurement model of the multiple parallel line lasers system, and introduce the concept that multiple base planes can help to deduce the unified formula of the measurement system and are used in simplifying the process of the calibration. Then, the constraint of the line spatial frequency, which maximizes the measurement efficiency while ensuring accuracy, is determined according to the height distribution of the object. Secondly, the simulation analyzing the variation of the systemic resolution quantitatively under the circumstance of a set of specific parameters is performed, which provides a fundamental thesis for option of the four system parameters. Thirdly, for the application of the precision measurement in the industrial field, additional profiles are acquired to improve the lateral resolution by applying a motor to scan the 3D surface. Finally, compared with the line laser, the experimental study shows that the present method of obtaining 41220 points per frame improves the measurement efficiency. Furthermore, the accuracy and the process of the calibration are advanced in comparison with the existing multiple-line laser and the structured light makes an accuracy better than 0.22 mm at a distance of 956.02 mm.

Real-time 3D shape measurement with dual-frequency composite grating and motion-induced error reduction

Phase-shifting profilometry has been increasingly sought and applied in dynamic three-dimensional (3D) shape measurement. However, the object motion will lead to extra phase shift error and thus measurement error. In this paper, a real-time 3D shape measurement method based on dual-frequency composite phase-shifting grating and motion-induced error reduction is proposed for a complex scene containing dynamic and static objects. The proposed method detects the motion region of a complex scene through the phase relations of the dual-frequency composite grating and reduces the motion-induced error with the combination of the phase calculated by a phase-shifting algorithm and the phase extracted by Fourier fringe analysis. It can correctly reconstruct the 3D shape of a complex dynamic scene and ensure high measurement accuracy of its static object as well. With the aid of the phase-shifting image ordering approach, the dynamic 3D shape of complex scenes can be reconstructed and the motion-induced error can also be suppressed in real time. Experimental results well proved that the proposed method is effective and practical.

3D shape measurement with an uncalibrated camera using the feature quantity type whole-space tabulation method

A prototype of a 3D shape measurement device with two cameras was developed, and the prototype was used to confirm the effectiveness of the 3D shape measurement method that does not require camera parameters. For 3D shape measurement using a fringe projection method, generally the pixel coordinate in the image and phase information of the projected fringe pattern are used; however, 3D coordinates can be obtained from only three fringe phase values. Recently, authors proposed this method as a feature quantity type whole-space tabulation method. There were no camera parameters required because pixel coordinates were not used, and thus a camera calibration-free 3D shape measurement can be realized. Moreover, the experimental evaluation was performed using the prototype having two cameras. Although these cameras were located at different positions and had lenses with different focal lengths, their measured shapes of an object were almost identical. An experiment of 3D shape measurement using an uncalibrated camera was performed. The effectiveness of the proposed method was quantitatively validated from experimental result obtained using the developed prototype.

Multiple angle digital holography for the shape measurement of the unpainted tympanic membrane.

The shape of the tympanic membrane (TM) plays an important role in sound transmission through the ear for hearing. Previously we developed a high-speed holographic system employing a tunable wavelength laser for rapid TM shape measurement. However, the tunable laser illumination was not sufficient to measure the shape of the unpainted TM due to the semi-transparency of the TM and short exposure time of the camera. This paper presents a new multiple angle illumination technique that allows us to use a higher power single wavelength laser to perform shape measurements on the unpainted TM. Accuracy of the new method is demonstrated by a measure of a step gauge provided by the National Institute of Standards and Technology. We successfully applied the new shape measurement method on a fresh postmortem human TM without any paint.

The Methods and Experiments of Shape Measurement for Off-Axis Conic Aspheric Surface.

The off-axis conic aspheric surface is widely used as a component in modern optical systems. It is critical for this kind of surface to obtain the real accuracy of the shape during optical processing. As is widely known, the null test is an effective method to measure the shape accuracy with high precision. Therefore, three shape measurement methods of null test including auto-collimation, single computer-generated hologram (CGH), and hybrid compensation are presented in detail in this research. Although the various methods have their own advantages and disadvantages, all methods need a special auxiliary component to accomplish the measurement. In the paper, an off-axis paraboloid (OAP) was chosen to be measured using the three methods along with auxiliary components of their own and it was shown that the experimental results involved in peak-to-valley (PV), root-mean-square (RMS), and shape distribution from three methods were consistent. As a result, the correctness and effectiveness of these three measurement methods were confirmed, which are very useful in engineering.

자동 비파괴검사 구현을 위한 3차원 형상 측정 및 경로 설계 방법

자동 비파괴검사 구현을 위한 3차원 형상 측정 및 경로 설계 방법

Precise wide-range three-dimensional shape measurement method to measure superfine structures based on speckle interferometry

With regard to the three-dimensional (3D) shape measurement, based on speckle interferometry, of an object with a fine structure beyond the diffraction limit of the objective lens, phase distribution of each speckle region in a speckle pattern and a specklegram is discussed. The experimental results confirmed that the phase distribution with respect to the shape of an object exists spatially even in the speckle region of the speckle pattern. However, the measurement results of a superfine structure by speckle interferometry indicated that the spatial continuity of the phase distribution does not exist in each speckle but in the specklegram. This feature was used to confirm that a wide range of 3D shape measurements of an object with a fine structure can be realized by analyzing specklegrams calculated from speckle patterns before and after a lateral shift in speckle interferometry. Furthermore, it is confirmed that the shape measurement of a nonperiodical structure can be performed.

Estimating the 3D shape of volcanic ash to better understand sedimentation processes and improve atmospheric dispersion modelling

The sedimentation rate of volcanic ash through the atmosphere influences its travel distance, with important implications for aviation and health. The fall velocity of a particle depends on its size and density, but also shape, and volcanic ash is not spherical. To capture the sedimentation of ash, atmospheric dispersion models use empirical drag equations calibrated using geometric shape descriptors. However, particle shape data are scarce and there is no standard method of shape measurement. In addition, shape measurements are not always available during an eruption, when dispersion models are used operationally to forecast ash hazard. We assess the variability in the shape of volcanic ash from Icelandic eruptions using X-ray computed tomography. To consider how good different drag equations and shape descriptors are at representing the sedimentation of volcanic ash we compare calculated fall velocities to measured fall velocities of volcanic ash in air in a settling column. We then suggest the best drag equations and shape descriptors for use in atmospheric dispersion models. We find that shape-dependent drag equations produce more accurate results than a spherical approximation. However, accurate drag calculations based on the shape descriptor sphericity, which is a function of surface area, require the imaging resolution to be within the range of 102 - 105 voxels per particle (where a voxel is a volumetric pixel) as surface area is sensitive to imaging resolution. We suggest that the large-scale form of the particle impacts sedimentation more than small-scale surface roughness. Shape descriptors based on ratios between principal axis lengths are more practical as they are less variable among particle size classes and much less sensitive to imaging resolution. Finally, we use particle shape data from this study and literature sources to make recommendations on default values for use with atmospheric dispersion models where no shape data are available.

A Projection-Based Method for Shape Measurement

This work addresses two main contributions for shape measurement: First, a new circularity measure for planar shapes is introduced based on their geometrical properties in the projection space of Radon transform. Second, a general-purpose evaluation criterion, power of discrimination, for assessing the efficiency of a shape measure is proposed. The new measure ranges over the interval [0, 1] and produces the value 1 if and only if the measured shape is a perfect circle. The proposed measure is invariant with respect to translation, rotation and scaling transformations. Moreover, it is also robust against border distortion of shapes. It is theoretically well founded and can be extended to other problems of shape measurement. Our approach can deal with complex shapes composed of connected components that cannot be handled by classical contour-based methods. Several experiments show its good behavior and demonstrate the efficiency and applicability of our proposed measure. Finally, we also consider our proposed evaluation criterion for assessing different circularity measures.

基于Brox光流估计的物体面形测量新方法

基于Brox光流估计的物体面形测量新方法

单像素成像在三维测量中的应用

Traditional optical 3D shape measurement methods, such as Fringe projection techniques, cannot acquire high-quality and high-accuracy 3D measurement results in the presence of global illumination. Typical global illumination effects contain interreflections and subsurface scattering. Interreflections occur in concave surfaces with glossy reflection, and subsurface scattering occurs in translucent materials. Single-pixel imaging (SI) techniques can capture a scene through a detector with no spatial resolution. However, traditional pixelated imaging sensors are commonly adopted in most modern digital cameras. Here, we extended SI to pixelated imaging sensors, in which every pixel on an imaging sensor was considered an independent unit that can simultaneously obtain an image. Our experiments show that the SI can completely decompose direct and global illumination. Furthermore, high-quality and high-accuracy 3D profile in the presence of global illumination can be reconstructed.

复合表面三维形貌测量方法的仿真与验证

复合表面三维形貌测量方法的仿真与验证

Dynamic three-dimensional shape measurement with a complementary phase-coding method

The traditional phase-coding (TPC) method has been widely used for three-dimensional (3D) shape measurement. However, the fringe order determined from the coding patterns cannot be precisely aligned with the wrapped phase calculated from the sinusoidal patterns when measuring dynamic objects. Consequently, phase unwrapping errors will occur around the 2π phase jumps of the wrapped phase. To address this problem, the present work proposes a complementary phase-coding (CPC) method for dynamic 3D shape measurement. Specifically, the projection of the sinusoidal and coding patterns forms a cycle and the se patterns are shifted by a half-period between even and odd cycles. Combining two fringe orders of adjacent even and odd cycles, the absolute phase map can be correctly recovered. Moreover, to improve the measurement speed, all 8-bit gray patterns are converted into 1-bit binary patterns by a binary dithering technique. Both simulations and experiments demonstrate the robustness and efficiency of the proposed method.

Calibration method for panoramic 3D shape measurement with plane mirrors.

High-speed panoramic three-dimensional (3D) shape measurement can be achieved by introducing plane mirrors into the traditional fringe projection profilometry (FPP) system because such a system simultaneously captures fringe patterns from three different perspectives (i.e., by a real camera and two virtual cameras in the plane mirrors). However, calibrating such a system is nontrivial due to the complicated setup. This work introduces a flexible new technique to calibrate such a system. We first present the mathematical representation of the plane mirror, and then mathematically prove that it only requires the camera to observe a set of feature point pairs (including real points and virtual points) to generate a solution to the reflection matrix of a plane mirror. By calibrating the virtual and real camera in the same world coordinate system, 3D point cloud data obtained from real and virtual perspectives can be automatically aligned to generate a panoramic 3D model of the object. Finally, we developed a system to verify the performance of the proposed calibration technique for panoramic 3D shape measurement.

3D shape measurement of translucent objects based on Fourier single-pixel imaging in projector-camera system.

3D shape measurement by structured light is a popular technique for recovering object surfaces. However, structured light technique assumes that scene points are directly illuminated by the light source(s). Consequently, global illumination effects, such as subsurface scattering in translucent objects, may cause measurement errors in recovered 3D shapes. In this research, we propose a 3D shape measurement method of translucent objects based on Fourier single-pixel imaging (FSI) technique. The 3D shapes of the translucent objects are reconstructed through stereo matching of direct illumination light, which is separated from the surface. Experimental results show that the proposed method can separate the direct illumination light and the subsurface scattering light. The feasibility and accuracy of the method are analyzed, and the qualitative and quantitative results of the method are provided.

3D shape measurement based on structured light field imaging.

In this paper, a three-dimensional (3D) shape measurement method based on structured light field imaging is proposed, which contributes to the biomedical imaging. Generally, light field imaging is challenging to accomplish the 3D shape measurement accurately, as the slope estimation method based on radiance consistency is inaccurate. Taking into consideration the special modulation of structured light field, we utilize the phase information to substitute the phase consistency for the radiance consistency in epi-polar image (EPI) at first. Therefore, the 3D coordinates are derived after light field calibration, but the results are coarse due to slope estimation error and need to be corrected. Furthermore, the 3D coordinates refinement is performed based on relationship between the structured light field image and DMD image of the projector, which allows to improve the performance of the 3D shape measurement. The necessary light field camera calibration is described to generalize its application. Subsequently, the effectiveness of the proposed method is demonstrated with a sculpture and compared to the results of a conventional PMP system.

Development of Quick Three-Dimensional Shape Measurement Projection Mapping System Using a Whole-Space Tabulation Method

A grating projection method is often used as a highly accurate 3D shape measurement method. A real-time 3D shape measurement system can also be applied to measure a wide and smooth curved surface, such as in sheet metal processing. In this case, operators take much effort to recognize the positions of some problem areas on an object from a measured result displayed on a monitor. This study develops a projection mapping system projecting an evaluation image, such as height, displacement, gradient, curvature factor, and area of defect, onto an object. These evaluation results are obtained from the measured 3D shape. The evaluation image should be deformed according to the 3D shape of the object because the camera and projector positions are different. Therefore, this study proposes a method to quickly produce a deformed evaluation image using a whole-space tabulation method. A coordinate transform table allowed the conversion of a camera pixel coordinate into a projector pixel coordinate by using reference planes to apply deformation to the evaluation image according to the measured 3D shape. The quick coordinate transformation from a camera pixel coordinate into a projector pixel coordinate was realized using the coordinate transform table. This is a key idea of this study. It was confirmed that the coordinate transformation from the camera pixel coordinate to the projector coordinate could be performed in 4.5 ms using the coordinate transform table. In addition, 3D shape measurement projection mapping was applied to a curved sheet metal with small deformation, and the deformation part was clearly shown by projecting the height distribution. The architecture and the experimental results are shown herein.