含孤立物体场景的高速、高密度三维面形采集

提出了一种用于采集含空间孤立物体场景的高速、高密度三维面形采集方法。该方法将三幅图案高速投影到被测物体上并同步采集图像,从而实现场景三维形貌及纹理的高速记录。其中两幅图案是互相具有π相移的正弦条纹,采用傅里叶变换法求解变形条纹相位。将拍摄到的两幅变形条纹图相加可得到物体表面纹理。另一幅图案用来确定条纹级次,实现绝对相位测量,解决高速形貌采集中孤立物体相位展开难题。它由一系列宽度与正弦条纹周期相同的竖条构成,采用三种灰度对竖条编码。每个竖条由单一灰度或两种在竖直方向上周期性分布的灰度构成,这样可编6个码。将竖条按由这些码构成的伪随机序列排列,得到编码图案。测量时,对拍摄的编码图案解码,通过子序列匹配来确定对应正弦条纹的级次。设计了采用DLP投影仪及高速摄像机的高速测量系统。采用提出的方法实现了640×480分辨率下每秒60帧和320×240分辨率下每秒120帧的三维形貌及纹理采集。     

Phase error compensation for three-dimensional shape measurement with projector defocusing

This paper analyzes the phase error for a three-dimensional (3D) shape measurement system that utilizes our recently proposed projector defocusing technique. This technique generates seemingly sinusoidal structured patterns by defocusing binary structured patterns and then uses these patterns to perform 3D shape measurement by fringe analysis. However, significant errors may still exist if an object is within a certain depth range, where the defocused fringe patterns retain binary structure. In this research, we experimentally studied a large depth range of defocused fringe patterns, from near-binary to near-sinusoidal, and analyzed the associated phase errors. We established a mathematical phase error function in terms of the wrapped phase and the depth z. Finally, we calibrated and used the mathematical function to compensate for the phase error at arbitrary depth ranges within the calibration volume. Experimental results will be presented to demonstrate the success of this proposed technique.     

A general gamma nonlinearity compensation method for structured light measurement with off-the-shelf projector based on unique multi-step phase-shift technology

ABSTRACT

Nonlinearities in the application of fringe projection metrology make it very difficult to acquire perfect 3D data. This paper describes a six-step phase-shifting technique for a structured light measurement system with an off-the-shelf projector. First, the phase error is analysed and a gamma model is established by deriving the relative expression between the wrapped phase and input images. This is then expressed in matrix form to derive a unique solution, which is used for the gamma solver. The complex gamma calibration and projector error compensation can be removed once the gamma value of the off-the-shelf projector has been determined. The ideal model reconstruction results are obtained through simulations and experiments, and the standard deviation of the phase error is found to be only 0.0039 radians. Hence, the proposed method eliminates the nonlinear errors associated with fringe projection technology using existing projectors and improves the overall image reconstruction quality.     

Uneven fringe projection for efficient calibration in high-resolution 3D shape metrology

A novel uneven fringe projection technique is presented whereby nonuniformly spaced fringes are generated at a digital video projector to give evenly spaced fringes in the measurement volume. The proposed technique simplifies the relation between the measured phase and the object's depth independent of pixel position. This method needs just one coefficient set for calibration and depth calculation. With uneven fringe projection the shape data are referenced to a virtual plane instead of a physical reference plane, so an improved measurement with lower uncertainty is achieved. Further, the method can be combined with a radial lens distortion model. The theoretical foundation of the method is presented and experimentally validated to demonstrate the advantages of the uneven fringe projection approach compared with existing methods. Measurement results on a National Physical Laboratory (UK) "step standard" confirm the measurement uncertainty using the proposed method.     

Generic nonsinusoidal phase error correction for three-dimensional shape measurement using a digital video projector

A structured light system using a digital video projector is widely used for 3D shape measurement. However, the nonlinear gamma of the projector causes the projected fringe patterns to be nonsinusoidal, which results in phase error and therefore measurement error. It has been shown that, by using a small look-up table (LUT), this type of phase error can be reduced significantly for a three-step phase-shifting algorithm. We prove that this algorithm is generic for any phase-shifting algorithm. Moreover, we propose a new LUT generation method by analyzing the captured fringe image of a flat board directly. Experiments show that this error compensation algorithm can reduce the phase error to at least 13 times smaller.     

Three-dimensional shape measurement and calibration for fringe projection by considering unequal height of the projector and the camera

In fringe projection, the CCD camera and the projector are often placed at equal height. In this paper, we will study the calibration of an unequal arrangement of the CCD camera and the projector. The principle of fringe projection with two-dimensional digital image correlation to acquire the profile of object surface is described in detail. By formula derivation and experiment, the linear relationship between the out-of-plane calibration coefficient and the y coordinate is clearly found. To acquire the three-dimensional (3D) information of an object correctly, this paper presents an effective calibration method with linear least-squares fitting, which is very simple in principle and calibration. Experiments are implemented to validate the availability and reliability of the calibration method.     

Multiple‐view Shape and Deformation Measurement by Combining Fringe Projection and Digital Image Correlation

Abstract: We present a new method that combines the fringe projection and the digital image correlation (DIC) techniques on a single hardware platform to simultaneously measure both shape and deformation fields of three‐dimensional (3‐D) surfaces with complex geometries. The method in its basic form requires only a single camera and single projector, but this can be easily extended to a multi‐camera multi‐projector system to obtain complete 360° measurements. Multiple views of the surface profile and displacement field are automatically co‐registered in a unified global coordinate system, thereby avoiding the significant errors that can arise through the use of statistical point cloud stitching techniques. Experimental results from a two‐camera two‐projector sensor are presented and compared with results from both a standard stereo‐DIC approach and a finite element model.     

基于条纹投影的复杂曲面测量技术

如何快速、高精度地测量复杂曲面的三维轮廓是目前的一个热点研究方向。与现有的测量方法相比,条纹投影轮廓测量技术具有非接触测量、测量速度快和重构点云密集等优点,在逆向工程等领域得到了广泛的应用。本文搭建了基于条纹投影轮廓测量技术的复杂曲面测量装置,并且对相位误差标定及补偿、投影仪精确标定、高阶系统模型简化以及有效点云快速识别等条纹投影轮廓测量的关键技术进行了深入地研究。最后使用该装置进行了叶片表面轮廓测量实验,实验结果表明,本文设计装置的测量偏差最大值不超过0.05 mm。     

Universal calculation formula and calibration method in Fourier transform profilometry

We propose a universal calculation formula of Fourier transform profilometry and give a strict theoretical analysis about the phase-height mapping relation. As the request on the experimental setup of the universal calculation formula is unconfined, the projector and the camera can be located arbitrarily to get better fringe information, which makes the operation flexible. The phase-height calibration method under the universal condition is proposed, which can avoid measuring the system parameters directly. It makes the system easy to manipulate and improves the measurement velocity. A computer simulation and experiment are conducted to verify its validity. The calculation formula and calibration method have been applied to measure an object of 22.00 mm maximal height. The relative error of the measurement result is only 0.59%. The experimental results prove that the three-dimensional shape of tested objects can be reconstructed exactly by using the calculation formula and calibration method, and the system has better universality.     

Acoustic grating fringe projector for high-speed and high-precision three-dimensional shape measurements

A new acoustic grating fringe projector (AGFP) was developed for high-speed and high-precision 3D measurement. A new acoustic grating fringe projection theory is also proposed to describe the optical system. The AGFP instrument can adjust the spatial phase and period of fringes with unprecedented speed and accuracy. Using rf power proportional-integral-derivative (PID) control and CCD synchronous control, we obtain fringes with fine sinusoidal characteristics and realize high-speed acquisition of image data. Using the device, we obtained a precise phase map for a 3D profile. In addition, the AGFP can work in running fringe mode, which could be applied in other measurement fields.     

三维重构视觉系统的标定

文章基于改进两步法的标定思想,在三维重构中提出了一种新的视觉系统参数标定与镜头畸变修正方法.该方法根据图像中心附近点畸变量较小的性质,利用中心附近点和全场视点对CCD相机和DLP投影仪的内外部参数标定和镜头畸变修正进行分离.在标定过程中,所设计的带标准圆阵列的靶标和伪随机连续方形编码可以实现特征点的自动识别和匹配.实验表明,该方法能快速、方便地对视觉系统参数进行标定和镜头畸变修正.     

Shape measurement by use of liquid-crystal display fringe projection with two-step phase shifting

The use of an optical fringe projection method with two-step phase shifting for three-dimensional (3-D) shape measurement of small objects is described. In this method, sinusoidal linear fringes are projected onto an object's surface by a programmable liquid-crystal display (LCD) projector and a long-working-distance microscope (LWDM). The image of the fringe pattern is captured by another LWDM and a CCD camera and processed by a phase-shifting technique. Usually a minimum of three phase-shifted fringe patterns is necessary for extraction of the object shape. In this method, a new algorithm based on a two-step phase-shifting technique produces the 3-D object shape. Unlike in the conventional method, phase unwrapping is performed directly by use of an arccosine function without the need for a wrapped phase map. Hence, shape measurement can be speeded up greatly with this approach. A small coin is evaluated to demonstrate the validity of the proposed measurement method, and the experimental results are compared with those of the four-step phase-shifting method and the conventional mechanical stylus method.     

Real-time tricolor phase measuring profilometry based on CCD sensitivity calibration

A real-time tricolor phase measuring profilometry (RTPMP) based on charge coupled device (CCD) sensitivity calibration is proposed. Only one colour fringe pattern whose red (R), green (G) and blue (B) components are, respectively, coded as three sinusoidal phase-shifting gratings with an equivalent shifting phase of 2π/3 is needed and sent to an appointed flash memory on a specialized digital light projector (SDLP). A specialized time-division multiplexing timing sequence actively controls the SDLP to project the fringe patterns in R, G and B channels sequentially onto the measured object in one over seventy-two of a second and meanwhile actively controls a high frame rate monochrome CCD camera to capture the corresponding deformed patterns synchronously with the SDLP. So the sufficient information for reconstructing the three-dimensional (3D) shape in one over twenty-four of a second is obtained. Due to the different spectral sensitivity of the CCD camera to RGB lights, the captured deformed patterns from R, G and B channels cannot share the same peak and valley, which will lead to lower accuracy or even failing to reconstruct the 3D shape. So a deformed pattern amending method based on CCD sensitivity calibration is developed to guarantee the accurate 3D reconstruction. The experimental results verify the feasibility of the proposed RTPMP method. The proposed RTPMP method can obtain the 3D shape at over the video frame rate of 24 frames per second, avoid the colour crosstalk completely and be effective for measuring real-time changing object.     

基于三次插值坐标变换的反向条纹投影技术

反向条纹投影技术是一种应用于在线或批量检测的快速而稳定的光学三维面形检测技术。本文提出了一种利用分片二元三次多项式插值来确定摄像机和投影器坐标变换关系的方法,它通过在摄像机10个像素点区域内拟和两个二元三次多项式,来求得该区域内投影器像素点对应的摄像机坐标值。计算机模拟和实物的对比实验表明,该方法能有效地提高反向条纹投影的精度。     

Three-dimensional shape measurement of large-aperture aspheric mirrors by off-axis null Ronchi test

An off-axis null Ronchi test is presented to measure the three-dimensional (3D) shape of a large-aperture aspheric mirror. The method designs curved fringe patterns as null sinusoidal gratings by means of phase information and ray tracing. In the process of measurement, the curved fringe patterns are displayed on a transmission-type liquid crystal display (T-LCD) screen, and a CCD camera records the fringe patterns containing the information of deviations of the mirror. The slopes of the deviations of the mirror are obtained by using the recorded fringe patterns. The deviations are restored by integrating, and then the 3D shape of the mirror can be reconstructed. Compared with the classical null Ronchi test, the method can provide enough measured data points and avoid the jagged edges of bands on the null gratings. Moreover, the method can conveniently change period and direction of the curved fringes and accurately control phase shifting. Computer simulations and a preliminary experiment are presented to show the performance of the method.     

Gamma correction for digital fringe projection profilometry

Digital fringe projection profilometry utilizes a digital video projector as a structured light source and thus gains great flexibility. However, the gamma nonlinearity of the video projector inevitably decreases the accuracy and resolution of the measurement. We propose a gamma-correction technique based on statistical analysis of the fringe images. The technique allows one to estimate the value of gamma from the normalized cumulative histogram of the fringe images. By iterating the two steps, gamma estimation and phase evaluation, the actual gamma value can be calculated. At the same time the phase distribution of the fringe pattern can be solved with higher accuracy. In so doing, neither photometric calibration nor knowledge of the device is required. Both computer simulation and experiment are carried out to demonstrate the validity of this technique.     

反向条纹投影技术及其在数字地球仪中的应用

本文提出一种基于反向条纹投影原理的数字地球仪.在数字地球仪中,显示屏是一个球面的漫反射屏,通过投影的方法可以实现数字地球仪任意方向的旋转显示.首先通过投影正弦条纹到球面显示屏上,从观察数字地球仪的方向用CCD相机获取变形条纹图像,通过相移算法,建立投影器和摄像机像素之间的几何传递关系.基于地球三维图形信息数据库,根据期望图像为投影器产生投影图像.本文建立了地球三维信息提取模型,可快速获取从任意角度观察地球的图形信息.实验使用一半径为25 cm的漫反射球体作为显示屏,将计算得到反向地图投影其上,得到相当好的实验结果.     

光栅投影式三维摄影测量仪的几何标定方法

光栅投影式三维摄影测量仪利用了时域结构光投影技术和立体视觉测量原理获得三维点坐标。针对传统标定方法易受镜头畸变影响和标定约束方程少导致精度下降的问题,采用了非线性的摄像机和投影机模型,并提出了二维的投影机模型;使用多平面法标定了系统测量所需的摄像机和投影机几何参数;为进一步提高参数精度,采用Levenberg-Marquardt算法优化了摄像机和投影机模型。实验结果表明,该方法操作简单,无需精确的位置和姿态调整,标定的绝对精度为0.2pixel,相对精度为1/5000。     

Three-dimensional shape measurement of aspheric mirrors with fringe reflection photogrammetry

Three-dimensional (3D) shape measurement of an aspheric mirror with fringe reflection photogrammetry involves three steps: correspondence matching, triangulation, and bundle adjustment. Correspondence matching is realized by absolute phase tracking and triangulation is computed by the intersection of reflection and incidence rays. The main contribution in this paper is constraint bundle adjustment for carefully dealing with lens distortion in the process of ray intersection, as compared to the well-known grating reflection photogrammetry. Additionally, a free frame is proposed to alleviate troublesome system geometrical calibration, and constraint bundle adjustment is operated in the free frame to refine the 3D shape. Simulation and experiment demonstrate that constraint bundle adjustment can improve absolute measurement accuracy of aspheric mirrors.     

彩色伪随机编码闪光投影系统的建模及其标定

为实现仅用一幅图象在真正的三维欧氏空间重构三维场景,尤其是动态的三维场景,系统需要对彩色伪随机编码闪光投影系统进行建模和预标定。当系统参数改变后,利用伪随机编码图案的几何约束,不需重新标定,可实现自适应重构三维场景。通过对投影仪像质的的无畸变性分析,用线性模型对投影仪成像过程进行建模,并提出一种高精度的投影系统直接标定方法,通过测出靶标上各投影编码特征点在空间的三维齐次坐标,求出内外参数实现了对投影仪的预标定。标定精度达到0.1单元格,欧氏重构结果较为理想。