One-step phase shift 3-D surface profilometry with grating projection

A 3-D profiling system has been developed using a grating projection approach and a one-step phase shift algorithm. In the system, a grating pattern projected on an object surface is acquired by a CCD camera, and the grating's phase deformation caused by the surface shape is extracted by spatial phase shift processing, which uses only one frame of digital image. One phase value can be calculated from a successive 3-pixel range if the fringe period is set to either 4-pixel width or 8-pixel width. The fixed phase distribution of the system is excluded by a standard plane calibration. With 8-bit input data, the system's RMS phase accuracy is developed up to 2π/60 in the experimental examinations.     

Quantitative phase contrast imaging using common-path in-line digital holography

We propose a method to carry out quantitative phase contrast imaging using in-line digital holography. The phase shifting digital holography is implemented in a common-path in-line configuration with the help of diffraction from a phase grating displayed on a spatial light modulator. The phase shifted interferograms are recorded by shifting the grating within a selected area corresponding to the dc spot in the Fourier transform plane. The feasibility of method is verified by using a multimode fiber as phase object. The method addresses a number of challenges faced by existing methods and dispenses the need for special optics.     

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.     

光学三维扫描仪光强传递函数的测量和校正

由于数字光栅投影仪的光强传递函数对于正弦投影条纹的质量以及相位测量精度起着至关重要的作用,本文提出了一种校正光学三维扫描仪光强传递函数的新方法。首先,分析了由于投影仪非线性响应引起的光栅谐波的相位测量误差;然后,通过投影一组不同灰度级的图像,并利用光功率计测出数字投影仪投出图像的亮度。接着,通过分析得到数字投影仪的非线性响应特性曲线,再经过数据处理,即可获得投影仪的光强传递函数;最后,对光强传递函数进行反函数逆变换,得到一个校正后的非正弦光栅,利用投影仪对该光栅的投影即可在被测物体表面上获得一个正弦光栅。数字投影仪对标准平板的测量结果表明,校正前平均误差为0.71 mm,校正后为0.55 mm;对于标准量块的测量,校正前的平均误差为0.62 mm,校正后为0.15 mm。上述结果表明,本文提出的方法可以减小由于系统非线性响应引起的测量误差并提高测量精度。     

Application of digital phase-shift shadow Moiré to micro deformation measurements of curved surfaces

The shortcomings of conventional shadow Moiré topography have in the past been improved by means of the phase-shift method which enhances the sensitivity and allows to process the fringe patterns automatically. This paper presents a digital implementation of the phase-shifting process, which requires only one image to be taken. The grating lines, projected onto the deformed object surface, are captured directly with a digital camera. Next the reference grating is superimposed numerically onto the projected grating lines. Then a number of phase-shifts are performed taking into account the non-linearities in the expression for the height-dependent intensity field. Experimental results prove that these non-linearities can considerably affect the micro deformation measurements of curved surfaces. The proposed method is very efficient and eliminates all causes of erroneous measurements due to the miscalibration of phase-stepping devices.     

基于莫尔拓扑与图像处理的三维形貌术

本文叙述了一种新型三维物体表面测量方法,该方法利用单光栅投射待测物体表面而获取变形光栅像,然后应用图像处理方法,通过微机计算出物体表面各点高度。该方法测试精度高,速度快。文中对其原理进行了详细的叙述。并讨论了该法的测量范围、灵敏度。     

Study on a novel phase-recovering algorithm for partial intensity saturation in digital projection grating phase-shifting profilometry

The phase error and its periodic behavior caused by the partial intensity saturation of fringe patterns in the digital projection grating phase-shifting profilometry are studied. A saturation coefficient K is defined to describe the saturation degree of the fringe patterns projected on a measured object. The distribution of the phase error is analyzed through a simulation method. Moreover, a novel phase-recovering algorithm is studied to resolve the phase error issue introduced by the partial saturated fringe patterns. The real phase can be recovered by the unsaturated intensity values. A series of results corresponding to different degrees of saturation defined by K are given to prove the validity of the proposed algorithm.     

三维形貌测试系统中的数字信号处理技术

本文采用一种基于数字滤波的正文解调算法,用于三维形貌测试系统中相位分布的计算。文中考察了频域理想低通滤波器、三阶巴特沃思滤波器、有限冲击响应滤波器以及空域均值滤波器,通过分析滤波器性能和比较处理结果,得出均值滤波器或有限冲击响应滤波器比较适用于类似于变形光栅的窄带信号。采用数字处理方法,可以由一帧变形光栅图迅速、精确地重建物体的形貌。     

Super-resolution imaging in digital holography by using dynamic grating with a spatial light modulator

A super-resolution imaging method using dynamic grating based on liquid-crystal spatial light modulator (SLM) is developed to improve the resolution of a digital holographic system. The one-dimensional amplitude cosine grating is loaded on the SLM, which is placed between the object and hologram plane in order to collect more high-frequency components towards CCD plane. The point spread function of the system is given to confirm the separation condition of reconstructed images for multiple diffraction orders. The simulation and experiments are carried out for a standard resolution test target as a sample, which confirms that the imaging resolution is improved from 55.7 μm to 31.3 μm compared with traditional lensless Fourier transform digital holography. The unique advantage of the proposed method is that the period of the grating can be programmably adjusted according to the separation condition.     

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.     

相位锁定循环投影技术及其应用

由一组规则栅线投影到物体表面的变形光栅,采用相位锁定循环解调算法解调出含有物体表面高度信息的相位.该技术的最大优势是不需传统的相位去包裹.利用该算法对二维栅线图扫描确定的相位.本文给出了一个典型试件的实验结果和分析.     

利用莫尔条纹测量物体三维形貌新方法研究

提出了以计算机控制光栅产生莫尔条纹来测量物体三维形貌的新方法.利用计算机控制空间光调制器（Space Light Modulator,SLM）产生可控制幅度及位相的理想光栅,将平行光波投影到待测物体上,其反射光通过参考光栅形成莫尔条纹,利用CCD接收并进行数字图像处理,恢复出待测物体的三维形貌.对此方法进行了理论分析,推导了变形莫尔条纹与待测物形貌变化的关系式.利用MATLAB对此关系式进行仿真计算,其准确度可达0.011 μm.     

Improved spatial phase detection for profilometry using a TDI imager

Performance of a time delay and integration (TDI) imager is analogous to a drum/periphery camera. Coupled to a modulated line generating laser diode, it is possible to use a TDI imager to encode the shape profile of a rotating cylindrical object as deformed gratings in a digital image. Among the various methods for extracting the phase from a deformed grating, the spatial phase detection (SPD) method is fast and easy to use. Errors are introduced in this method if the phase gradient is high over a grating interval. Here we propose a method to reduce the phase gradient by using a TDI feature which makes it possible to record images at variable lateral magnification.     

Measurement of non-monotonous phase changes in temporal speckle pattern interferometry using a correlation method without a temporal carrier

Recently, a phase evaluation method was proposed to measure nanometric displacements by means of digital speckle pattern interferometry when the phase change introduced by the deformation is in the range [0,π) rad. This method is based on the evaluation of a correlation coefficient between two speckle interferograms generated by both deformation states of the object. In this paper, we present a novel technique to measure non-monotonous displacements in temporal speckle pattern interferometry using a correlation method without a temporal carrier. In this approach, the sign ambiguity is resolved automatically due to the introduction of a function that determines the correct sign of the displacement between two consecutive speckle interferograms. The rms phase errors introduced by the proposed method are determined using computer-simulated speckle interferograms. An application of the phase retrieval method to process experimental data is also presented.     

Several factors impairing the phase measurement accuracy

In the course of processing deformed grating patterns and obtaining an object's height distribution with a digital filter, several factors, such as dynamic and frequency ranges of phase signal, background luminance and reflection coefficient of the measured object, grating period, filter passband, time drift of image data, etc., may exert an influence on the phase measurement accuracy. Through simulation and experiment, the influence is discussed and the conclusion is that, by choosing a suitable grating period and filter frequency characteristic according to the frequency range of the phase signal, the phase measurement error will be reduced.     

Speckle interferometry for measurement of continuous deformations

Improvements of a method for measurement of continuous displacements and deformations with digital phase shifting speckle pattern interferometry are presented. The method is based on an algorithm that, with the knowledge of the initial phase, only needs one image at a time to evaluate continuos phase changes due to object deformations. In the improved method, the initial random phase of the speckle pattern is evaluated using a number of phase-shifted images before the deformation under study. This is used for increasing the accuracy of the initial phase estimation and reducing influences from image noise and other measurement disturbances. The phase-shifted speckle patterns are used as references for comparison with the speckle patterns of the deformed object, thereby increasing the reliability and accuracy of the phase estimations of the deformed patterns. The technique can be used for measuring deformations such as transients and other dynamic events, heat expansion as well as other phenomena where it is difficult to accomplish phase shifting during deformation.     

Digital moiré fringe measurement method for alignment in imprint lithography

Accurate layer-to-layer alignment, which is of prime importance for the fabrication of multilayer nanostructures in integrated circuits, is one of the main obstacles for imprint lithography. Current alignment measurement techniques commonly involve an image detection process for coarse alignment followed by a grating interference process for fine alignment. Though this kind of two-level alignment system is reasonable for measurement, when it is used in real imprint lithography, it is inconvenient because of the existence of a complex loading system that needs space for alignment. In this study, we propose a fine alignment method using only image detection using grating images and digital moiré fringe technology. In this method, though the gratings are also selected as alignment marks for accurate measurement, they do not interfere with the physics. The grating images captured from the template and wafer are used to measure angular displacement and to form parallel digital moiré fringes. The relative linear displacement between the template and wafer is determined by detecting the spatial phase of parallel digital moiré fringes. Owing to the magnification effect of digital moiré fringes, this method is capable of generating accurate measurements. According to the experimental results, this digital moiré fringe technique is accurate to less than 10 nm. In addition, without a complex grating interference system, this method has the advantage of being easy to operate.     

Application of wavelet transform to 3D shape measurement

A new method for analyzing the phase distributions of deformed grating images on the surface of three-dimensional (3D) object to obtain its shape information has been presented. In the conventional technique, Fourier transform profilometry (FTP), there is an intrinsic problem of extracting the fundamental frequency component if the deformation of the grating pattern is either considerable or complicated, which will definitely bring bad influence to the analysis' accuracy. That means FTP is not appropriate to deal with the complex surfaces of 3D objects. The approach that we here introduce to solve this problem is to utilize Gabor wavelet transform (GWT), a tool excelling for its multiresolution in time-frequency domain, to analyze the phase distributions.     

Automatic Analysis of the Phase Object Using Projection Moire Deflectometry

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The photonical, pure grid method

The paper presents an introduction on the pure grid method for deformation measurements in experimental mechanics. The pure grid method involves that the grid images are processed separately, and subsequently the results of these separate processings are substrated from each other in order to obtain a quantified deformation indication.The recording and processing of the grid images are currently performed photonically by means of digital image measurement systems. The basic data processing relations and set-ups of four different applicabilities of the photonical, pure grid method are presented in this paper. The applicabilities are discussed. Strains can be measured with errors smaller than 200 micro strain and displacements with errors smaller than of the diameter of the object as visible in the grid image. These figures can be improved substantially by future application of high resolving-power CCD cameras. Two examples are shown. The paper also contains an extensive bibliography for further explorations.