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.     

Profile measurement of a moving object using an improved projection grating phase-shifting profilometry

3-D profile measurement of a moving object using a novel phase-shifting technique is introduced. Digital gratings with two steps phase-shifting are projected periodically onto a measured object surface. The deformed fringe patterns are captured by a frame CCD camera within a short exposure time. By synchronizing the projector and the CCD camera accurately, there is an overlapping part which is the same part of the object among three neighbouring frames. The length of an overlapping part can be controlled as one third of a frame length. Hence the intensity values at the same surface point modulated by three neighbouring gratings can be obtained, and its phase value can be computed by an improved phase-extracting algorithm. The profile of a specimen is detected by the proposed method. Experimental results demonstrate that this method is effective for the profile measurement of a moving object.     

On-line phase measuring profilometry based on a single frame of deformed pattern

Three frames of deformed patterns are needed at least in conventional Phase Measuring Profilometry (PMP). It is generally applied to the profile measurement of a static object. For on-line measurement, because of the moving object, it is difficult to capture three or more frames of deformed patterns that satisfy the requirement of PMP. A new method of on-line 3-D shape measurement through only one frame deformed pattern in PMP is presented. A static sinusoidal fringe is projected and any one frame of real-time deformed patterns is captured by CCD. N frames of sub-images are extracted from the captured deformed pattern. Improved Stoilov algorithm is proposed to get phase. Computer simulation and experimental results show its feasibility and affectivity to reconstruct a 3-D shape and the accuracy is higher than Fourier Transform Profilemetry (FTP) which is also a method that only needs one frame of deformed pattern.     

Surface profile measurement of moving objects by using an improved π phase-shifting Fourier transform profilometry

The π phase-shifting Fourier transform technique is introduced into the surface profile measurement of moving objects. A digital grating comprising two regions, which have a π phase shifting is projected onto the object. Two line-scan CCD cameras are used to capture two deformed fringe patterns with π phase shifting at the same time. As the object is moving, each point at the object surface can be captured twice. The digital correlation method is used to calibrate the experimental system. The zero-order component can be eliminated by subtracting intensities of the same surface point in two captured images. And then the phase can be extracted by Fourier transform without the disturbance of zero-order component. Experimental results demonstrate that this method is feasible for the moving surface profile detection and the measurable slope of height variation can be extended.     

一种用于在线三维测量的五步非等步相移算法

提出了一种五步非等步相移算法,并成功应用于在线三维测量中。仅投影一固定正弦光栅条纹到物体上,通过物体在线运动产生等效相移,在一个条纹周期范围内任意采集五帧变形条纹图,通过像素匹配使各帧条纹图中的物点一一对应并计算出相应的等效相移量。采用所提出的五步非等步相移算法,即可重构物体。计算机模拟与实验验证了该方法的可行性和有效...     

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.     

利用预失真条纹校正PMP系统投影仪畸变的研究

依据摄像机畸变模型提出了一种投影条纹相位畸变校正方法来简化相位-高度映射关系.该方法首先通过投两套互相垂直的相移正弦条纹,以相位值代替投影仪像素坐标,将投影仪当成摄像机看待,标定出投影仪的内参量.然后根据标定出的投影仪镜头畸变参量对理想相位施加反向的畸变,在投影时反向畸变的光栅通过镜头畸变,又成为理想的光栅,从而简化了相位-高度映射关系.实验中,虽然由于测量误差的影响,校正后的投影仪径向畸变系数还是比原来小了1个数量级.     

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。     

Dynamic 3-D shape measurement method based on FTP

In this paper, we propose a method for dynamic three-dimensional (3-D) shape measurement based on Fourier transform profilometry. A sequence of dynamic deformed fringe images can be grabbed by a CCD camera and saved on a disk rapidly. By a Fourier transform, filtering and inverse Fourier transform, a sequence of phase-maps can be obtained. By unwrapping these phase maps in 3-D phase space, we can obtain the shape of the dynamic object at different times. In this paper we also propose the algorithm of a phase difference between two deformed fringes, and the 3-D phase unwrapping method based on the phase difference algorithm. The computer simulation and experiment results show that this method can efficiently deal with the dynamic 3-D shape measurement.     

A novel 3D measuring method for discontinuous object by non-integral twin-frequency grating

A new 3D shape measurement method based on non-integral twin-frequency grating projection is proposed. In this paper, the projected composite grating is composed of two sinusoidal gratings, and the quotient of whose frequencies is not an integer. By using appropriate phase-shifting algorithms, two wrapped phases can be obtained from sixteen frames of the distorted grating patterns. In aid of appropriate phase unwrapping method, the unwrapped phase of high frequency fringe is obtained only from the relation of the two wrapped phases by a pixel-to-pixel phase unwrapping technique. Therefore the unwrapped phase of high frequency fringe pattern is independent of the low frequency fringe pattern, different from traditional integral twin-frequency grating projection methods in which the phase unwrapping error of low frequency fringe pattern may be propagated onto the unwrapped phase of high frequency fringe pattern. The new theory proves that the proposed method is applicable to measure discontinuous object, and has considerable measurement accuracy.     

A numerical spatial carrier for single fringe pattern analysis algorithm

Hilbert transform and continuous wavelet transform are combined to form an algorithm for the analysis of a single fringe pattern with open or closed fringes. Only one recorded fringe pattern is needed to extract the phase information. A second π/2 phase shifted fringe pattern should first be generated from the other using Hilbert transform to superpose numerically the spatial carrier. Several phase extraction techniques are conceived to demodulate fringe patterns. In this paper, the wavelet technique is used to obtain the required phase distribution. The algorithm offers an advantage that it is appropriate when the spatial carrier is impossible to be added experimentally. Finally, a simulation was carried out to validate the algorithm, giving good results.     

利用预失真条纹校正PMP系统投影仪畸变的研究*

依据摄像机畸变模型提出了一种投影条纹相位畸变校正方法来简化相位-高度映射关系.该方法首先通过投两套互相垂直的相移正弦条纹,以相位值代替投影仪像素坐标,将投影仪当成摄像机看待,标定出投影仪的内参量.然后根据标定出的投影仪镜头畸变参量对理想相位施加反向的畸变,在投影时反向畸变的光栅通过镜头畸变,又成为理想的光栅,从而简化了相位-高度映射关系.实验中,虽然由于测量误差的影响,校正后的投影仪径向畸变系数还是比原来小了1个数量级.     

Multi-frequency inverse-phase fringe projection profilometry for nonlinear phase error compensation

A new multi-frequency inverse-phase method was proposed to compensate for nonlinear phase errors in fringe projection profilometry and to measure the three-dimensional shape of discontinuous objects. After introducing a phase offset of π/4 into the multi-frequency four-step phase-shifting method the corresponding nonlinear phase error reversed its sign, which allowed the addition of unwrapped phases before and after the phase-offset operation to compensate for the error. For the four-step phase-shifting method, simulation analysis showed that the nonlinear phase error had quadrupled the fringe frequency. Moreover, experimental results verified the feasibility and applicability of the proposed method.     

Fourier transform profilometry: : a review

Fourier transform profilometry is one of the popular non-contact 3-D measurement methods, where a Ronchi grating or sinusoidal grating is projected onto a diffuse three-dimensional surface, and the resulting deformed grating image is detected by a CCD camera and processed by a computer. This method requires only one frame (or two frames) of the deformed fringe pattern in some algorithms to retrieve the surface of measured object, so it has obvious advantage for real time data acquisition and 3-D measurement of dynamic process. In this paper, we review some algorithms in FTP, discuss some important problems, including frequency spectra overlapping, phase unwrapping, sampling, and 3-D measurement of dynamic process. With the development of computer hardware and software and availability of high-resolution image grabber, FTP method will be a promising one for acquiring 3-D data of object, and more and more researchers pay attention to it.     

Generalized phase-shifting algorithm for dynamic phase measurement in electron-wave interferometry

A generalized phase-shifting algorithm is implemented in the electron-wave interferometry with a transmission electron microscope, based on simultaneous measurement of the initial phases of the interferograms. The initial phase of each interferogram that has inherent linear carrier fringes is calculated using the Fourier co-efiicients of the interferogram itself corresponding to the carrier-frequency. Taking advantage of this phase-shifting method in both spatial resolution and precision, the phase distribution of a biological weak phase object is successfully measured. This promises to be one of the most spectacular application fields for this new technology.     

基于傅里叶频谱分析的相位测量轮廓术系统Gamma非线性校正方法

数字投影和成像系统的Gamma非线性效应是导致相位测量轮廓术（PMP）测量误差的重要原因。目前大多采用多帧条纹图进行Gamma校正,使测量的实时性受到限制。提出了一种Gamma校正方法,利用正交光栅像的傅里叶频谱分布计算Gamma值,再根据此Gamma值对投影相移条纹进行Gamma逆变换,实现投影条纹输入值的提前校正,以获取具有良好正弦性的结构条纹,从而降低PMP相位测量误差。校正过程中只需一帧条纹图,而且考虑了测量系统的离焦效应。实验证实了该方法的有效性和正确性。     

Phase measuring profilometry based on elliptically pattern grating

The present study proposes a new method for measuring the surface shape of an object using elliptically pattern grating projection. Based on phase measuring profilometry (PMP), elliptically pattern grating is projected on the surface of the object to measure its shape in 3D. The computing formula for solving the phase by the phase-shifting fringe method is derived, and the 3D shape formula for the altitude is reestablished. The error-contrastive analysis of the object's surface shape is re-established based on the proposed method and traditional PMP. The proposed method was shown to have a strong anti-noise ability and able to measure objects under high noise. More accurate measurement results were obtained by computer simulation and experiment to verify the feasibility of the proposed method.     

利用电子散斑相移技术测量物体三维面形的方法

为了获得准确的面形测量,提出了一种相移电子散斑干涉技术测量物体面形的测量方法.利用电子散斑干涉产生载波条纹,该载波条纹受到物体表面高度的调制变得弯曲,引起载波条纹相位的变化,可运用相移技术提取物体的相位信息,最后根据高度和相位之间的关系得到物体的面形.介绍了该方法的原理,利用该方法对球冠物体进行了面形测量,证明该方法测量物体面形是可行性的.由于是采用散斑干涉的方法产生干涉条纹,因此该方法测量物体面形具有灵敏度高的优点.     

Automatic fringe analysis for moiré topography

Two digital systems are developed for the automatic measurement of 3-D shapes using moiré techniques—an automatic 3-D shape measuring system using the scanning moiré method and an interactive fringe analysing system for moiré fringe photographs. In the automatic 3-D shape measuring system, a deformed grating is scanned and sampled with an electronic image scanning device so that moiré fringes are generated in a computer. This technique of electronic fringe generation eliminates ambiguity with regard to the sign of the moiré fringes. The interactive fringe analyser provides a flexible and versatile tool for moiré fringe analysis. Medical applications of these analysing systems are discussed.     

A study on the 3-D measurement by using digital projection moiré method

Moiré topography method is a well-known non-contacting 3-D measurement method. Recently, the automatic 3-D measurement technique by moiré topography has been developed in order to apply to the engineering and medical fields. The projection moiré topography is very attractive because of its high measuring speed and high sensitivity. In this paper, using the two-wavelength methods of projection moiré topography was investigated to measure the 3-D shape of an object with 2π-ambiguity problems. Rapid measurement can be accomplished by the synchronization between CCD camera and projector. The experimental results prove that the proposed scheme is capable of finding absolute fringe orders, so that the 2π-ambiguity problems can be effectively overcome so as to treat large step discontinuities in measured objects.