An algorithm for estimating both fringe orientation and fringe density

In this paper, an algorithm is proposed which can estimate good fringe orientation and estimate fringe density at the same time. This algorithm accumulates differences along four orientations and then obtains the local orientation and estimates local fringe density according to the differences. The obtained orientation results are more accurate and more robust than the plane-fit method. And it will be shown both theoretically and experimentally that the accumulated differences can estimate fringe density roughly.     

基于Gabor滤波的散斑条纹图平滑方法

提出了一种基于伽博(Gabor)滤波的散斑条纹图平滑方法.通过加窗傅里叶运算提取散斑条纹图的条纹频率和条纹梯度方向,并利用它们确定具有频率和方向选择性的Gabor滤波器对散斑条纹图进行Gabor滤波.数值模拟和实验结果表明,该方法在滤除散斑噪声的同时能够有效的保留散斑条纹图的条纹结构,为从单幅散斑条纹图中进一步提取条纹相位场奠定了良好的基础.     

Anisotropic partial differential equation noise-reduction algorithm based on fringe feature for ESPI

Noise reduction is one of the most exciting problems in electronic speckle pattern interferometry. We present a new anisotropic partial differential equation noise-reduction algorithm based on fringe orientation for interferometric fringe patterns. The proposed equation performs diffusion along the two directions of fringe gradient and isophote line, which are extracted accurately according to fringe feature. By restriction of diffusion in the gradient direction of fringe patterns, this method can provide optimal results in denoising but does not destroy fringe edges. The experimental results show that this technique is more capable of significantly improving the quality of the fringe patterns than the classical anisotropic diffusion equation proposed by Perona and Malik. Based on our filtered fringe patterns, the phase map obtained by phase-shifting technique can be extracted more accurately. It is an effective pre-processing method for electronic speckle pattern interferometry.     

A method for fringe normalization by Zernike polynomial

A new approach for fringe normalization by Zernike polynomial fitting to cancel background illumination in an interferogram is proposed. With this method, background illumination can be suppressed, high frequency noise is immunized and the contrast is improved by normalization. The main idea for this paper is to use the Zernike polynomial fitting interferogram to cancel background illumination; the high frequency noise is then filtered by a Wiener filter. Finally, the paper uses the method of local region contrast modulation to enhance fringe contrast. This method can overcome the problem of the non-uniformity illumination of fringe patterns resulting from the marginal reflection of optical components and a non-uniformity light source     

散斑条纹图的自适应窗口滤波方法

针对散斑噪声很难用常用的滤波方法进行滤除,在已有等值线滤波方法的基础上,提出一种更优的自适应窗口滤波方法。由于等值线窗口是在条纹方向图的基础上得到的,深入研究条纹方向的求取方法,提出了一种更为可靠的条纹方向求取算法,在得到高精度条纹方向的同时,还能估计出条纹的密度。使用等值线窗口技术,保持了窗口形状的自适应能力,然后利用对条纹密度的估计,根据条纹的宽度来确定滤波窗口的大小,实现了滤波窗口大小的自适应。最后,根据条纹方向和滤波后的图像可以直接得到条纹密度变化较大的单幅散斑图的相位结果。     

Determination of skeleton and sign map for phase obtaining from a single ESPI image

A robust method of determining the sign map and skeletons for ESPI images is introduced in this paper. ESPI images have high speckle noise which makes it difficult to obtain the fringe information, especially from a single image. To overcome the effects of high speckle noise, local directional computing windows are designed according to the fringe directions. Then by calculating the gradients from the filtered image in directional windows, sign map and good skeletons can be determined robustly. Based on the sign map, single image phase-extracting methods such as quadrature transform can be improved. And based on skeletons, fringe phases can be obtained directly by normalization methods. Experiments show that this new method is robust and effective for extracting phase from a single ESPI fringe image.     

散斑干涉相位条纹图的频域滤波处理

为了解决在数字散斑干涉技术测量时,散斑干涉相位条纹图像中大量噪声对相位解包裹结果和精度产生严重影响的问题,介绍了一种条纹正余弦分解和频域低通滤波结合的方法,实现了散斑干涉相位条纹图的高精度滤波。该方法的基本思路是在对相位图像进行滤波处理前,先将相位图通过正余弦函数进行映射转换成两幅图,分别经过频域滤波,然后再合成为相位图。这种分解频域滤波方法可以在滤波的同时,有效保留相位跳变信息。实验结果表明：与传统的图像降噪方法相比,该方法能够在保留图像“尖峰”信息的基础上,较好地滤除图像中的散斑噪声,方法简单有效,有效解决了传统滤波方法应用在相位条纹图中,相图灰度信息丢失10%~40%的问题。     

Fringe pattern denoising using averaging based on nonlocal self-similarity

Digital image processing for fringe patterns is an important procedure in optical interferometry. Filtering off noise from fringe patterns is one of the key tasks for extraction of the phase field. Spin filters proposed by Yu et al. [Appl. Opt. 33(1994), 41(2002), et al.] have been proven to be effective denoising methods. In this paper, we develop a nonlocal self-similarity filter, which averages similar pixels searched for in whole image instead of in a local fringe direction as the spin filters do. Although simple and free of the fringe orientation estimation, involving more pixels with higher similarity levels, our algorithm has stronger robustness against noise and thus denoises fringe patterns more effectively. Simulation and experimental results show that our algorithm outperforms related filters both in preserving smooth fringes and in reducing blurring effects and quantitative errors.     

A novel color fringe projection based Fourier transform 3D shape measurement method

A novel Fourier transform 3D shape measurement method based on color fringe projection is proposed in order to solve the spectrum overlapping and phase unwrapping problems existed in Fourier transform profilometry (FTP). The R and G components of the color fringe are set to two sinusoidal patterns with different frequencies and the B component is set to the average value of R or G component. Then this pattern is projected to the object and the deformed fringe image is captured. Three gray patterns are separated from the color fringe, the background and high frequency noise can be eliminated using our method and the accurate unwrapped phase can be got. Only one shot color pattern is projected to get the 3D information of the object. Experiment results show that the 3D information of an object can be obtained rapidly and accurately.     

Multivariate empirical mode decomposition approach for adaptive denoising of fringe patterns

An adaptive approach is presented for noise reduction of optical fringe patterns using multivariate empirical mode decomposition. Adjacent rows and columns of patterns are treated as multichannel signals and are decomposed into multiscale components. Fringe patterns are reconstructed with less noise by simply thresholding coefficients in different scales. The proposed approach can better concentrate local main components of fringe signals into single scale, compared with the conventional multiscale denoising method. A simulated pattern and an actual example are examined. Signal-to-noise ratio (SNR) of the simulated pattern is more than doubled.     

基于条纹等值线相关的散斑条纹图处理新方法

在数字散斑干涉术中,通常由物体变形前后得到的两幅原始散斑场用相减方法来得到条纹图,并由相移后的多幅(三幅以上)条纹图来求取相位场。介绍了一种基于条纹等值线相关的条纹图生成新方法,并在此基础上提出了基于单幅干涉条纹图的相位场提取新方法和基于条纹等值线相关的单步相移新方法。实验结果表明,该方法具有良好的结果和发展前景。     

Adaptive quadrature filters for multiple phase-stepping images

We present a new technique for the recovery of local phase from multiple phase-stepping fringe images that uses adaptive quadrature filters constructed by use of Bayesian estimation theory and complex-valued Markov random fields as prior models. It is shown that with this technique it is possible to perform accurate phase reconstructions even for extremely noisy fringe images and that the performance of this technique is nearly independent of the particular noise model, as long as the noise spectrum is wideband.     

Phase difference determination by fringe pattern matching

A method of phase difference determination in interferometry is presented. In this method, the phase difference between two interferograms is determined by fringe pattern matching with subpixel accuracy. The signal-to-noise ratio is significantly improved due to the region-based fringe pattern matching and its effect of averaging noise. The experiment shows that this method is useful for the determination of phase difference between two equi-spaced fringe patterns, and it has the advantages of high precision of measurement and high resistance to noise.     

Removing harmonic distortion of measurements of a defocusing three-step phase-shifting digital fringe projection system

Binary defocusing method was adopted in 3D profilometry as it allows real-time measurement and does not need to handle the luminance nonlinearity of a projector. Current patch-based binary fringe patterns are periodic and carry strong harmonic distortion as compared with the ideal sinusoidal fringe patterns, which affects the measuring performance remarkably. In this paper, we propose a framework for generating aperiodic fringe patterns based on optimized patches. The produced fringe patterns can significantly lower the noise floor and suppress the harmonic distortion in the constructed phase map. Accordingly, the achieved depth measuring performance can be significantly improved. Special care is also taken during the optimization of the patches in our framework such that the depth measuring performance is robust to fringe period and defocusing extent.     

The governing equations of Moiré interferometry II. Gratings at ±45° to the measurement axes

The effects of tilting of the grating plane on moiré interferometric fringe patterns are studied using the method of Livnat and Post (Experimental Mechanics, 25(4) (1985) 6–360). Tilting may result either from rigid-body rotations or from out-of-plane displacement gradients. Tilting may introduce a significant error if it is assumed that the fringes represent contours of in-plane displacement, particularly if the in-plane deformation is small compared with the out-of-plane displacement gradient. Knowledge of the surface slope appears to be sufficient to correct the error. It is also shown that the fringe patterns do not capture the added displacement caused by rigid-body rotations exactly. The implications of these effects are briefly discussed for an experiment measuring the deformation at the tip of a crack in a ductile steel, in which the out-of-plane displacement gradients are relatively large.     

基于CCD采集的Mach-Zehnder干涉条纹图的处理算法

Mach-Zehnder干涉仪适用于研究气体密度迅速变化的状态。由于气体折射率的变化与其密度的变化成正比,而折射率的变化将使通过气体的光线有不同的光程,因此可通过干涉臂变化对干涉条纹图像效果的影响得到气体密度。实测中,采用图像采集卡和CCD来接收Mach-Zehnder干涉仪产生的条纹图像,再通过计算机对条纹图像的条纹间距进行处理,从而得到气体密度的变化状态。从光干涉理论出发,对Mach-Zehnder干涉条纹图像特征进行了分析,建立了Mach-Zehnder干涉条纹的数学模型,并根据此模型设计了处理Mach-Zehnder干涉条纹图像的算法。算法包括图像的预处理(即图像的噪声提取)、图像的二值化及图像的细化。     

Homomorphic partial differential equation filtering method for electronic speckle pattern interferometry fringes based on fringe density

Noise reduction is one of the most exciting problems in electronic speckle pattern interferometry. We present a homomorphic partial differential equation filtering method for interferometry fringe patterns. The diffusion speed of the equation is determined based on the fringe density. We test the new method on the computer-simulated fringe pattern and experimentally obtain the fringe pattern, and evaluate its filtering performance. The qualitative and quantitative analysis shows that this technique can filter off the additive and multiplicative noise of the fringe patterns effectively, and avoid blurring high-density fringe. It is more capable of improving the quality of fringe patterns than the classical filtering methods.     

Measurement of surface topography by RGB Shadow-Moiré with direct phase demodulation

In this paper we present the application of a direct demodulation method for the measurement of surface topography by means of Shadow-Moiré. In our set-up, we use three LEDs (with green, red and blue peak wavelengths) to illuminate the grating. Due to the different position of these light sources, a polychromatic Shadow-Moiré fringe pattern is produced, which can be described as the superposition of three monochromatic (red, green and blue) fringe patterns. Taking the image of this polychromatic fringe pattern with a RGB CCD camera, we get a monochromatic fringe pattern stored at each RGB channel of the CCD. The direct demodulation algorithm employed uses these fringe patterns to calculate the wrapped phase map. After unwrapping the phase map using a standard multi-grid technique, we implemented an automatic procedure to detect the area of interest of the phase map by removing low modulation zones and to calculate the absolute value of the phase. In this way it is possible to determine the topography of a surface with a single RGB snapshot maintaining a simple experimental set-up, which is an important feature, especially for the study of dynamic phenomena such as deformations. We present the experimental results obtained after measuring different objects with both smooth and rough surface textures.     

Automatic analysis of three-dimensional displacement field using ESPI

Electronic speckle pattern interferometry (ESPI) has been used to study the in-plane and out-of-plane displacements of the object. In order to improve the accuracy, a Fourier filtration algorithm has been used to remove the speckle noise and get the holographic-quality ESPI fringe pattern. The processing steps of this method are described in detail in this paper. In addition, a phase shifter, which is easily used with simplified structure and high stability, is also presented. It can be applied to various coherent arrangements in experiments to obtain phase shifted fringe patterns. Experiments of determining the 3D displacement field of a circular fixed plate with a uniform load have been carried out using these methods. The results presented in this paper indicate that the accuracy of this method is satisfactory.