大剪切电子散斑干涉的载频调制与位移场测量

将电子散斑干涉场的载波调制引入到大剪切电子散斑干涉中,通过对参考物的微小偏转引入载波条纹;利用傅里叶变换法,解调出了变形场的相位,从而实现了物体变形场的精确测量。讨论了大剪切载频的调制机理,理论分析表明,调制条纹的空间频率与参考面偏转的角度成正比;因此,控制参考面的偏转角度可实现不同位移量系统的调制。利用中心加载周边固定圆盘进行了典型实验,实验结果证明在大剪切电子散斑干涉技术中可以通过参考面的旋转高质量地实现电子散斑干涉条纹的调制,求解位移场。该系统具有系统简单,不需要专门引入参考光,条纹质量好等优点。该技术可扩展电子散斑干涉的应用范围,有一定的实际应用价值。     

The separation of out-of-plane displacement from in-plane components by fringe carrier method based on large image-shearing ESPI

A fringe carrier method for separating out-of-plane displacement from in-plane components based on large image-shearing electronic speckle pattern interferometry (ESPI) is presented. If the test object is respectively illuminated by two expanded symmetric illuminations in large image-shearing ESPI, two interferometers are formed. Carrier fringe patterns can be introduced by tilting reference surface a small angle. The carrier fringe patterns are demodulated after deformation of the object. Two phase maps, which include out-of-plane and in-plane displacement, can be obtained by using Fourier transform. Then out-of-plane displacement can be easily separated from in-plane displacement by simple operation between two unwrapped phase distributions. The principle of spatial carrier frequency modulation in large image-shearing ESPI is discussed. A typical three-point-bending experiment is completed. Experimental results are offered. The results show that the method offers high visibility of carrier fringes. And the system presented does not need a special beam as a reference light and has simple optical setup.     

Modified Fourier-transform method for phase-shift calibration

A fast convergent algorithm to accurately measure phase-shift for phase shifter is proposed. In the presence of a spatial carrier frequency, an error function in the Fourier-domain is introduced and then the unknown phase-shift between two phase-shifted fringe patterns is determined by minimization of the error function with the help of a golden section search approach. Compared with the conventional Fourier-transform method, the modified method proposed in the paper is more immune to random noise and hence can give a more accurate result. The translation curve of a liquid-crystal spatial light modulator is also experimentally calibrated.     

Calibration of fringe projection profilometry with bundle adjustment strategy

The measurement accuracy of fringe projection profilometry (FPP) largely depends on the calibration procedure. A more reliable calibration approach based on the stereo vision model of the FPP scheme in conjunction with the bundle adjustment strategy is presented. It can adjust the coordinates of benchmarks and thereby estimate the scheme parameters more accurately even with an imperfect target. The experiment results shows that the proposed approach can reach highly accurate calibration by solely using a printed target pattern, which verifies the proposed approach.     

Twin-image problem in digital holography—a survey(Invited Paper)

Zero-order and twin images are a serious obstacle in achieving a high-quality output in in-line digital holography （DH）. They decrease the useful bandwidth of the off-axis DH. Over the years the twin image removal problem was approached both by instrumental and numerical means. The paper provides an extended survey of the proposed solutions with their pros and cons as a guide for further advance in this field. Processing of a single spatial carrier fringe pattern involves spatial filtering in the frequency domain, spatial phase-shifting （PS） or wavelet transform. A point source digital holographic microscopy （DHM）, introduction of calibration measurements or various modifications of PS technique are instrumental solutions to the twin image problem for in-line DH. Numerical solutions to the same problem include iterative and non-iterative approaches, diffraction-based and inverse problem solutions, reconstruction of purely real or phase objects and of complex objects, reconstruction of plane and volume objects. Elimination only of the zero-order image relies on non-linear filtering or additional calibration measurements.     

The design of a non-cube beam-splitter used for electronic speckle pattern interferometry

A non-cube beam-splitter (NCBS) is proposed, by which an incident beam can be separated largely in a direction and then the lights from the test object and the lights from a reference surface placed adjacently to the test object can be combined to construct a simple electronic speckle pattern interferometry (ESPI) system. Two mainly useful quantitative ways, to calculate the phase change of the test object, the phase-shift and the fringe carrier method with Fourier transform, can be achieved in the ESPI system with the NCBS. Experiments with phase-shifting and fringe carrier method are completed. The experimental results show that the monolithic design of the proposed NCBS is effective in ESPI measurement and immunity to vibrations.     

小波相位分析测量成像径向畸变

为了测量光学成像像面各个像素的径向畸变大小,提出将小波变换载频条纹相位分析应用于径向畸变测量。采用正弦载波条纹作为测量模板,把径向畸变转化为径向调制相位。应用条纹相位分析导出径向调制相位和径向畸变的转化关系。采用小波频率估计和相位估计提取变形条纹的相位,由于变形条纹中心点是零畸变,中心点的瞬时频率和相位可以计算参考条纹的基频相位。两种基频相位之差就是与所有像素径向位置畸变分布对应的三维调制相位——称为径向畸变分布。利用校正公式和立方卷积插值算法对彩色畸变图像进行校正,给出详细的理论分析和实验结果。     

Application of the holographic carrier fringe and FFT technique for deformation measurement

This paper describes a holographic system based on the use of fibre optics and automatic spatial carrier fringe pattern analysis. Carrier fringes are generated by simply translating the object beam between two exposures. Single-mode optical fibres are used to transfer both the object and reference beams. The fast Fourier transform method is used to process the interferograms: it extracts phase from fringe patterns resulting from the interference of tilted wavefronts. The method is illustrated by measuring the deformation of an arbitrarily clamped, uniformly loaded circular plate. The results are given for the perspective plot of the out-of-plane deformation field, the maps of wrapped and unwrapped phase, and a contour map of the unwrapped phase.     

一种基于傅里叶变换的分析载波条纹的新方法

针对传统傅里叶变换法处理光载波干涉条纹图时会有边缘效应产生的问题,提出了一种基于傅里叶变换法的外推延拓方法,并从理论上进行了数学推导。为了验证这种方法的正确性,分别对一维数字信号和二维空间载波条纹图进行了数值模拟,进一步分析了误差产生的原因,并与传统的傅里叶变换法对比。结果表明该法可以有效抑制传统傅里叶变换法处理光载波干涉条纹图时边缘效应所造成的较大误差,在基于空间域相位调制技术的波面干涉测量中,对空间载波条纹图进行处理,可以使相位的计算精度达到3.3 mrad。     

Third-order ghost interference with thermal light

A scheme for third-order ghost interference with thermal light is proposed. The visibility and resolution of the interference fringe related to the bandwidth of the spatial frequency spectrum of the source are analysed. The results show that the visibility of the third-order ghost interference fringe is much higher than that of the second-order one.     

基于傅里叶条纹分析的多摄像机标定方法

提出一种新的摄像机标定方法,该方法基于2D共面参照物摄像机标定方法和傅里叶条纹分析方法.将已知相位分布的平面二维正弦灰度调制条纹图作为平面标定靶,通过傅里叶条纹分析方法计算出两个截断正交相位分布,利用截断正交相位分布并结合二维正弦条纹图特点提取相应的图像特征点,建立像素坐标与2D平面坐标的对应关系.将该二维平面靶在摄像机成像空间中放置不同的位置,并完成相应的特征点提取,根据2D共面参照物摄像机标定方法即可完成摄像机标定.该方法利用平面相位测量的高准确度来提高标定特征点的提取准确度,从而提高标定准确度.实验对双摄像机系统进行了标定,标定后该系统对标定靶进行测量,标准偏差达到0.010 mm.     

A two-dimensional diffraction pattern sampling system for determining the optimum parameters of a matched spatial filter

The synthesis of a matched spatial filter based on holographic methods requires that the spatial frequency band in which the holographic fringe pattern with the best modulation is formed be tuned to the appropriate weighting at the Fourier transform plane of the spatial frequencies of the input object to be studied. For this purpose both the spectral intensity distribution of an input object at the Fourier transform plane and the intensity distribution of a reference beam at that plane must be accurately known beforehand. A two-dimensional diffraction pattern sampling system has been constructed which enables the Fourier spectral intensity distribution of the input object and the reference beam intensity distribution to be faithfully recorded. A preliminary experimental study shows the usefulness of this system.     

A neat semi-Gaussian laser beam with no diffraction fringes: Theoretical analysis

We propose a simple optical device to convert a Gaussian laser beam into a neat semi-Gaussian laser beam without any diffraction fringe by using a spatial light modulator and a thin, sharp blade, and numerically calculate the diffracted, relative intensity distributions of both the semi-Gaussian laser field and the semi-Gaussian, pseudo-thermal light. We also study the dependence of the border width of the semi-Gaussian beam on the waist of the Gaussian beam. Our study shows that the proposed scheme can be used to cancel all diffraction fringes from both the straight edge of the blade and a finite lens aperture in all the planes vertical to the z axis and obtain a neat semi-Gaussian beam without any diffraction fringe, and find that the border width w_B of the generated semi-Gaussian beam is not dependent on the waist of the incident Gaussian beam.     

Shifted-phase calibration for a 3-D shape measurement system based on orthogonal composite grating projection

This paper proposes a novel method for reducing measurement error caused by spectrum overlapping in orthogonal-composite-grating-based 3-D measurement method. For 3-D measurement systems based on orthogonal composite grating projection, spectrum overlapping causes phase of each deformed phase-shifting fringe changed differently, which violates the principle that the shifted phases between adjacent deformed fringes must be equivalent to 2π/3, and therefore results in phase measurement error. The proposed shifted-phase calibration method is based on that phase variation of each deformed fringe is independent of height and reflectivity of the measured object. Three composite gratings are projected on the reference plane, and each carrier channel includes three phase-shifting gratings needed in phase measuring profilometry (PMP). Because the adjacent phase-shifting fringes demodulated from the same carrier channel have the phase difference of 2π/3, we can respectively calculate the reference plane's phases of three carrier channels by the phase algorithm of PMP method, and the shifted phases between them are obtained. When an object is measured, the shifted phases between deformed phase-shifting fringes can be calibrated. A new 3-D measurement mathematical model is set to reconstruct object. Our experiments prove that the proposed method can effectively restrain the effect of spectrum overlapping and improve measurement accuracy almost one times.     

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.     

Angular multiplexing in pulsed digital holography for aperture synthesis

A new aperture-synthesis approach in a pulsed digital holography system for obtaining superresolution is proposed and experimentally demonstrated in which, with only a single laser pulse divided into two trains of subpulses, angular multiplexing can be applied to both the reference beam for different carrier frequency and the object beam for off-axis and on-axis illuminations. Furthermore, in the recording plane, multiple subholograms covering different spatial frequency ranges diffracted from the object can be recorded in a single frame of a CCD. Our analysis and results show that the resolution of the reconstructed image synthesized upon the reconstructed complex amplitudes of the subholograms can be improved effectively.     

High-speed fringe analysis by using stair-shaped virtual grating demodulation

This article describes a novel fringe analysis technique using stair-shaped virtual grating demodulation algorithm for extracting the phase information from a single fringe pattern. In contrast to the Fourier transform technique and quadrature multiplicative moire method, the new method processes a fringe pattern in the integer signal domain instead of the frequency domain and real-signal domain. The spatial carrier of fringe image is not limited to any particular frequency as long as it fulfills the sampling theorem. The errors analysis of this technique is conducted by computer simulation and experiments.     

基于希尔伯特变换的干涉条纹相位解调新算法

提出了一种新的应用希尔伯特变换解调干涉条纹相位的算法,可以从单幅干涉条纹图中解调出全场相位分布.在实际应用中,常借助傅里叶变换实现希尔伯特变换算法,但是会忽略负频率成分,造成相位信息的丢失.对于相位分布非单调变化的干涉条纹,提出了一种判断函数,用来计算相位信息零频率点的分布.利用相位的零频率点分布构造了一个二元模板,使用该模板对本文提出的两次希尔伯特变换法产生的包裹相位图进行修正.对修正后的包裹相位图进行解包裹处理,可以得到连续的全场相位分布.对该方法用计算机模拟进行了验证.     

利用反馈光路的弹光调制器定标及稳定控制

为了实现弹光调制器（photoelastic modulator,PEM）精确定标和长时间稳定工作,提出了一种利用反馈光路的相位延迟幅值定标及控制方案,理论计算并仿真分析了PEM通光孔径上相位延迟幅值的空间分布。在偏离PEM中心的位置设计了集成化的定标反馈光路;结合倍频项比值的相位延迟幅值定标方法,采用数字锁相技术同时提取反馈光路调制光强信号中倍频项,求解出PEM相位延迟幅值。按照上述方案加工制作了PEM实物,并进行了定标及稳定控制实验。实验结果表明,PEM中心相位延迟幅值的定标值与实测值相对偏差不超过0.22%;利用反馈光路控制约100 min,PEM相位延迟幅值标准偏差为0.001 8 rad,最大偏差低于0.42%,实现了PEM相位延迟幅值精确、实时定标,同时实现了PEM长时间稳定控制。     

一种基于参数标定的投影条纹周期简易校正方法

基于三角测量原理的条纹投影轮廓测量系统中,倾斜投影到参考平面上的条纹将产生周期展宽现象,引起相位失真甚至影响测量精度。论文以条纹位置为控制变量推导出条纹周期校正的线性数学模型,通过简便的标定获得模型参数,由此反算出新的待投影条纹,并在参考平面上获得周期分布的投影条纹。实验结果表明校正后的条纹周期变化范围在±0.1像素内,并且该方法能够获得更为精确的三维轮廓测量结果。