Error analysis in the absolute phase maps recovered by fringe patterns with three different wavelengths

In a recently published work, we proposed a technique to recover the absolute phase maps from the wrapped ones with three different fringe wavelengths. It was noticed that when the wrapped phase maps are obtained by three-step phase shifting method, errors in fringe order still occur, leading to significant error in the recovered absolute phase maps. In this paper, the characteristic and reason of the errors are analysed, and a method to avoid these errors is also proposed. The theoretical conclusions in this paper are validated with experimental results.     

An online triple-frequency color-encoded fringe projection profilometry for discontinuous object

Abstract

An online triple-frequency color-encoded fringe projection profilometry is proposed to measure the complex and discontinuous object at straight-line movement. N frames of color fringe patterns are specially designed. Three grayscale sinusoidal grating patterns with geometric progression frequency growth are encoded into red (R), green (G), and blue (B) channels separately to compose a color-encoded fringe pattern. If these three grayscale sinusoidal grating patterns are phase-shifted N steps with an equivalent shift phase of 2π/N, they can compose the corresponding N frames of color-encoded fringe patterns as above respectively. In order to avoid the movement’s interference to the phase shifting, position adjustment should be done to guarantee the phase-shifting direction to be perpendicular to the moving direction. While these N frames of specially designed color-encoded fringe patterns are projected onto the moving object one by one, the corresponding deformed color patterns are captured by a CCD camera in real time. By color separating, color crosstalk compensation, pixel matching, and phase calculation, three wrapped phase at different frequencies can be extracted. The unwrapped phase can be solved by a simplified algorithm based on temporal phase unwrapping method from the relationship of the three wrapped phase at the same pixel. Thus, it is very suitable to measure the online complex and discontinuous objects at straight-line movement. The experimental results show the feasibility and the validity of the proposed method.     

Numerical analysis of fringe patterns recorded in holographic interferometry using high-order ambiguity function

This letter introduces a new approach for the demodulation of fringe patterns recorded in holographic interferometry using high-order ambiguity function (HAF). The proposed approach is capable of retrieving the phase from a single fringe pattern. The main advantage of this approach is that it directly provides an estimation of the continuous phase distribution and thereby avoids the necessity of using a cumbersome 2D phase unwrapping procedure. This method first computes the discrete-time analytic signal of the recorded fringe pattern. Then, by modelling this analytic signal as a polynomial phase signal embedded in additive complex white Gaussian noise, a parametric estimation procedure based on HAF is employed to directly estimate the unwrapped phase distribution. Numerical simulations and experimental results demonstrate the potential of the proposed approach.     

光学三维测量中结构光栅投影系统的开发

为解决结构光三维测量系统中的光栅投影质量问题,提出并实现了以物理光栅为核心的结构光栅投影系统。该系统以现代光栅制造技术制造的精密光栅元件为核心,基于幻灯投影原理实现高质量的光栅条纹投影,利用步进电机带动高精密滚轴丝杆进行平移实现投影光栅的切换。实验结果表明,基于该系统实现的光学三维测量系统的可以达到1：100以上的对比度,具有较大的光强和良好的景深,同时能获得连续的强度分布及较好的正弦性,测量误差小于0．04mm,测量精度约为0．03mm,满足工业应用的要求。     

Design of adaptive digital filters for phase extraction in complex fringe patterns obtained using the Ronchi test

A powerful technique is presented for processing complex fringe patterns with high noise levels and arbitrary distributions of spatial frequencies, which can successfully extract the phase information. Artifacts that arise from phase extraction in local filtering approaches are avoided by using a simple design and implementation strategy for the adaptive filter, based on the theory of digital filter design used in electronics, and applied to pixel rows (or columns) in the fringe-pattern. The filter designed in this manner is then applied to phase extraction in an experimental fringe pattern measured in a digital Ronchi test setup using a Carré phase-shifting procedure. The filtering strategy has a very low computational cost and allows phase extraction in noisy ronchigrams regardless their spatial frequency distribution, provided the fringes are still visible.     

Unified approach for rough phase measurement without phase unwrapping by changing the sensitivity factor

Phase evaluation is extraordinarily important in optical, acoustic and radar techniques where coherent signals are employed as information carriers. In most of the cases, phase information are obtained from an inverse trigonometric function and wrapped into ?π to π. A phase unwrapping process is thus required to obtain the final unwrapped phase which represents the ultimate physical quantity to be measured. One-dimensional phase unwrapping is easily achieved by adding or subtracting an integer multiple of 2π to the wrapped phase to establish a smooth phase map. Two-dimensional phase unwrapping, however, is quite troublesome and an elegant unwrapping routing should be chosen in most of the cases to deal with phase residues caused by noise and other error sources. It would be valuable if two-dimensional phase unwrapping can be avoided and the physical quantity obtained directly. In the past, researchers have proposed other methods such as the multiple wavelengths approach which incorporates information from multiple wavelengths to eliminate the need for phase unwrapping. In this study, we extend the multiple wavelengths approach by varying the sensitivity factor, which is more convenient and cost-effective, to achieve the aim of requiring no phase unwrapping. Furthermore, an elegant phase derivative approach is used to solve the phase ambiguity problem in the multiple wavelengths method. Both simulation results and real experiment data of shadow moiré and shearography demonstrate the usefulness of this method, especially for discontinuous surface profile measurements such as steps. Advantages and disadvantages for the proposed method are also discussed in this paper.     

载频条纹相位分析自适应滤波器的设计

提出了一种基于统一准则的自适应滤波器的设计算法,并结合空间滤波处理技术及数字图像处理分析技术,根据每一幅光学条纹图像的频谱分布状况,自动提取+1级频谱信息,实现对载频条纹图像的自适应滤波,最终达到自动化数值分析的目标。文中以三维形貌测量为例,首先通过计算机数值模拟,指出分析位相质量与滤波窗口的选择是紧密相关的。而光学条纹图像的频谱分布则因待测物体而异,因此在空间滤波过程中,要针对不同的待测物体对滤波窗口的形状以及大小进行精确选取。文章给出了自适应滤波器精确选取的法则与步骤。最后以三维石膏像为测量物体,给出实验验证,证明该方法的可行性与有效性。     

On the analysis of the thermal diffusivity measurement method with modulated heat input

The present paper proposes a simplified way to analyze thermal diffusivity experiments in which the phase shift is measured between the modulations of the temperatures on either face of a disk-shaped sample. The direct application of complex numbers mathematics avoids the use of the cumbersome formulae which hitherto have hampered a wider confirmation of the method and which restricted the range of the phase lag to an angle of 180°. The algorithm exposed makes it more practical to refine the analysis, which may lead to a higher accuracy and a wider use of the method. The origins of some possible errors in the calculated results are briefly reviewed.Nomenclature a Thermal diffusivity, m² · s^–1 - c Index denoting a constant part, dimensionless - c _l, c ₀ Inverse extrapolation length, m^–1 - C _p Specific heat, J · kg^–1 · K^–1 - f Modulation frequency, Hz - l Thickness of disk-shaped sample, m - Q _c Equilibrium energy per unit surface deposited on surface x=l, W · m^–2 - Q _m(t) Energy of modulation per unit surface deposited on surface x=l, W · m^–2 - Q(t) Total energy per unit surface deposited on surface x=l, W · m^–2 - q Complex energy modulation amplitude, W · m^–2 - T _l Equilibrium temperature of heated surface, K - t ₀ Equilibrium temperature of nonheated surface, K - T(x, t) Total temperature of any plane at distance x and at time t, K - T _m(x, t) Modulation temperature at any distance x and at time t, K - t Time, s - x Distance perpendicular to the specimen's surface and with the nonheated surface as the reference, m - Thermal linear expansion coefficient, dimensionless - Intermediary parameter, m^–2 - Phase difference between heated and nonheated specimen face, radian - ₀ Phase difference between energy modulation and nonheated face, radian - _l Phase difference between energy modulation and heated face, radian - Total emissivity, dimensionless - _s Spectral emissivity, dimensionless - Temperature, amplitude of modulated part argument, K - Thermal conductivity, W · m^–1 · K^–1 - Density, kg · m^–3 - Stefan-Boltzmann constant, 5.66961×10^–8W · m^–2 · K^–4 - Angular frequency=2f, s^–1     

An explicit eighth order method with minimal phase-lag for the numerical solution of the Schrödinger equation

A new explicit hybrid eighth algebraic order two-step method with phase-lag of order twelve is developed for computing eigenvalues and resonances of the one-dimensional Schrödinger equation. Based on this new method and on the method developed recently by Simos we obtain a new variable-step procedure for the numerical integration of the Schrödinger equation. Numerical results obtained for the integration of the resonance problem for the well known case of the Woods-Saxon potential and for the integration of the eigenvalue problem for the well known case of the Morse potential show that this new method is better than other variable-step methods.     

双波长激光量块干涉仪减小量块中心长度测量不确定度的措施

该文总结了双波长激光干涉仪研制过程中减小量块中心长度测量不确定度的几项重要措施,该干涉仪对量块中心长度的测量不确定度达到(0.02±0.2L)μm,并已成功应用于高等级量块的自动测量。     

Influence of surfactant on the thermal behavior of marigold oil emulsions with liquid crystal phases

Vegetable oils have been largely consumed owing to the interest of pharmaceutical and cosmetic industries in using natural raw materials. The production of stable emulsions with vegetable oils challenges formulators due to its variability in composition and fatty acids constitution within batches produced. In the present work, it was studied that the influence of the size of carbon chain and the number of ethylene oxide moieties of the surfactant on the thermal behavior of eight emulsions prepared with marigold oil stabilized by liquid crystal phases. Differential scanning calorimetry (DSC) was used to determine the thermal behavior of the emulsions. The ratio of bound water was calculated, being between 29.0 and 42.0%, confirming the extension of the liquid-crystalline net in the external phase. Changing the lipophilic surfactant from Ceteth-2 to Steareth-2, there was an increase in the temperature of phase transition of the liquid crystal influencing the system stability. Calorimetric study is very useful in understanding the performance of liquid crystals with the increase of temperature and to estimate emulsions stability.     

测量精度达3.2nm的在线表面粗糙度外差干涉仪信号处理系统

介绍了用于磨床加工的光外差表面粗糙度在线干涉测量仪整机的信号处理系统,着重讨论了其中的两项关键技术,即利用负反馈构成的宽动态范围测量信号的自动电压控制以及依据计大数和测小数相结合的高精度动态相位测量,系统的测量精度达２．６°（相当于３．２ｎｍ）,允许测量中最大多普勒频移±１０ｋＨｚ（对应高度的变化率±８．７５×１０＾－３ｍ／ｓ）完全满足磨床加工中表面粗糙度在线测量的要求。现场测试证实了这一点,这对     

低频振动传感器幅值和相移测量的不确定度

深入研究影响测量结果的不确定度来源和大小,参考ISO 16063-11:1999不确定度分量表,根据实验结果和经验数据,对低频振动国家副基准测量高精度低频振动传感器套组灵敏度幅值和相移进行测量不确定度的分析和评估,为修订国家振动传递系表提供了参考依据,其灵敏度幅值和相移测量的不确定度（ =2）为16Hz参考点,0.30%和0.19;0.1Hz120Hz通频带,0.66%和0.65。     

Measurement of surface microrelief for a set of images with a different position of the focus

A method of reconstructing surface relief based on a set of microscope images with different positions of the focus is proposed, minimizing the restoration error with prescribed reliability of the model used. The method of restoration is invariant to illumination conditions, optical instrument construction, image formation, and it may be applied to a wide variety of surfaces. __________ Translated from Izmeritel’naya Tekhnika, No. 1, pp. 14–17, January, 2007.     

An adaptive fixed mesh method for modelling and simulating of unsteady two‐phase flows with sharp physical interfaces

We present in this paper a new computational method for simulation of two‐phase flow problems with moving boundaries and sharp physical interfaces. An adaptive interface‐capturing technique (ICT) of the Eulerian type is developed for capturing the motion of the interfaces (free surfaces) in an unsteady flow state. The adaptive method is mainly based on the relative boundary conditions of the zero pressure head, at which the interface is corresponding to a free surface boundary. The definition of the free surface boundary condition is used as a marker for identifying the position of the interface (free surface) in the two‐phase flow problems. An initial‐value‐problem (IVP) partial differential equation (PDE) is derived from the dynamic conditions of the interface, and it is designed to govern the motion of the interface in time. In this adaptive technique, the Navier–Stokes equations written for two incompressible fluids together with the IVP are solved numerically over the flow domain. An adaptive mass conservation algorithm is constructed to govern the continuum of the fluid. The finite element method (FEM) is used for the spatial discretization and a fully coupled implicit time integration method is applied for the advancement in time. FE‐stabilization techniques are added to the standard formulation of the discretization, which possess good stability and accuracy properties for the numerical solution. The adaptive technique is tested in simulation of some numerical examples. With the test problems presented here, we demonstrated that the adaptive technique is a simple tool for modelling and computation of complex motion of sharp physical interfaces in convection–advection‐dominated flow problems. We also demonstrated that the IVP and the evolution of the interface function are coupled explicitly and implicitly to the system of the computed unknowns in the flow domain. Copyright © 2005 John Wiley & Sons, Ltd.     

Possibilities and extension of XRD material response analysis in failure research for the advanced evaluation of the damage level of Hertzian loaded components

Due to clearly distinguishable damage symptoms, it is differentiated between the surface and sub‐surface failure mode of rolling bearings. Material states red out by X‐ray diffraction (XRD) residual stress measurements point to a variety of loading conditions especially at raceway surfaces that are associated with several competing failure mechanisms. The corresponding lifetime reduction can range from the lower fatigue strength region to material ratcheting in extreme cases. Relevant position of the microstructural changes and nature of the failure mechanisms are characterized. The time alteration of the XRD material parameters measured at or near the surface and at the depth of the maximum equivalent stress correlates, in a different manner, with the statistical parameter of the 10 % bearing life. Both failure modes are illustrated by concrete examples. Contaminated lubricant and boundary lubrication, which represent practically important surface‐induced failures, are discussed in more detail. Gray staining, i.e. shallow pitting, often occurs without distinct indication of global material aging by means of XRD characteristics. Here, scanning electron microscopy observations and electron microprobe analyses point to corrosion fatigue as acting surface failure mechanism. The interaction between material and lubricant under complex loading regimes particularly of mixed friction and corrosion opens further failure research areas in the field of tribology.