采用双频光栅投影的快速傅里叶变换轮廓术

傅里叶变换轮廓术中通过反正切计算出的相位是截断的,如果被测物高度变化引起的相邻点的非截断相位变化过大,就无法直接进行正确的相位展开。故提出一种采用双频光栅的快速傅立叶变换轮廓术：从一帧条纹图中获取同一物体对应于不同等效波长的两组截断相位,先展开对应于低频的低精度截断相位,并以此为参考,根据双频光栅两个频率之间的关系,展开对应于高频的高精度相位。经过模拟比较,在误差范围内比传统方法恢复的图形有了较大的改善,相对误差率由2．26％下降到1．79％。     

Enhanced dual-frequency pattern scheme based on spatial-temporal fringes method

One of the major challenges of employing a dual-frequency phase-shifting algorithm for phase retrieval is its sensitivity to noise. Yun et al proposed a dual-frequency method based on the Fourier transform profilometry, yet the low-frequency lobes are close to each other for accurate band-pass filtering. In the light of this problem, a novel dual-frequency pattern based on the spatial-temporal fringes (STF) method is developed in this paper. Three fringe patterns with two different frequencies are required. The low-frequency phase is obtained from two low-frequency fringe patterns by the STF method, so the signal lobes can be extracted accurately as they are far away from each other. The high-frequency phase is retrieved from another fringe pattern without the impact of the DC component. Simulations and experiments are conducted to demonstrate the excellent precision of the proposed method.     

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.     

Precise and fast phase wraps reduction in fringe projection profilometry

Phase wraps in a 2D wrapped phase map can be completely eliminated or greatly reduced by frequency shifting. But it usually cannot be optimally reduced using conventional fast Fourier transform (FFT) because the spectrum can be shifted only by a integer number in the frequency domain. In order to achieve a significant phase wrap reduction, we propose a fast and precise two-step method for phase wraps reduction in this paper, which is based on the iterative local discrete Fourier transform (DFT). Firstly, initial estimate of the frequency peak is obtained by FFT. Then sub-pixel spectral peak with high resolution is determined by iteratively upsampling the local DFT around the initial peak location. Finally, frequency shifting algorithm that operates in the spatial domain is used to eliminate phase wraps. Simulations and experiments are conducted to demonstrate the superb computing efficiency and overall performance of the proposed method.     

基于格莱姆-施密特正交化两步相移轮廓术

将格莱姆-施密特正交化法引入投影栅形貌测量,提出了一种新的两步相移轮廓术.首先将2幅随机相移正弦条纹通过DLP投影仪投射到待测物体上,由CCD相机采集受物体形貌调制的变形光栅条纹图,再选择合适大小窗口经像素逐点均值法消除变形栅线图中的背景成分,然后对消背景栅线图进行格莱姆-施密特正交化,得到2幅消背景相移栅线图对应的正交基,由正交基解调出相位数据.最后对面膜样品进行了实际测量,并与其它方法进行了比较分析,实验结果证明了该方法的有效性.     

基于波长移相的改进加权多步算法

在斐索干涉仪中测量光学平板受到多面反射光束的影响,而波长移相干涉技术是通过光源波长的改变来实现干涉信号的移相,原理上可以实现各个干涉信号的分离,在算法上要求能对多次谐波进行较好的抑制,加权多步移相算法可以实现这样的目的.笔者提出了加权多步移相算法的改进算法,可以提高算法对误差的抑制能力,最后用实验验证了改进算法的有效性.     

High-precision measurement of low reflectivity specular object based on phase measuring deflectometry

Phase measuring deflectometry (PMD) is a robust, noncoherent technique for the characterization of specular surface. For measuring high specular reflectivity surface, PMD can deliver micron radian range local gradient. However, when the measured surface has low specular reflectivity, the accuracy of the measured gradient is low since the captured fringe pattern shows low signal to noise ratio. The phase error characteristics in PMD system when testing low reflectivity surfaces are analyzed. The analysis illustrates that the random phase error increases rapidly while the nonlinear error drops slowly with the decreasing of the tested surface reflectivity. In order to attain high precision measurement of low reflectivity specular surface, a robust error reduction method based on wavelet de-noising is proposed to reduce the phase error. This error reduction method is compared with several other normally used methods in both simulation and experiment work. The method based on the wavelet de-noising shows better performance when measuring the low reflectivity specular surface.     

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。     

Full-field phase error compensation method based on relationship between unwrapped phase and phase error

The three-dimensional reconstruction in phase-measuring profilometry (PMP) usually involves the phase error caused by the gamma effect of the projector. In this study, the relationship between the unwrapped phase and the phase error of every pixel is analysed, and an effective full-field phase error compensation method based on this relationship is proposed for the reduction of every pixel error. In our optimized PMP system, the full-field phase error can be detected by directly fitting the unwrapped phase of the reference plane. In addition, the relationship between the unwrapped phase and the phase error can be established by creating a phase-error lookup table for the phase error compensation of every pixel. The experimental results demonstrate the effectiveness of the proposed method in practical PMP, and the measurement errors can be reduced by a factor of least 10.     

Extended depth-range dual-wavelength interferometry based on iterative two-step temporal phase-unwrapping

For dual-wavelength interferometry (DWI), we propose an extended depth-range phase-shifting interferometry technique of extracting phase distributions from randomly phase-shifted interferograms. First, the generalized phase-shifting algorithm is utilized to retrieve the single-wavelength phase from interferograms with random phase shifts. Then, the phase difference and phase-sum are calculated from the wrapped single-wavelength phases, and iterative two-step temporal phase-unwrapping is introduced to unwrap the phase-sum. Finally, the height of objects is determined. Simulations and experiments are conducted to demonstrate the excellent precision and overall performance of the proposed method. As the limitation of being exclusively applicable to interferograms with special phase shifts is broken, the proposed method will greatly facilitate the practical application of DWI. Furthermore, because the phase-sum and iterative two-step temporal phase-unwrapping is introduced to extend the depth-range, the sensitivity and precision of the retrieved phase are greatly improved.     

A fast 3D shape measurement method based on sinusoidal and triangular fringe projection

Existing methods to measure 3D shape of complex object involve processing more than six captured images to obtain the absolute phase, which limit the measurement speed. This paper presents two sinusoidal fringes and two triangular wave fringes which is used to measure 3D shape of complex object. The two-step phase-shifting sinusoidal fringes and two-step phase-shifting triangular wave fringes are calculated to obtain the wrapped phase, and then the two-step phase-shifting triangular wave fringes are used to determine the fringe order. Due to decrease the number of projection fringes, the speed of measurement increases. The triangular wave fringe carries more information of the object than linear increasing/decreasing ramp fringe in the actual measurement, more noise in the base phase to be overcome, thus improving the measurement accuracy. The benefits can be widely applied in high-speed, real-time 3D measurement of complex shape. Experimental results have demonstrated that the proposed method is simple, but effective.     

A new phase retrieval algorithm with pure generalized three-step phase-shifting under matrix norm processing

Phase-shifting interferometry (PSI) is one of the most effective techniques in imaging a phase specimen, in which the phase retrieval is a basic and significant process. A new phase retrieval method based on the matrix norm algorithm in PSI is proposed in this paper. In this algorithm, the value of phase shift can be determined by three different matrix norms of the intensity difference between two phase-shifted interferograms, and then the phase can be retrieved. Neither the iterative calculation nor the extra measurements of other parameters are necessary on account of this algorithm which only requires three phase-shifted interferograms. The feasibility and accuracy of this algorithm are demonstrated by the simulated results. Experimentally, the generalized phase shift can be realized by a simple device which adjusting the angle of glass accurately. It is found that this algorithm has a good application prospect in the field of dynamic imaging.     

基于LMS算法的移相干涉仪环境振动控制器

环境振动严重影响移相干涉测量的过程。在运用光学外差法测得移相干涉仪环境振动信号的前提下,设计了采用高速DSP芯片的振动控制器,它对电压形式的振动信号进行采样,用自适应LMS算法分析振动信号,同时输出反馈控制信号。反馈控制信号驱动PZT光学移相器对振动引起的光程差(或波前相位)变化进行实时补偿。通过这种闭环控制,系统能够对幅频积小于100waves*Hz的环境振动进行有效补偿,实验中获得了稳定的移相干涉条纹,保证了光学测试的正确性。     

Statistical estimation method for phase shift in generalized two-step phase-shifting interferometry

Based on the statistical property of the phase and the spatial frequency relationship between the object and reference waves, a simple estimation method for phase shift extraction is proposed for generalized two-step phase-shifting interferometry. In this method, a phase shift constrained within 0–π is firstly worked out with statistics, and then it is corrected as its principal value within the range (0, 2π) except the singular value of π, according to the sign of tangent form of one half of the relative phase shift. Thus, this method provides a possible method to solve the uncertainty of the phase shift existing in some common algorithms. After the determination of the phase shift, a phase can be retrieved easily. The feasibility and the accuracy of the method were verified by numerical simulations and an optical experiment. In addition, this method is applicable to two or more frames off-axis generalized PSI, including slightly off-axis situation.     

相移条纹投影三维形貌测量技术综述

结构光三维形貌测量系统目前得到了越来越广泛的应用和研究,相移条纹投影三维形貌精密测量技术是其重要的发展方向。对结构光相移条纹投影三维形貌测量系统的应用发展、工作过程、不同系统构成方式、相移条纹的各种形式及特点、相位误差校正方法、不同相位解包裹算法及其优缺点和适用场合、测量系统数学模型的实现方法及其相应的优缺点、高动态范围测量技术等进行了详细的分析。对相移条纹投影系统的工作流程、实现方法、关键技术的发展及其存在问题等进行了比较全面的梳理,为三维形貌精密测量技术进一步满足先进制造中更高精度的要求指出了后续的研究方向。     

A fast pixel matching method based on phase feature extraction in online phase-measuring profilometry

A fast pixel matching method based on phase feature extraction in online phase-measuring profilometry is proposed, which is used to solve the problem where the object motion is along a straight line. The movement of the object results in the displacement of images in the captured deformed patterns, so pixel matching is carried out to modify the positions of images, which not only realizes the point-to-point correspondence of the object, but extracts the equivalent phase-shifting deformed patterns. So, the 3D surface shape of the object moving on the pipeline can be reconstructed successfully with an equivalent phase-shifting algorithm. The equiphase surface phase feature extracted from the phase distributions of the object obtained by Fourier transform profilometry is used to assist pixel matching in this paper. Normalization and further binarization of the phase feature extraction improve pixel matching’s accuracy and speed. The simulation and experiments verify the feasibility and validity of the proposed method.     

Optical information encoding and image watermarking scheme based on phase-shifting interferometry and singular value decomposition

A robust image watermarking scheme based on phase-shifting interferometry (PSI) and singular value decomposition (SVD) is proposed, in which, a grayscale image watermark is encrypted into multiple interferograms using the techniques of double random-phase encoding (DRPE) and PSI. By choosing the appropriate weighting factor, the interferograms are embedded in the singular values of the R, G, and B components of the host image. The scheme achieves a high level of security due to DRPE and at the same time preserves high imperceptibility and robustness due to SVD properties. Simulated results of the proposed scheme are provided to demonstrate the high robustness, not only against the geometric distortion attacks but also against general image processing attacks.     

基于遗传算法和自适应的平面线轮廓度误差评定方法

 为了解决在测量平面线轮廓度中由于存在被测轮廓与其测量基准间存在位置误差而影响评定精度的问题，提出了一种基于遗传算法和自适应的计算平面线轮廓度误差的新方法。该方法满足最小条件原理，它利用样条插值函数拟合理论轮廓，并在评定过程中能自动地实现被测轮廓与理论轮廓之间的适应性调整，从而能够分离并消除被测轮廓与其测量基准之间的位置误差对轮廓误差评定结果的影响，在遗传优化中获得全局最优解。实例计算验证了这一结果。这种算法简单明确，具有精度高、收敛速度快、易于计算机程序实现、易于推广应用等特点。     

A novel algorithm for pose estimation based on generalized orthogonal iteration with uncertainty-weighted measuring error of feature points

In this paper, we investigate the effect of anisotropic and correlated non-identical distributions of feature points’ gray level on pose estimation in stereo vision system. The generalized orthogonal iteration (GOI) algorithm for pose estimation with uncertainty-weighted measuring error of feature target is proposed. In this method, the inverse covariance matrix is applied to describe the uncertainty of feature points, and weighted contribution of uncertainty to the error objective function is analysed. By transforming the uncertainty into the covariance-weighted data space, a novel objective function based on spatial collinear error is constructed. The orthogonal iterative algorithm is extended to stereo vision system for pose estimation and the GOI algorithm is deduced, by which the optimized solution to a novel objective function is given. Finally, simulation and actual experimental results show high accuracy and strong robustness of the proposed approach, and should therefore, have potential for a variety of engineering applications.     

基于改进测量系统的非定步距相位轮廓测量技术研究

提出一种基于改进测量系统,该系统放宽了传统测量光路的3个约束,降低对系统结构的要求;同时结合非定步距轮廓测量技术,与传统相位轮廓测量技术相比较,无需保证等步距相移量,且仅需两幅畸变光栅图像就可以重建物体的三维轮廓。通过理论分析,推导出高度与相位之间的非线性映射函数关系式。实验证明,在满足一定精度要求的同时,该系统对结构条件要求较低,测量速度较快,具有较强的可操作性。