Surface profile measurement of moving objects by using an improved π phase-shifting Fourier transform profilometry

The π phase-shifting Fourier transform technique is introduced into the surface profile measurement of moving objects. A digital grating comprising two regions, which have a π phase shifting is projected onto the object. Two line-scan CCD cameras are used to capture two deformed fringe patterns with π phase shifting at the same time. As the object is moving, each point at the object surface can be captured twice. The digital correlation method is used to calibrate the experimental system. The zero-order component can be eliminated by subtracting intensities of the same surface point in two captured images. And then the phase can be extracted by Fourier transform without the disturbance of zero-order component. Experimental results demonstrate that this method is feasible for the moving surface profile detection and the measurable slope of height variation can be extended.     

Surface profile inspection of a moving object by using dual-frequency Fourier transform profilometry

The 2π phase ambiguity caused by surface isolations and large height step can be solved by dual-frequency projection grating profilometry. However, in the Fourier transform profilometry (FTP) of a moving object, only one single deformed fringe pattern can be obtained. In order to introduce the dual-frequency technique into the FTP of moving object, a novel experimental system is designed to capture two fringe patterns with different frequency at the same time. A grating structure comprising two regions with different frequencies is projected upon the surface of the detected object. Two line-scan CCD cameras are used to capture the surface images encoded by the two kinds of patterns, respectively. By getting the corresponding image intensity at the same point of the object surface in the two acquired images, the dual-frequency technique is applied to extract the real phase without phase ambiguity. The surface profile of a specimen with a large height step is measured to prove the feasibility of the proposed method. The experimental results show that the proposed method can solve the 2π phase ambiguity problem successfully in the surface profile inspection of a moving object.     

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.     

Advanced bidirectional subdivision algorithm for orthogonal fringes in precision optical measurement instruments

Subdivision is one of the essential methods to improve the measurement resolution of optical instruments. A novel method is studied to solve the λ/2ⁿ⁺² bidirectional counting of orthogonal interference signals by constructing n sets of reference signals and using the zero-cross detection. The advantage of this method is that the effective bidirectional fringe counting can be achieved easily by the computer programming. This method can be used widely in the signal processing system of the optical measurement instruments, such as the Moiré fringe measurement instruments and the laser interferometers.     

基于双色条纹投影的薄膜振动模式分析

结构光投影和条纹时间平均分析技术已被用于振动模式分析中,但由于投影单色正弦条纹时振动薄膜变形条纹傅里叶谱中零频涵盖范围较大,会限制滤波窗的选取范围,从而影响模式的最终重建结果。为提高振动模式重建的准确性,提出了一种利用π相移正弦条纹投影进行薄膜振动模式分析和振幅重建的方法,通过处理两个通道的条纹分量达到消除零频的目的。给出了该方法的理论分析,完成了相应的计算机模拟,分析了影响测量精度的因素。通过与投影单色正弦条纹的振动模式重建结果对比,表明该方法有较高的重建精度。不同激励频率下的实际薄膜振动实验结果也证明了该方法正确可行。     

Measurement of a transparent object by using an automated Talbot interferometer

It is reported that the first partial derivative of the phase distribution for a transparent object can be measured automatically by a personal computer with an image processor. The moire pattern is formed by superimposing the Fourier image distorted by the transparent object on the master grating. But if only the moire patterns are observed, it is not shown if the fringe order numbers increase or decrease. The fringe scanning method is presented to overcome the fringe order numbers. The four-step method is used to calculate the first partial derivative. By a simple experiment, the first partial derivative can be shown in the three dimensional graphics.     

Analysis on 3D object measurement based on fringe projection

A coordinate measuring method is presented, which is specially devised to perform the measurement of coordinates with projected fringe techniques of projectors in three dimensions. The system is composed of two parts: one is a target which can move freely in three dimensions, and the other is a stationary two-dimensional array of photodetectors. The mini-projector is tied to the target, and the projected fringe is monitored by the photodetectors. The phase of the photodetectors can be precisely measured with the phase-shifting algorithm, so that, the xyz location of the target can be determined with the geometric model of multilateration using the method of optimization. In this paper, the measuring principle, iterative method, computer simulation and preliminary results are given. The phase-shifting technique has the advantages of high accuracy and noise endurance. The method will provide the basis for follow-up iterative optimization calculation. The experimental results prove that the proposed coordinate measuring method is of high precision.     

An improved stair phase encoding method for absolute phase retrieval

An improved phase unwrapping method is proposed to reduce the projection fringes in three-dimensional (3D) surface measurement. Color fringe patterns are generated by encoding with sinusoidal fringe and stair phase fringe patterns in red and blue channels. These color fringe patterns are projected onto the tested objects and then captured by a color CCD camera. The recorded fringe patterns are separated into their RGB components. Two groups of four-step phase-shifting fringe patterns are obtained. One group of the stripes are four sinusoidal patterns, which are used to determine the wrapped phase. The other group of stripes are four sinusoidal patterns with the codeword embedded into stair phase, whose stair changes are perfectly aligned with the 2π discontinuities of sinusoidal fringe phase, which are used to determine the fringe order for the phase unwrapping. The experimental results are analyzed and compared with those of the method in Zheng and Da (2012. Opt Express 20(22):24139–24150). The results show that the proposed method needs only four fringe patterns while having less error. It can effectively reduce the number of projection fringes and improve the measuring speed.     

A windowing technique for the automated analysis of holo-interferograms

A systematic method for measuring surface deformations is described which includes the use of real-time holographic interferometry, the incorporation of a carrier fringe pattern to achieve fringe linearization, and the application of image digitization and automated computer analysis for rapid quantitative interpretation. In this method, regions of interest can be selected by the use of a windowing technique in which the operator specifies the desired subregion. The problem of correctly numbering fringes which originate or vanish at the boundary where the scanning begins is solved by an algorithm which ensures correct identification of the fringe orders. The output includes a perspective plot of the out-of-plane deformation field.This method is demonstrated by its application to a measurement of the out-of-plane deformation of a hermetically sealed plastic housing loaded by internal pressurization.     

双计算机光栅莫尔拓扑术

提出了利用双计算机光栅实现莫尔拓扑检测的方法.理论分析表明,投影光栅核的横向偏导数为常数是实现灵敏度均匀性检测的必要条件.适当设计光栅核,就可用等间距直条纹来表征标准面形.被测实物面形的缺陷就可通过莫尔条纹相对于背景直条纹的偏移而定量且直观地反应出来.最后,以轮胎镜为例进行了计算机模拟和实验验证.     

Nanoscale deformation measurement by using the hybrid method of gray-level and holographic interferometry

This study extends the use of holographic interferometry to measure the nanoscale out-of-plane displacement with high surface resolution. It is noted that if the deformation is less than half of the optical wavelength, it is hard to find an obvious fringe pattern. Under such a situation, in general, the phase shift method is used. However, it needs to take more than 3 images for phase shifting and phase reconstruction In this paper, a more simple hybrid method of gray-level and holographic interferometry is used to extract fringe skeletons, in which it just needs to take one or two images for the normal deformation measurement directly, even if there exists no obvious fringe pattern. The displacement field with high surface resolution can also be obtained. The proposed method yielded a theoretical precision of 0.15 nm for out-of-plane displacement with a monochromatic CCD camera of 10-bit gray scale (1024 gray scales) sensitivity and microscale surface resolution for millimeter scale object with 640×480 pixels image resolution by an He–Ne LASER (632.8 nm wavelength) light source. The gray-level method is proposed to calculate the non-obvious interferometry fringe by traditional holographic interferometry hologram, and the result showed that this method works for this purpose.     

Digital Holographic Particle Tracking Velocimetry for 3-D Transient Flow around an Obstacle in a Narrow Channel

Digital holographic particle tracking velocimetry (PTV) is developed by single high-speed camera and single double pulsed laser with high frequency pulses. This system can directly capture 1000 hologram fringe images for 1 second through a camera computer memory. The 3-D particle location is made of the reconstruction by using a computer hologram algorithm in a personal computer. This system can successfully be applied to instantaneous 3-D velocity measurement in the water flow with a square obstacle, and can obtain an average of 300 instantaneous velocity vectors.     

Deformation and profile measurement using the digital projection grating method

This paper presents a digital projection grating method for full field measurement of out-of-plane deformation and shape of an object. Two grating patterns on an object before and after deformation are captured by a CCD camera and stored in a computer. With the aid of Fast Fourier Transform (FFT) and signal demodulating techniques, a wrapped phase map is generated. The phases are expanded in the range of 0–2π and compared with the resulting moiré pattern. An unwrapping procedure is used to obtain a continuous phase. In addition, a digital method for fractional fringe multiplication is also developed. Results on deformation and object profile measurements are presented.     

Pulsed digital holographic interferometry by using a flexible fiber endoscope

A system based on digital holographic interferometry in combination with a flexible fiber endoscope is described. A Q-switched pulsed laser is used. Two digital holograms of the test object, corresponding to the two laser pulses, are captured at separate video frames of a CCD-camera, transferred in a frame grabber and further processed in a PC. If the object undergoes a deformation during the interval between the two laser pulses (usually in the range of 5–600 μs), a fringe pattern will result from the difference between the two holograms. This fringe pattern has the information needed to evaluate quantitatively the amount of the deformation. A compact system has been developed to be used for various applications, both mechanical and biological, where measurements need to be performed at “hidden” surfaces or inside more or less closed objects. The quality of the results obtained by using mechanical objects is usually better than for biological objects. This can be explained easily by the fact that a biological surface is much more complex, in particular some parts of the surface may reflect the light well whereas some other parts may absorb it. Experimental results are presented.     

Fast full-field out-of-plane deformation measurement using fringe reflectometry

Full-field out-of-plane deformation measurement of specular surfaces can be implemented quickly and conveniently using fringe reflectometry. The system configuration is simple and processing is fast. With the assistance of an advanced fringe pattern processing technique, the windowed Fourier ridges method, only a single two-directional fringe pattern is necessary for determination of the deformed surface profile. Thus, the whole measurement only requires a single image with the potential for high speed or even real time measurement.     

A derivative based simplified phase tracker for a single fringe pattern demodulation

In this paper, a novel fringe demodulation method for the estimation of phase and its first-order derivative from a closed-fringe interferogram is proposed. The proposed method determines the phase derivatives in both x&y directions from fringe orientation and density. The phase derivatives are subsequently used to determine phase values using a novel simplified phase tracker. In the phase tracking model, the complexity of the cost function is reduced using predetermined derivatives so computation time required for phase tracking is reduced considerably. The proposed model is more robust while dealing with saddle points in fringes than the conventional phase tracker model. Hence it does not require any specialized scanning strategy. The proposed method is validated with simulated and experimental fringe patterns (obtained using electronic speckle pattern interferometry and optical holographic interferometry) and a comparison study is carried out with conventional regularized phase tracker. The simulation results show that the proposed method has good accuracy and requires less computation time than existing phase-tracking algorithms. The experimental results demonstrate the robustness of the proposed method against speckle noise and its practical applicability for static and dynamic applications.     

Deformation measurements of specularly reflecting objects using holographic interferometry with diffuse illumination

It is demonstrated that, by using diffuse object illumination, deformation measurements with holographic interferometry can be performed on a specularly reflecting object without the use of any additional coating of the object surface. An analytical expression for the secondary fringe formation is found, and the system is demonstrated only to be sensitive to deformations along the surface normal. A method for carrying out topographic measurements on specularly reflecting surfaces is suggested. The fringe visibility is studied for a rigid rotation of the object by using matrix methods. It is found that maximum fringe visibility is obtained if the recording camera is focused on the surface of the object.     

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.     

载频调制大剪切电子散斑干涉系统

大剪切电子散斑干涉技术不需要引入参考光，具有条纹质量好等特点。提出将干涉场的载频调制技术引入到大剪切电子散斑干涉中，可形成具有载频调制功能的新的电子散斑干涉系统。该系统具有对测量环境的隔振振动要求低，能方便定量求解物体的变形场等优点。首先讨论大剪切载频的调制机理，然后利用中心加载、周边固定的圆盘进行典型实验，设计了可用计算机控制且可对参考物进行精确偏转的步进电机系统，进而实现了对电子散斑干涉场的自动控制调制。最后，利用傅里叶变换法对调制条纹进行解调，解调出变形场的相位，并通过相位与位移的转换计算，得到精确的物体变形场。实验结果证明，该系统能够调制电子散斑干涉场，求解物体的位移场。     

纳米云纹法条纹倍增技术研究

提出了一种纳米云纹法的条纹倍增技术，可用于单晶材料纳米级变形测量.在测量中，单晶材料的晶格结构由透射电镜（TEM）采集并记录在感光胶片上作为试件栅，几何光栅作为参考栅.对纳米云纹条纹的形成原理，透射电镜放大倍数与试件栅的频率关系，条纹倍增技术，位移、应变测量方法等进行了详细讨论.该方法不仅能够测量连续力学参量，如应变和位移，而且能够表征纳观非连续参量，如位错、夹杂.