应用时域相位解包方法的三维形貌测量系统

设计一套基于时域相位解包方法的三维形貌测量系统 ,克服了传统解包方法中的误差传播效应 ,可以应用于复杂物体表面及复杂环境下的三维形貌测量。由计算机生成光栅并通过液晶投影仪投射到待测物体表面 ,用CCD摄像机采集图像并通过图像采集卡存贮到计算机中进行处理 ,实现了测量的自动化 ,完成一次高精度的测量仅需几秒钟时间。用两个特殊的人头像完成的实验证明了系统的优越性     

A temporal phase unwrapping algorithm for photoelastic stress analysis

Photoelastic stress analysis is a full-field optical technique for experimental stress analysis whose automation has received considerable research attention over the last 15 years. The latest developments have been made possible largely due to the availability of powerful calculators with large memory capacity and colour, high resolution, cameras. A further stimulus is provided by the photoelastic resins now used for rapid prototyping. However, one critical aspect which still deserves attention is phase unwrapping. The algorithms most commonly used for this purpose have been developed in other scientific areas (classical interferometry, profilometry, moiré, etc.) for solving different problems. In this article a new algorithm is proposed for temporal phase unwrapping, which offers several advantages over those used today.     

Profilometry of three-dimensional discontinuous solids by combining two-steps temporal phase unwrapping,co-phased profilometry and phase-shifting interferometry

In this work we review and combine two techniques that have been recently published for three-dimensional (3D) fringe projection profilometry and phase unwrapping, namely: co-phased profilometry and 2-steps temporal phase-unwrapping. By combining these two methods we get a more accurate, higher signal-to-noise 3D profilometer for discontinuous industrial objects. In single-camera single-projector (standard) profilometry, the camera and the projector must form an angle between them. The phase-sensitivity of the profilometer depends on this angle, so it cannot be avoided. This angle produces regions with self-occluding shadows and glare from the solid as viewed from the camera׳s perspective, making impossible the demodulation of the fringe-pattern there. In other words, the phase data is undefined at those shadow regions. As published recently, this limitation can be solved by using several co-phased fringe-projectors and a single camera. These co-phased projectors are positioned at different directions towards the object, and as a consequence most shadows are compensated. In addition to this, most industrial objects are highly discontinuous, which precludes the use of spatial phase-unwrappers. One way to avoid spatial unwrapping is to decrease the phase-sensitivity to a point where the demodulated phase is bounded to one lambda, so the need for phase-unwrapping disappears. By doing this, however, the recovered non-wrapped phase contains too much harmonic distortion and noise. Using our recently proposed two-step temporal phase-unwrapping technique, the high-sensitivity phase is unwrapped using the low-frequency one as initial gross estimation. This two-step unwrapping technique solves the 3D object discontinuities while keeping the accuracy of the high-frequency profilometry data. In scientific research, new art are derived as logical and consistent result of previous efforts in the same direction. Here we present a new 3D-profilometer combining these two recently published methods: co-phased profilometry and two-steps temporal phase-unwrapping. By doing this, we obtain a new and more powerful 3D profilometry technique which overcomes the two main limitations of previous fringe-projection profilometers namely: high phase-sensitivity digitalization of discontinuous objects and solid׳s self-generated shadow minimization. This new 3D profilometer is demonstrated by an experiment digitizing a discontinuous 3D industrial-solid where the advantages of this new profilometer with respect to previous art are clearly shown.     

Iterative two-step temporal phase-unwrapping applied to high sensitivity three-dimensional profilometry

Although temporal phase unwrapping method can be applied to solve some problems to measure an object with steep shapes, isolated parts or fringe undersampling in three-dimensional (3D) shape measurement, it needs to acquire and process a sequence of fringe pattern images which would take much time. Servin et al. proposed a 2-step temporal phase unwrapping algorithm, which only needs the 2 extreme phase-maps to achieve exactly the same results as standard temporal unwrapping method. But this method is only validated by computer simulation, shortage of experimental demonstration, its sensitivity coefficient G is limited, and it cannot be used when the G value is larger. We proposed an iterative two-step temporal phase-unwrapping algorithm which is an extension of Servin׳s method. First, add a fringe pattern with an intermediate sensitivity, project the fringe patterns of different sensitivity onto the tested object’s surface, and collect deformed fringe patterns with a CCD camera. Then we obtain the unwrapped phase with larger sensitivity coefficient G by cascading the sensitivity coefficients. And we derive the initial phase conditions of the 2-step temporal phase unwrapping algorithm. Finally, the experimental evaluation is conducted to prove the validity of the proposed method. The results are analyzed and compared with Servin׳s method. The experimental results show that the proposed method can achieve higher sensitivity and more accurate measurement, and it can overcome the main disadvantages encountered by Servin׳s method.     

Comparison of eight unwrapping algorithms applied to Fourier-transform profilometry

Phase unwrapping is a task common to many applications like interferometry imaging, medical magnetic resonance imaging, solid-state physics, etc. Fourier transform profilometry (FTP) values the height distribution of object, elaborating the interference between a plane reference grating and a deformed object grating. Since the height information is extracted from the phase of a complex function, the phase unwrapping is a critical step of the process. Several unwrapping algorithms are proposed in literature, but applied to measurement technologies different from FTP. The purpose of this paper is to define the performances of eight different unwrapping algorithms applied to FTP optical scan method and to define the best one. The algorithms chosen are: Goldstein's algorithm, quality guided path following method, Mask cut method, Flynn's method, multi-grid method, weighted multi-grid method, preconditioned conjugate gradient method and minimum L_p-norm method. The methods were tested on real images acquired by a FTP scanner developed and calibrated for these experiments. The objects used vary from simple geometries, like planes and cylinders, to complex shapes of common use objects. Algorithms were qualified considering the phase unwrapping errors, execution time and accuracy of the shape of objects obtained from the scan method in comparison with real ones. The results show that quality guided algorithm best fits in FTP application.     

A correlation-based phase unwrapping method for Fourier-transform profilometry

A new phase unwrapping algorithm based on correlation map for Fourier-transform profilometry (FTP) method is presented in this paper. It is a quality-guided phase-unwrapping method. The modulation is used as an effective parameter to indicate the reliability of the fringe image for the quality-guided phase-unwrapping method. A filtering window is introduced to calculate the modulation easily. A correlation-map function is proposed to calculate the reliability of the fringe image and to avoid choosing the width of the window in calculating the modulation. As the value of the correlation-map function is lower in areas of the local shadow and abrupt discontinuity than that in other areas, the correlation-map function is used as a guide to find the optimized phase-unwrapping path. The experimental results show that the method is feasible.     

A method for enlarging absolute phase unwrapping range by active phase setting

An active phase-setting method applied to a frequency-modulated grating is proposed for enlarging the absolute phase unwrapping range. It is found that the absolute phase unwrapping range is related to initial phase of grating. Therefore, the grating is optimized by presetting two different initial phases, which one is constant in frequency-modulation term and the other is related to the ratio of two frequency in linear phase-modulation term. By using absolute phase unwrapping algorithm, which is improved for suiting the new grating, absolute phase unwrapping range successfully is enlarged and achieves the theoretical range. The experimental results show the feasibility and validity of new method.     

Micro-phase measuring profilometry: Its sensitivity analysis and phase unwrapping

Global illumination affects shape measurement accuracy, and phase unwrapping is an important problem in phase measuring profilometry. In this paper, a micro-phase measuring profilometry is proposed to reduce the effects of global illumination. The wrapped phase error level of the proposed method is lower than that of the traditional micro-phase shifting method. First, a frequency selection rule is developed in combination with the micro-phase rule to design the frequencies of the proposed phase measuring profilometry. The frequency rule is obtained by analysing the uncertainty of the wrapped phase caused by intensity noise. Then, phase unwrapping is regarded as a congruence problem, and the closed-form robust Chinese remainder theorem algorithm is adopted to determine the correspondence. Finally, the comparative experiments are conducted on a projector-camera system. Experimental results show that the effects of global illumination can be effectively reduced with the proposed phase measuring profilometry, and the proposed frequency selection rule is valid. In addition, the performance of the robust Chinese remainder theorem in addressing the phase error is better than that of traditional Chinese remainder theorem. Furthermore, the unwrapping accuracy can nearly reach 100% if the frequency selection rule is satisfied. Otherwise, the performance degrades.     

基于位相测量轮廓术的三维数字化仪的实验研究

介绍了基于位相测量轮廓术的三维数字化仪的原理和系统结构 ,阐述了一种有效的三维数字化方法。该方法具有精度高、速度快、可实现自动测量等特点。     

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.     

Temporal phase unwrapping using orthographic projection

This paper proposes a novel temporal phase unwrapping method which is a generalization of the three commonly proposed approaches: hierarchical, heterodyne, and number theoretical phase unwrapping. The proposed unwrapping method is based on the orthographic projection of wrapped phases from the measurement space to the space of co-dimension 1. In the space of co-dimension 1 all unknown integer period-order numbers are computed simultaneously using a nearest-neighbor search on a fixed constellation of points. The proposed method offers new key insights about relationship between unwrapping success rate, noise limit, and maximum unwrapping range. We give example how the proposed method may be applied in the multiple frequency phase shifting profilometry.     

最小二乘相位解包络方法

介绍一种最小二乘解相位包络的方法 ,该法的优点在于把图像作为一个整体处理 ,图像上每一个像素点的值由方程唯一确定 ,而且解得的相位图与原包裹的相位图偏差平方加权最小 ,具有局部解相法所不具有的优点。实验证明 ,它能够处理局部处理方法难以解决的相位图 ,并给出几幅实际相位图的处理结果     

基于图像分析技术的实用相位恢复去包裹技术

相位恢复去包裹技术是相移干涉中的重要环节。本文介绍一种去包裹的新算法 ,该算法基于相位连续平滑的特点 ,在传统算法的基础上 ,提出包裹点判断门限的智能确定方法。引入图像分析处理技术 ,以识别并修正传统算法产生的误差点和由于误差点延伸产生的畸变点。应用结果表明 ,此算法不但计算量小 ,速度快 ,而且极大地降低了去包裹操作引起的相位信息变形失真的可能性 ,保证了较高的相位恢复精度。该算法在连续平滑相位相移干涉测量中具有很好的实用性     

Load-stepping photoelasticity: new developments using temporal phase unwrapping

A new approach to load-stepping photoelasticity is presented in which the isochromatic phase is unwrapped between load steps rather than spatially. This is based on the technique known as ‘temporal phase unwrapping’ that has mainly been applied in shape measurement. The potential advantages of temporal phase unwrapping are based on the notion that each pixel is unwrapped independently of its neighbours. The benefits for load-stepping photoelasticity for reducing the effects of measurement error are discussed in this paper. New developments using temporal phase unwrapping are applied to experimental data obtained from a bimaterial interface specimen loaded in three-point bend. The results show that a modified approach to unwrapping significantly reduces the effects of systematic noise present in the data.     

抑制相位测量轮廓术饱和误差相位融合算法

在相位测量轮廓术中,由于被测物体表面反射率过大,导致照相机捕获的图像中部分像素点强度值超过照相机的最大量化值,即光强度饱和。分析了光强度饱和引起的相位误差,提出一种相位融合算法。该算法通过查找归一化后的最大调制强度,提取其对应的相位,并将该相位作为三维重建的最终相位。实验结果表明,在理想情况及测量系统存在Gamma畸变时该算法均能有效地修复饱和误差。当测量系统存在Gamma畸变时,校正后相位误差均方根值相对于传统技术减小了58.86%。     

利用颜色编码辅助计算绝对相位的傅里叶轮廓术

针对传统去卷积算法时间需求的弊端,提出一种新的使用颜色编码辅助的绝对相位并行计算方法。该算法采用对光栅数目需求最少的傅里叶变换轮廓术（FTP）做为卷积相位求取的方法;颜色编码光栅被用来标识轮廓的序数。直接使用FTP计算出的卷积相位以及从彩色光栅中获得的轮廓序数,即可方便求出当前像素的绝对相位值;同时只用一副图像标识轮廓序数也比其他轮廓序数标识方法简单。本方法由于使用绝对相位计算方法,局部相位误差不会扩展。实验结果也证明了此算法对于多个分离物体以及复杂物体的有效性。     

含噪声包裹相位图的加权最小二乘相位展开算法研究

二维相位展开广泛应用在精密光学测量、自适应光学、合成孔径雷达、图像处理等领域中。为处理含噪声包裹相位图,以预条件共轭斜量法求解权重最小二乘相位展开方程。引入非加权二维离散余弦变换求解泊松方程得到的最小二乘相位解作为共轭斜量法的初始解,从而加快了收敛速度,同时提出一种新质量图确定算法求解过程中的权重项。计算机模拟和试验表明算法计算速度快,能有效地消除传统路径积分法在处理信噪比低包裹相位图时的"拉线"现象,是一种有效的相位展开方法。     

A novel algorithm for branch cut phase unwrapping

Branch cut method is a powerful noise-immune algorithm for correct phase unwrapping of noisy phase maps. The shortest branch cut length promises the optimal unwrapping result of the wrapped phase maps. A new algorithm is proposed to search for the shortest branch cut length by simple exchange operation. Although the algorithm is on the basis of stochastic search techniques, it has a high probability of finding the shortest branch cut length or an approximation of it. Compared with the traditional algorithms, the algorithm is fast and competitive.     

Phase locked loop profilometry

An innovative technique for obtaining automatic three-dimensional shape information of a diffuse surface is presented. The technique is based on a new approach of phase measuring from a fringe pattern. The target to be studied is first modulated by projecting a linear grating onto its surface. The linear fringes are deformed according to the surface shape. Demodulation is carried out by determining the phase of these deformed fringes using a novel digital phase locked loop demodulation algorithm. The technique has the main advantage that the traditional phase unwrapping process is not required. The phase is determined continuously as the algorithm scans the two-dimensional fringe pattern. Owing to its sequential nature, this phase detection technique can be implemented using a special purpose video processor for phase determination at video rates, making it a very fast algorithm. The algorithm along with experimental results of real surface profiles are presented.     

Matched data storage in ESPI by combination of spatial phase shifting with temporal phase unwrapping

We combine the spatial phase-shifting technique with the real-time fringe counting capability of temporal phase unwrapping to provide simple solutions for some practical tasks in ESPI. First, we develop a method for automatically matched data storage intervals and apply this technique to a long-term observation of a biological object with strongly varying deformation rate. Second, we easily obtain on-line displacement and deformation data during the observation of a complexly structured discontinuous object.