Parallel computing for fringe pattern processing: A multicore CPU approach in MATLAB environment

In the process of measurements such as optical interferometry and fringe projection, an important stage is fringe pattern analysis. Many advanced fringe analysis algorithms have been proposed including regularized phase tracking (RPT), partial differential equation based methods, wavelet transform, Wigner–Ville distribution, and windowed Fourier transform. However, most of those algorithms are computationally expensive. MATLAB^® is a general algorithm development environment with powerful image processing and other supporting toolboxes. It is also commonly used in photomechanical data analysis. With rapid development of multicore CPU technique, using multicore computer and MATLAB^® is an intuitive and simple way to speed up the algorithms for fringe pattern analysis. The paper introduces two acceleration approaches for fringe pattern processing. The first approach is task parallelism using multicore computer and MATLAB^® parallel computing toolbox. Since some algorithms are embarrassing problems, our first approach makes use of this characteristic to parallelize these algorithms. For this approach, parallelized windowed Fourier filtering (WFF) algorithm serves as an example to show how parallel computing toolbox accelerates the algorithm. Second, data parallelism using multicore computer and MATLAB^® parallel computing toolbox is proposed. A high level parallel wrapping structure is designed, which can be used for speeding up any local processing algorithms. WFF, windowed Fourier ridges (WFR), and median filter are used as examples to illustrate the speedup. At last, the results show that the parallel versions of former sequential algorithm with simple modifications achieve the speedup up to 6.6 times.     

成像型任意反射面速度干涉仪数据处理方法

 采用傅里叶变换方法,列出了对成像型任意反射面速度干涉仪得到的干涉条纹图进行处理的过程。利用文献结果,处理了冲击波整形时产生的有间断干涉条纹图,对处理结果进行了分析。结果表明：条纹图要干净,条纹间距清晰、均匀,应使用１维傅里叶变换的方法处理条纹图,减小滤波的难度。研究了冲击波测试当中条纹丢失的问题,提出了间断条纹图间断起始点相位确定的方法。对透明和不透明靶产生条纹图的不同进行了讨论,得出对透明靶产生的条纹图应采用适当的条纹外延技术进行预处理后再进行常规处理。     

Automated optical analysis of young's fringes— optical autocorrelation

Extraction of displacement or velocity data from laser speckle photography or particle image velocimetry transparencies requires measurement of the spacing and orientation of several thousand Young's fringe patterns. In contrast with classical interferometry, fringes formed in this way have poor visibility and it is generally desirable to compute the two-dimensional Fourier transform in order to extract the fringe frequency. The large amount of data produced makes digital acquisition and image processing computationally intensive and time consuming. This paper introduces an automated processor which utilises a photorefractive crystal of bismuth silicon oxide to perform this analysis in a fast and cost-effective manner.     

Application of the FFT method for the quantitative extraction of information from high-resolution interferometric and photoelastic data

This paper describes the application of a digital Fourier transform to phase encoded intensity distribution. Attention is drawn to a method of extracting quantitative information automatically from the interferometric fringe data. To achieve this, a set of carrier fringes has been added to interferometric fringe data. This has made it possible to form a phase map using a FFT (fast Fourier transform) algorithm. A minimum spanning tree (MST) phase unwrapping strategy has been used to create a contiguous map of the whole fringe field. Finally, the measurement parameter related to the fringe field has been calculated from one single image. Experimental results are given for the burner flames, a compressible flow and photoelastic fringe data. It has been shown that the methods developed have the potential for use as reflection analysis systems suitable for applications to non-stationary objects and complicated fringe fields.     

Characterizing Young's fringes’ orientation and spacing by Fourier transform and Radon transform

Orientation and spacing are important features of fringe patterns, especially in speckle photography when the displacement information of the object is determined by pointwisely filtering the double-exposure specklegram. The Fourier transform and Radon transform are both simple and effective tools for solving this problem, which extract the information in spectral domain and spatial domain, respectively. A hybrid method combining Radon transform and Fourier transform is also possible. The results can be further improved by enhanced Fourier transform and enhanced Radon transform. The theories, as well as real applications, are given in this paper.     

Automatic processing of Young''s fringes in speckle photography

A new method for the automatic processing of Young's fringes in speckle photography is described, based on the technique of spatial phase detection. The amount of calculation is reduced, yet accuracy is of an order comparable with that of the Fourier transform method. Furthermore, orientation of fringes is determined as well as fringe spacing.     

A comparison of phase shifting and fourier methods in the analysis of discontinuous fringe patterns

Phase Shifting Interferometry is a highly accurate data acquisition technique that efficiently utilizes several frames of information for each measurement. In this work, the advantages of phase shifting have been applied to a conventional moiré interferometer, yielding a system capable of recording phase shifted fringe patterns for both in-plane displacement components. Using this method, the phase of a wavefront of interest can be determined at each detector location, so that the resolution of the phase measurements is limited primarily by the detector discrimination and geometry. Unlike traditional Fourier fringe analysis, the noise rejection of phase shift processing algorithms does not degrade image fidelity in the presence of edges and discontinuities. A general discussion of both the phase shifting technique and the Fourier fringe analysis method is included to provide insight into the problems of processing discontinuous fringe patterns.     

Young's fringes analysis with a computer image-processing system

A two-dimensional Fourier transform analysis is presented for numerically processing the Young's fringes diffraction pattern from a double- exposure speckle photograph. The fringe spacing and orientation are determined using only one Young's fringes pattern without any other diffraction halo patterns. This algorithm is based on the 2-D FFT of the fringe pattern with 256 × 256 pixels. Therefore, it enables automatic analysis to be performed on specklegram with noisy and poor fringe patterns. The measurement of deformation by the laser speckle method can be carried out with high accuracy, reliability and speed.     

Photorefractive Fourier transform profilometer for the measurement of 3-D object shapes

In the present work dynamic moiré-like fringe patterns, produced by photorefraction with low spatial frequencies, applied for profile determination of small objects is proposed. Basically, a Fourier transform profilometry technique is developed for an automated profile determination. This means, as far as we know, a new experimental procedure that exploits the real time holographic two wave mixing in Bi₁₂TiO₂₀ crystal sample. Besides, the mainly advantages of this procedure are, comparatively to the classical fringe projection method using the Michelson interferometer, best fringe pattern contrast, less speckle noise, absence of noises produced by spurious reflections and, the most significant, a pure sinusoidal shape obtained by dynamic holographic moiré-like process using photorefraction.     

傅里叶变换求取叠栅条纹微小位移的精度分析

提出了借助于傅里叶变换提取叠栅条纹相位分布的途径来获得条纹微小位移量的方法中，图像的截断必然会产生频谱泄漏，从而引入数据处理的误差。详细分析了傅里叶变换中频谱泄漏产生的原因及其对测量误差的影响，提出了图像处理时，通过外插值将截断区域延拓为叠栅条纹周期整数倍时可以减小甚至忽略频谱泄漏所引起的相位计算误差，并对此进行了数值模拟以及初步的实验验证，证实了该方法的有效性，为叠栅偏折法应用于微细尺度流动与传热的实验研究提供了有效的技术途径。     

Comparison of results of interferometric phase extraction algorithms for three-dimensional flow-field tomography

A comparison of the results of interferometric phase information retrieval and subsequent tomographic reconstruction from deformed wavefront projections by phase unwrapping is presented. In interferogram processing, conventional fringe tracking and Fourier transform methods have been utilized for comparison. With these methods by injecting carrier fringes, the projection data of any axial cross section can be extracted in all projection directions to implement three-dimensional tomographic reconstruction. The results of experiments of a simulated temperature field prove that the phase extraction based on the Fourier transform method produces tomographic reconstruction much superior to the conventional fringe tracking technique.     

三维测量中一种新的自适应窗口傅里叶相位提取法

针对多尺度窗口傅里叶变换中,窗口尺寸的自适应选取及提取基频时的频谱混叠等问题,提出基于希尔伯特-黄变换(HHT)的自适应窗口傅里叶相位提取法。对变形条纹信号进行HHT后,通过谱分析,自适应确定能够准确描述条纹信号变化情况的瞬时频率及条纹图的背景分量。根据所得的瞬时频率,给出自适应定位条纹信号局部平稳区域的步骤,进而确定窗口尺寸。不需额外计算,可有效去除背景分量以减少基频提取过程中零频频谱的干扰。与现有的用最大脊法确定窗口尺寸的方法相比,本方法不受被测相位必须线性逼近且变化缓慢的前提约束。实验证明本方法有效、可行,且对测量携带陡峭边缘或面形复杂的物体也能进行较为精确有效的测量。     

Neural network applied to reconstruction of complex objects based on fringe projection

The neural network has been introduced into the reconstruction of the complex object based on fringe projection. In this method, the neural network with powerful property of approximation is used to get the continuous approximate function of a discrete fringe pattern captured by an image frame grabber. The depth-related phase of the measured object modulated into the fringe pattern can be demodulated by dealing with the approximate function. Compared with the Fourier transform profilometry (FTP), in the network method, one deformed fringe pattern is needed to reconstruct the tested object, and a high spatial resolution is maintained for no filtering process. Therefore, this method performs better than FTP in the measurement of the complex object. Moreover, the network method is capable of demodulating more depth-related phase even in the case that the local shadow exists in the fringe pattern. Computer simulations and experiments validate the feasibility of this method.     

Using coloured structured light in 3-D surface measurement

The widest used algorithms for 3-D surface measurement using structured fringe patterns are phase stepping and Fourier fringe analysis. The techniques currently employed use mostly monochrome fringe patterns as a tool for phase information measurement and further surface reconstruction. However, the information contained in colour images is much more than that of monochrome, in this case, a new colour technique can be employed to analyse a measured scene with colour fringe patterns.This paper presents a new method for improving the measurement of 3-D shapes by using colour information of the measured scene as an additional parameter. The new method is based on primary colours (red, green and blue) to increase the number of the illuminated fringe patterns, which will remove or significantly reduce the common drawbacks of existing methods. The proposed technique produces a number of coloured structured lighting patterns, which are projected from different angles onto the scene. These patterns are analysed using masking algorithms, a specially adapted multi-colour version of the standard Fourier fringe analysis method and calibration routines. In this way a number of the standard difficulties are overcome.     

利用联合付里叶变换谱干涉法测量透镜焦距

本文提出了采用联合付里叶变换频谱干涉法测量透镜焦距的方法。输入面上两个分布完全相同的图像经光学付里叶变换在频谱面上得到二者付里叶变换频谱的干涉条纹，通过测量干涉条纹的间距即可得到透镜的焦距。该方法装置简单、操作调整方便；易于采用实时空间光调制器、ＣＣＤ及微机实现快速自动测量，且具有较高的精度。文中进行了原理分析和实验验证。     

Fourier transform profilometry: : a review

Fourier transform profilometry is one of the popular non-contact 3-D measurement methods, where a Ronchi grating or sinusoidal grating is projected onto a diffuse three-dimensional surface, and the resulting deformed grating image is detected by a CCD camera and processed by a computer. This method requires only one frame (or two frames) of the deformed fringe pattern in some algorithms to retrieve the surface of measured object, so it has obvious advantage for real time data acquisition and 3-D measurement of dynamic process. In this paper, we review some algorithms in FTP, discuss some important problems, including frequency spectra overlapping, phase unwrapping, sampling, and 3-D measurement of dynamic process. With the development of computer hardware and software and availability of high-resolution image grabber, FTP method will be a promising one for acquiring 3-D data of object, and more and more researchers pay attention to it.     

Method for eliminating zero spectrum in Fourier transform profilometry

Windowed Fourier transform (FT) is introduced into Fourier transform profilometry (FTP) to extract zero component included in deformed fringe pattern without capturing two fringe patterns with π phase difference. First, we extract zero component of deformed fringe image using windowed FT and normalize it, then calculate the normalized Fourier spectra of deformed fringe image, finally subtract the zero component from Fourier spectra of deformed fringe image. We give the theoretical analysis of the proposed method. The experiment is carried out to demonstrate that the method can eliminate zero component and extend the measurable slope of height variation to nearly three times of the conventional FTP.     

Measurement of Stress Intensity Factors of a Mixed-Mode Interface Crack by a Speckle Photography

The image-processing system based on a two-dimensional Fourier transform is presented for the analysis of Young’s fringes pattern created from a double-exposure speckle photograph. The fringe spacing and orientation are determined using only one Young’s fringes pattern without any other diffraction halo patterns. The stress-intensity factors of a mixed-mode interface crack were measured by speckle photography. A compact normal and shear specimen with an interface crack was employed. This specimen enables us to carry out the experiment under various kinds of mixed-mode loading. A steel and an epoxy resin were used as dissimilar materials. The displacement along the crack lines at the free surface was measured by speckle photography. The K₁ and K₁₁ values were determined by a least squares method using displacement data along the crack lines. Three-dimensional finite element analysis was carried out on the same specimen. An accuracy of stress intensity factors obtained by the speckle photography was discussed by comparison of results obtained by the finite element analysis.Presented at 1996 International Workshop on Interferometry (IWI ‘96), August 27–29, Saitama, Japan.     

Error-compensating algorithms in phase-shifting interferometry: a comparison by error analysis

In this paper, two families of phase-shifting algorithms with π/2 phase steps are studied. In family I, three new algorithms are derived by using the averaging technique based on the Surrel six-sample algorithm with phase shifts of π/2. Family II includes four well-known algorithms derived by the averaging technique based on the conventional four-sample algorithm with π/2 phase steps. A polynomial model of phase-shift errors used to describe general expressions for calculation of the correct object phase via the Fourier spectra analysing method as a function of the harmonic order in the fringe signal is presented. The error-compensating properties of the algorithms in families I and II are investigated by the Fourier spectra analysing method. It is found that the averaging technique, when used in any of the algorithm with π/2 phase steps, can improve the phase-shifting algorithm property: it is insensitive to phase-shift error when the fringe signal contains the first harmonic, but it can't be used to enhance the phase-shifting algorithm properties when the fringe signal contains higher order harmonics (n2). P–V (peak–valley) phase errors are calculated by the computer simulation and tables and plots are presented, from which the algorithms in families I and II are compared. It is shown that the algorithms in family I are more insensitive to phase-shift errors when the fringe signal contains the second harmonic and the algorithms in family II are more insensitive to phase-shift errors when the fringe signal is a sinusoidal waveform.