A composite-structured-light 3D measurement method based on fringe parameter calibration

This paper proposes a novel method for reducing measurement error caused by spectrum overlapping in composite-structured-light 3D measurement systems. For a composite-structured-light 3D measurement system, spectrum overlapping causes parameters of each deformed phase-shifting fringe to change, and therefore leads to phase measurement errors. The proposed fringe parameter calibration method is based on the fact that variations in each deformed fringe's parameters are independent of height and reflectivity of the measured object. Three frames of composite grating are projected on the reference plane, and each carrier channel includes the information of three phase-shifting sinusoidal gratings used in Phase Measuring Profilometry (PMP). With the parameter calculation formulas of PMP, the parameters of fringes demodulated from the same carrier channel can be calculated, and therefore parameter relation coefficients between fringes demodulated from different carrier channels may be obtained. When an object is measured, these relation coefficients can be used to calibrate the parameters of the deformed phase-shifting fringes. A new 3D measurement mathematical model is established to reconstruct the shape of the object. Experimental data proved that the proposed method can effectively restrain the effect of spectrum overlapping and improve measurement accuracy by more than three times.     

Shifted-phase calibration for a 3-D shape measurement system based on orthogonal composite grating projection

This paper proposes a novel method for reducing measurement error caused by spectrum overlapping in orthogonal-composite-grating-based 3-D measurement method. For 3-D measurement systems based on orthogonal composite grating projection, spectrum overlapping causes phase of each deformed phase-shifting fringe changed differently, which violates the principle that the shifted phases between adjacent deformed fringes must be equivalent to 2π/3, and therefore results in phase measurement error. The proposed shifted-phase calibration method is based on that phase variation of each deformed fringe is independent of height and reflectivity of the measured object. Three composite gratings are projected on the reference plane, and each carrier channel includes three phase-shifting gratings needed in phase measuring profilometry (PMP). Because the adjacent phase-shifting fringes demodulated from the same carrier channel have the phase difference of 2π/3, we can respectively calculate the reference plane's phases of three carrier channels by the phase algorithm of PMP method, and the shifted phases between them are obtained. When an object is measured, the shifted phases between deformed phase-shifting fringes can be calibrated. A new 3-D measurement mathematical model is set to reconstruct object. Our experiments prove that the proposed method can effectively restrain the effect of spectrum overlapping and improve measurement accuracy almost one times.     

A flexible 3D profilometry based on fringe contrast analysis

This paper proposed a flexible 3D profilometry based on fringe contrast analysis. A series of sinusoidal fringes are projected on the surface of the testing object that is laid in front of the imaging plane of the fringes, and captured through a beam splitter by a CCD camera in the same direction as the axis of the projection. After the fringe contrast obtained using phase-shifting technique, the height of the object can be restored through searching the look-up table of the contrast and the height. In the measurement process, we only need to capture fringe patterns in one position, without changing the imaging plane of the fringes, so it is faster and more convenient than the existing method based on fringe contrast analysis. Our system is simple and flexible by reason of no special devices used. In this paper, the principle of this method, the setup of the measurement system and primary experiment results are given. The experimental results prove this method can restore the height of the complex object accurately and effectively.     

An improved stair phase encoding method for absolute phase retrieval

An improved phase unwrapping method is proposed to reduce the projection fringes in three-dimensional (3D) surface measurement. Color fringe patterns are generated by encoding with sinusoidal fringe and stair phase fringe patterns in red and blue channels. These color fringe patterns are projected onto the tested objects and then captured by a color CCD camera. The recorded fringe patterns are separated into their RGB components. Two groups of four-step phase-shifting fringe patterns are obtained. One group of the stripes are four sinusoidal patterns, which are used to determine the wrapped phase. The other group of stripes are four sinusoidal patterns with the codeword embedded into stair phase, whose stair changes are perfectly aligned with the 2π discontinuities of sinusoidal fringe phase, which are used to determine the fringe order for the phase unwrapping. The experimental results are analyzed and compared with those of the method in Zheng and Da (2012. Opt Express 20(22):24139–24150). The results show that the proposed method needs only four fringe patterns while having less error. It can effectively reduce the number of projection fringes and improve the measuring speed.     

基于正弦和三角波条纹投影的三维测量方法

在现有的针对复杂物体表面形貌的三维测量方法中, 为了完成绝对相位的测量, 通常需要处理至少6幅条纹图像, 限制了测量速度。提出了采用2幅正弦条纹和2幅三角波条纹图来获得物体三维形貌的方法。利用两步相移正弦条纹和两步相移三角条纹得到截断相位, 再利用两步相移三角波条纹得到条纹级次, 减少了投影条纹幅数, 提高测量速度。在得到条纹级次时, 计算三角波条纹强度调制和强度对比度, 与计算相位相比, 可以减少数据处理的时间, 进一步提高测量速度, 同时能减小物体表面反射率的影响, 提高了测量精度。测量最大高度为39 mm的阶梯状标准块, 得到的最大绝对误差和最大的RMS误差分别为0.045 mm和0.041 mm。验证了该方法的有效性和实用性, 在高速实时的复杂形貌三维测量中有广泛的应用前景。     

基于液晶显示投影技术的数字影栅云纹相移实现方法

影栅云纹是物体离面变形和表面形貌测量常用的一种比较简单的方法,用单纯的影栅云纹法即便在最好的光学系统配置情况下测量精度也只有1~100μm左右,在影栅云纹测试方法中引进相移技术是提高测量精度的主要手段。采用液晶投影仪和数字图像处理技术实现数字影栅云纹测量的准确数字相移,避免了在影栅云纹法中使用结构比较复杂或特制的相移机构。由计算机产生相移条纹图经液晶显示投影,应用实时图像灰度算术相减技术得到数字相移影栅云纹条纹图。该方法具有“基准栅”的栅距和相移步长实时可调,配置高速图像采集系统和图像后处理软件,可将相移技术引入动态测量中,从而提高动态测量的精度的优点。最后的悬臂梁实验结果证实了该方法的有效性。     

Microscopic surface contouring by fringe projection method

This paper describes the use of optical fringe projection method for 3D surface profile and deformation measurement of micro-components. In this method, sinusoidal linear fringes are projected on a micro-component surface by a grating phase shifting projector and a long working distance microscope (LWDM). The image of the fringe pattern is captured by a high-resolution CCD camera and another LWDM and processed by phase-shifting technique. A simple procedure is described which enables calibration of the optical set-up for subsequent quantitative measurement of micro-components of unknown shapes. This method is relatively simple and accurate, and is capable of conducting fully automated measurements. In this paper, two micro-components, a micro-mirror (0.1 mm×0.1 mm) and a micro-electrode pad are used to demonstrate deformation measurement and microscopic surface contouring.     

Vibration Analysis by Phase Shifting Digital Holography

Phase-shifting digital holography has been used for the study of vibrating objects. The time-averaged complex amplitude of Fresnel diffracted field due to a vibrating object was obtained by using a three-step phase-shifting algorithm. Taking the inverse Fresnel transform of the complex amplitude resulted in an image of the object superimposed with Bessel fringes. The Bessel fringes are contour map of the vibration amplitude. By sinusoidally modulating the phase of the reference beam at the vibration frequency, the brightest fringe could be shifted to points of interest, thus extending the measurable range of vibration amplitude.     

用于三维测量的快速相位解包裹算法

减少条纹投影轮廓术的条纹图数量一直是本领域的研究热点。传统的时间相位解包裹算法,一般需要额外的条纹信息来确定条纹级次,导致条纹图数量过多。提出一种用于三维测量的快速相位解包裹算法,只需要N步标准相移正弦条纹图,就可以完成绝对相位的计算。首先,利用标准相移算法计算包裹相位和消除背景的掩膜;然后,直接利用包裹相位和掩膜,根据连通域标记算法计算条纹级次,进而求得绝对相位。该方法最少只需3幅条纹图,就可以完成三维测量,数据处理速度快。计算机仿真和实验结果验证了该方法的有效性和鲁棒性。     

A fast and accurate gamma correction based on Fourier spectrum analysis for digital fringe projection profilometry

In digital fringe projection profilometry, the gamma effect of the used electronic devices seriously affects the accuracy of three-dimensional (3D) topography measurements. Previous gamma correction methods do not take full advantage of the Fourier spectrum of the captured spatial-carrier phase-shifting fringe patterns. Hence, dozens of phase-shifting fringe patterns are required to carry out gamma pre-calibration. In this paper, a fast and accurate gamma correction technique based on a Fourier spectrum analysis is proposed. Only two spatial-carrier fringe patterns with different pre-encoded gamma values are needed and the number of fringe patterns required for gamma pre-calibration is significantly reduced without loss of accuracy. The proposed method is validated by experiments.     

一种改进型Stoilov算法相位测量轮廓术

提出了一种采用主动控制相移量的改进型Stoilov算法,按主动设定的相移量事先设计好五幅完全等相移正弦光栅图,由计算机编程控制数字投影仪依次投影该五幅光栅至待测物体表面,并对应采集五帧变形条纹,用所设定的相移量直接替代Stoilov算法中由变形条纹图解算的相移量,提高了相位提取和三维重构准确度.实验结果表明,平均绝对误差优于0.07,均方差优于0.07.     

Phase-shifting whole-field speckle photography technique for the measurement of in-plane deformations in real time

A new real-time phase-shifting readout system is developed for quantitative evaluation of full-field correlation fringes obtained by means of Fourier filtering in speckle photography. The proposed method, which uses photorefractive crystals as the recording medium, is capable of mapping the whole-field displacement data from the recorded phase-shifted fringe patterns. Experimental results are presented on a diffuse surface subjected to rotation in its own plane.     

Phase-shifting windowed Fourier ridges for determination of phase derivatives

Determination of the phase or phase derivative from interferometric fringe patterns is an important task in optical interferometry. The use of wavelet ridges was recently shown to be an effective method for phase retrieval from a single fringe pattern. One necessary requirement in this method is the need for carrier frequency. In cases when carrier frequency is not available, the novel phase-shifting windowed Fourier ridges method can be used. Phase derivatives with the proper sign can be directly retrieved even in the presence of noise. An application for curvature determination from speckle shearographic fringes demonstrates the effectiveness of the method.     

Analysis of a multi-wavelength multi-camera phase-shifting profilometric system for real-time operation

Real-time accomplishment of a phase-shifting profilometry through simultaneous projection and recording of fringe patterns requires a reliable phase retrieval procedure. In the present work we consider a four-wavelength multi-camera system with four sinusoidal phase gratings for pattern projection that implements a four-step algorithm. Successful operation of the system depends on overcoming two challenges which stem out from the inherent limitations of the phase-shifting algorithm, namely the demand for a sinusoidal fringe profile and the necessity to ensure equal background and contrast of fringes in the recorded fringe patterns. As a first task, we analyze the systematic errors due to the combined influence of the higher harmonics and multi-wavelength illumination in the Fresnel diffraction zone considering the case when the modulation parameters of the four gratings are different. As a second task we simulate the system performance to evaluate the degrading effect of the speckle noise and the spatially varying fringe modulation at non-uniform illumination on the overall accuracy of the profilometric measurement. We consider the case of non-correlated speckle realizations in the recorded fringe patterns due to four-wavelength illumination. Finally, we apply a phase retrieval procedure which includes normalization, background removal and denoising of the recorded fringe patterns to both simulated and measured data obtained for a dome surface.     

单周期条纹双四步相移投影仪的标定方法

针对投影仪标定方法中存在畸变及倾斜投影引起条纹周期、条纹级数变化的问题,提出一种单周期条纹双四步相移投影仪的标定方法.设计生成横向和纵向各两组单周期条纹图像,经投影仪投影到带有圆形标识的标定板上,相机同步采集标定板图像,叠加由双四步相移获得的两幅相位主值图,对叠加相位主值图相位展开,利用展开的绝对相位值计算投影仪像素坐标值,最终将投影仪标定转换为成熟的相机标定.实验结果表明:仿真投影仪标定实验准确度的最大重投影误差约为0.4pixel,均方根误差为0.132 96pixel;实际投影仪标定实验准确度的最大反投影误差约为0.46pixel,均方根误差为0.143 12pixel;实验结果与仿真结果的最大反投影误差相差15%,均方根误差相差7.6%.与现有的采用三频相位展开进行投影仪标定的方法相比,投影光栅图像数可减少8幅.该方法改善了现有投影仪标定方法的不足,标定准确度和标定效率均得到提高.     

移相器微位移旋转误差的分析及测试

以压电陶瓷(PZT)微位移器为主要研究对象, 引入一种处理静态干涉图的新方法--虚光栅移相叠栅条纹法,设计实验对一台实际使用的移相器微位移旋转误差进行测试研究,对其引起的波面旋转情况进行了定量的计算分析,并给出测试结果.用虚光栅移相叠栅条纹法处理实验中加有载频的干涉图时,不需要使用任何移相器件,可以进行动态位相的检测,整个移相过程用计算机进行控制,避免了引入额外的移相误差.     

Measurement of refractive index homogeneity of parallel optical component

In this paper, we present a method for enhancing the measurement capability of refractive index homogeneity for parallel optical components, which phase-shifting interferometry cannot handle with. With the help of wavelength-modulation phase-shifting interferometry, a series of multiple-surface interference fringes are obtained and analyzed by Fourier transform. Based on the fact that the interference fringe corresponding to each interference cavity has its own variation frequency, the wavefront aberrations induced by each interference cavity are obtained and the refractive index homogeneity is then obtained. It is proved by experiment that the enhanced method can measure the refractive index homogeneity of parallel optical components more accurately and conveniently compared with the traditional measurement approach. Therefore, it will have potential application forwards in optical measurement field.     

A real-time,full-field,and low-cost velocity sensing approach for linear motion using fringe projection techniques

A velocity sensing approach using the fringe projection technique is presented. The moving object is projected with a sinusoidal fringe pattern. A CCD camera located at a different view angle observes the projected fringes on the dynamic object. The long exposure time of the CCD camera makes the fringes blurred by linear motion. The blurred fringes provide additional information to describe the depth displacement, and therefore the velocity vector can be identified. There is no need to take multiple-shot measurements to address the change in 3D positions at a sequence of time. Only one-shot measurement is required. Consequently, there is no need to perform image registration. The full-field approach also makes it possible to simultaneously inspect several objects.     

Gerchberg迭代法在三维面形测量中的应用

在基于结构光照明的三维面形测量中,针对有孤立区域物体的条纹图像存在不规则缺陷的问题,提出先对其进行Gerchberg迭代,消除或减少条纹缺陷,获取较完善的迭代条纹,然后再利用傅里叶变换轮廓术(FTP)重建面形。设计了迭代流程,并分析了影响迭代精度的因素,解决了光学加工用具磨盘表面不完善条纹Gerchberg迭代过程中存在的问题,成功地重建了磨盘的三维面形。该工作为表面存在孤立区域的被测物体三维面形测量提供了可供参考的技术方案,也给可实时形变的应力盘三维面形动态测量奠定了基础。     

Hybrid two-dimensional continuous wavelet transform for analysis of phase-shifted interferograms

In interferogram or fringe pattern analysis, a technique capable of automatically analyzing interferograms that contain complex fringes and high-level noise as well as defects is highly demanded. In this paper, a hybrid technique combining the concepts of the two-dimensional continuous wavelet transform technique and the phase-shifting technique is proposed. The novel technique takes the advantages of the two existing techniques, and has the ability to accurately and automatically analyze multiple phase-shifted complex interferograms involving noise and defects. The validity of the technique is demonstrated by both computer simulation and real experiment.