Measurement of sub-surface delaminations in carbon fibre composites using high-speed phase-shifted speckle interferometry and temporal phase unwrapping

A high-speed phase-shifted speckle interferometer has been developed recently for studying dynamic events. Speckle interferograms are continuously recorded by a CCD camera operating at 1 kHz with temporal phase shifting carried out by a Pockels cell running at the same frequency. Temporal phase unwrapping through sequences of more than 1000 frames allows the determination of time-varying absolute displacement maps. This paper presents the application of this speckle interferometry system to the detection and measurement of sub-surface delamination defects in carbon fibre specimens. The influence of re-referencing the temporal phase unwrapping algorithm after different time intervals is analysed to reduce the random phase errors produced by speckle decorrelation and vibration. The performance of several phase-shifting algorithms to minimize the influence of the vibration noise caused by the vacuum pump used to load the specimen is also investigated.     

The new method of topological charge determination of optical vortices in the interference field of the optical vortex interferometer

In this paper, the new method of determination of the topological charge of vortex points in the interference field obtained by three plane waves interference is presented. Such optical fields are used in the optical vortex interferometer (OVI) and the determination of vortex points’ topological charge allows of unique determination of the relative phase between interfering waves (phase unwrapping problem). The new method uses additional plane wave, which produce a characteristic fork-like fringe structure in the neighbourhood of vortex points. By analysing the orientation of these fork-like patterns one can read the sign of the topological charge of the given vortex point. The method is simple and can be used for OVI calibration performed before the measurements.     

Identification of three-dimensional electric conductivity changes from time-lapse electromagnetic observations

We present a novel solution algorithm for 3D parameter identification based on low frequency electromagnetic data. With focus on large-scale applications such as monitoring of subsea oil production, CO₂ sequestration, and geothermal systems, the proposed solution algorithm is designed to meet challenges related to low parameter sensitivity, nonuniqueness of the inverse solutions, nonlinearity in the mapping from the data to the parameter space, and costly numerical simulations. Motivated by earlier investigations on the relation between sensitivity, nonlinearity and scale, the proposed solution approach is based on a reduced, composite parameter representation. Though a reduced representation restricts the solution space, flexibility with respect to which parameter functions that can be represented is obtained by facilitating the estimation of the structure and smoothness of the representation itself. Moreover, the resolution of the parameter function is detached from the computational grid and determined as part of the estimation. The performance of the proposed solution algorithm is illustrated through numerical examples for identification of underground electric conductivity changes from time-lapse electromagnetic observations.     

On the performance of some unwrapping algorithms

This work attempts an objective comparison in terms of performance and execution speed of some of the best known phase unwrapping algorithms. First the algorithms chosen, grouped into 4 classes (sequential methods, residues methods, global least square integration methods, others) are described. Then the influence of the weighting function on each of them is investigated. So as to obtain quantitative results it is necessary to use synthetic images, so that the exact solution is known, the technique for generating these images is also illustrated. Lastly, the algorithms performance in terms of influence of the weight functions, robustness and execution time are discussed.     

A simple phase unwrapping approach based on filtering by windowed Fourier transform

Phase unwrapping is an interesting yet challenging problem in optical interferometry. In this paper, we limit our interest to unwrapping noisy phase maps as it is a common but difficult task. Our aim is to propose a simple solution to phase unwrapping. We first remove the noise by a novel windowed Fourier transform approach and then use sequential line scanning method for phase unwrapping. This simple approach is verified to be very effective.     

Object adapted pattern projection—Part I: generation of inverse patterns

Fast and robust 3D inspection is of big importance for industrial quality control. Therefore, reliable optical techniques are needed that use as few images as possible for measurement. One promising technique for this aim is the inverse fringe projection which has the following advantages:The technique includes the information of a preceding measurement into the projected inverse pattern. Therefore, it is possible to do differential measurement using only one camera frame for each state. Because the camera takes images with user-defined patterns (e.g. fringes with constant frequency), one always has optimized patterns for sampling independently of the object shape. The hardware needs are as low as just a programmable projector and a standard camera.Till now the technique had drawbacks concerning the robust pattern generation and the quantitative (instead of only qualitative) evaluation of differential phases. In this paper, we concentrate our investigations on the robust pattern inversion. We show how the process can be simplified by separating the different inversion problems. Different methods and examples for generating the inverse pattern will be shown and compared to each other.     

Application of robust color composite fringe in flip-chip solder bump 3-D measurement

This study developed a 3-D measurement system based on flip-chip solder bump, used fringes with different modulation intensities in color channels, in order to produce color composite fringe with robustness, and proposed a multi-channel composite phase unwrapping algorithm, which uses fringe modulation weights of different channels to recombine the phase information for better measurement accuracy and stability. The experimental results showed that the average measurement accuracy is 0.43μm and the standard deviation is 1.38 µm. The results thus proved that the proposed 3-D measurement system is effective in measuring a plane with a height of 50 μm. In the flip-chip solder bump measuring experiment, different fringe modulation configurations were tested to overcome the problem of reflective coefficient between the flip-chip base board and the solder bump. The proposed system has a good measurement results and robust stability in the solder bump measurement, and can be used for the measurement of 3-D information for micron flip-chip solder bump application.     

一种两步相移相位解算方法

提出一种将傅里叶与相移法结合的三维物体快速测量方法.通过时域提取精确的均值包络与频域滤波结合的方法预处理条纹,结合基于相位半角的两步相移,只需要两幅相移条纹图,即可得到精确的相位信息.通过仿真和实验将本文方法与现有方法进行了分析对比,实验结果证明,本文方法可以获得优于现有两步相移方法的准确度,一般测量环境下的均方根误差在3×10     

数字全息干涉法用于变形测量

介绍了数字全息干涉法的原理,针对激光散斑噪声对包裹干涉相位图样的影响,将小波去噪分析用于图样预处理,可以提高解相精度.用该方法对四周固定、中心加载典型试件的位移进行了测试.实验结果表明,该方法简单、快速、可行.     

一种相对距离导向的相位展开算法

提出了一种相对距离导向的相位展开算法,根据相邻像素相位数据的特点,在复数平面上定义一个像素间的相对距离,构成相对距离树,用来标识相位展开路径的可靠性,由距离树导向进行相位展开.给出了距离树的物理意义和算法设计,以相位测量轮廓术为例给出了新算法的应用实例.实验结果表明,算法是合理的和有效的.相位展开的路径总是沿着具有最小距离值的路径到较高距离值的路径方向进行,所以在最坏的情况下误差也被限制在局部最小区域.     

Estimation of the optical properties of seawater from measurements of exit radiance

An inverse analysis for simultaneous estimation of the radiation phase function, single scattering albedo and optical thickness in natural waters, from the knowledge of the exit radiance measurements, is presented. A forward and an inverse model are utilized in our analysis. The forward model uses an analytical discrete-ordinates method for solving the radiative transfer equation and the inverse model contains an algorithm for least-squares estimation that is iteratively solved for retrieving the desired optical properties. The experimental data are simulated with synthetic data corrupted with noise. The results show that the optical properties, with the exception of the optical thickness, can be recovered with high accuracy, even for data with up to 10% noise.     

A quasi-one-frame phase-unwrapping algorithm through zone-switching and zone-shifting hybrid implementation

This study presents a wrapped-data-switching model and a corresponding regional unwrapping algorithm for 2D phase fields retrieval. In contrast to earlier techniques, which only produce successive frames of transient unwrapping, the proposed method can produce correct unwrapping in quasi-one frames. The approach tolerates isolated phase inconsistencies, and thus is quite effective for unwrapping speckle-coded contour map with numerous discrete inconsistencies. Since the analysis is based on a wrapped-data-switching model, the proposed criterion is path independent and error-propagation free. Additionally, the criteria are simple, concise, efficient, and easily implemented. The criteria and characteristics of the algorithm are demonstrated by simulating ideal and problematic cases, as well as by conducting experiments.     

局部噪声斑块InSAR干涉图相位解缠算法

针对干涉合成孔径雷达干涉图由于局部噪声、阴影或条纹断裂等原因导致残差点集中、产生不可靠数据点噪声斑块,从而引起相位解缠困难的情况,提出基于掩膜滤波的质量图引导权值的四向加权最小二乘相位解缠迭代算法.首先对噪声斑块区域进行掩膜滤波处理,有效保留该区域真实相位信息,防止大误差传播.再结合最大相位梯度和相位导数变化的质量图法来定义权值,构造新的四项最小二乘迭代法,并用其对掩膜区域进行填充,抑制误差传递、提高运算速度、改善过度平滑作用.模拟及真实数据实验表明,该方法解缠精度高,能真实还原干涉合成孔径雷达干涉图局部噪声斑块的原始相位.与传统最小二乘法相比,其差分方程矩阵带宽变大,填充效果更好,迭代次数更少,精确度更高,解决了因噪声集中导致干涉合成孔径雷达图像解缠难度大的问题.     

A simple method for phase wraps elimination or reduction in spatial fringe patterns

In this paper, we propose a simple method for processing a 2D wrapped phase map that contains a spatial carrier signal in order to completely eliminate, or greatly reduce, the number of phase wraps in the image. The 2D Fourier transform of the wrapped phase map is calculated. Then the spectrum is shifted to the origin in frequency space. After that, the inverse 2D Fourier transform is computed. Finally, a four-quadrant arctangent function is used to calculate the angle of the complex array that was produced by the inverse 2D Fourier transform. This produces a phase map with a smaller number of 2π phase jumps than the original phase map. In some cases, all of the phase wraps are eliminated and there is therefore no need to unwrap the resultant phase map. The reduction of the number of 2π phase jumps can reduce the execution time and improve the noise performance of some phase unwrapping algorithms such as the Flynn method. The validation of the proposed algorithm is demonstrated experimentally and also via computer-simulation.     

Self-marking phase-stepping electronic speckle pattern interferometry (ESPI) for determining a phase map with least residues

Different from most of the electronic speckle pattern interferometry (ESPI) approaches, which involve the correlation fringe formulation followed by speckle noise elimination (or filtering), to develop a wrapped phase map, this study adopts the approach proposed by Creath in 1985 instead. However, Creath's approach is so critical of its applying interferograms, the influence of which is dependent on the robustness of the applied phase-shifting algorithm and the accuracy of the phase shifter. The self-marking technique proposed by Huang and Chou in 2000 is adopted herein to help overcome any unfavorable conditioning, including hysteresis, nonlinearity or plane tilting, of the pieozo-electrical transducer (PZT), to enable the successful implementation of the Creath's method. With its help, the whole phase stepping history of a practical work (i.e., an ESPI experiment for the present study) can be fully recorded and monitored. Thus, the required phase stepping frames can be accordingly decided and their further calculation will yield a phase map with least number of residues.