Fringe-pattern demodulation using an iterative linear digital phase locked loop algorithm

A novel technique called an iterative linear digital phase locked loop (DPLL) for fringe-pattern demodulation is presented. The proposed technique has better noise immunity than the basic one-dimensional DPLL algorithms (e.g., conventional and linear DPLLs) because it processes a fringe pattern in two dimensions. In the first iteration of the proposed algorithm, it uses a flat reference to estimate the phase of the fringe pattern. The estimated phase map resulting from the first iteration is smoothed using a moving average window and then it is used as a reference to estimate the phase of the fringe pattern in the second iteration. In the third iteration, the phase map resulting from the second iteration is smoothed and used as a reference to estimate the phase of the fringe pattern in the fourth iteration and so on until the demodulated phase map has a good signal-to-noise ratio.     

A numerical spatial carrier for single fringe pattern analysis algorithm

Hilbert transform and continuous wavelet transform are combined to form an algorithm for the analysis of a single fringe pattern with open or closed fringes. Only one recorded fringe pattern is needed to extract the phase information. A second π/2 phase shifted fringe pattern should first be generated from the other using Hilbert transform to superpose numerically the spatial carrier. Several phase extraction techniques are conceived to demodulate fringe patterns. In this paper, the wavelet technique is used to obtain the required phase distribution. The algorithm offers an advantage that it is appropriate when the spatial carrier is impossible to be added experimentally. Finally, a simulation was carried out to validate the algorithm, giving good results.     

嵌入式三维数字成像系统

提出一种基于数字信号处理器(DSP)的嵌入式三维数字成像系统设计方案。该方案的硬件平台由条纹投影模块、数据采集模块、条纹自动分析模块及储存器等其他辅助电路组成。条纹投影模块将DSP输出的正弦光栅条纹, 经视频编码后用DLP投射到物体表面; 数据采集模块通过CCD相机采集被物体表面三维信息调制后的变形条纹图, 并进行视频解码; 条纹自动分析模块中利用相移算法计算折叠相位, 再结合相位展开算法求绝对相位分布。系统软件采用多线程技术并行控制三个模块。在相位解调过程中以软件流水线为主综合运用了循环展开、数据预取和内联函数等多种方法优化解调程序。实验结果表明, 该系统可以高速、准确地实现三维轮廓测量,优化后相位展开程序速度是优化前的7倍。     

Simultaneous estimation of unwrapped phase and phase derivative from a closed fringe pattern

We propose a new approach for the direct estimation of the unwrapped phase from a single closed fringe pattern. The fringe analysis is performed along a given row/column at a time by approximating the phase with a weighted linear combination of linearly independent basis functions. Gaussian radial basis functions with equally distributed centers and a fixed variance are considered for the phase approximation. A state space model is defined with the weights of the basis functions as the state vector elements. Extended Kalman filter is effectively utilized for the accurate state estimation. A fringe density estimation based criteria is established to select whether the phase estimation is performed in a row by row or column by column manner. In the seed row/column decided based on this criteria, the optimal basis dimension is computed. The proposed method effectively renders itself in the simultaneous estimation of the phase and the phase derivative. The proposed phase modeling approach also allows us to successfully demodulate the low density fringe patterns. Simulation and experimental results validate the practical applicability of the proposed method.     

Window fringe pattern demodulation by multi-functional fitting using a genetic algorithm

We present a new way to demodulate complicated fringe patterns containing closed fringes using a genetic algorithm (GA). The entire fringe pattern is divided into a set of partially overlapping smaller sub-image windows. Each of these has a lower dimensionality and as a consequence is faster and can be demodulated more reliably. The demodulation process proceeds row-by-row way passing from one sub-image in a neighborhood until the whole interferogram is processed. The modulating phase of each sub-image is modeled as a parametric analytic function whose parameters are optimized using a GA. The technique is demonstrated demodulating some normalized fringe patterns that have two main difficulties: closed fringes within the interferogram and regions of under-sampled fringes. These fringe images cannot be demodulated by techniques such as the regularized phase tracker (RPT).     

Three-dimensional Fourier Fringe Analysis

Over the years two-dimensional Fourier Fringe Analysis (2D-FFA) has demonstrated both its capability and its relative robustness in analysing fringe patterns within a short time-frame from static objects. Nowadays, there is an increasing demand to measure dynamic objects. Today 2D-FFA is seen as a fast and flexible method of processing fringe patterns for dynamic objects. But it is still inherently a 2D approach, i.e. it deals with three-dimensional data (video sequences) on an individual 2D frame-by-frame basis. In this paper, a novel three-dimensional Fourier Fringe Analysis (3D-FFA) algorithm is proposed to demodulate fringe pattern sequences taken from dynamic objects. This technique processes the stack of fringe patterns as a single 3D volume, not as a set of individual 2D frames that are each processed in isolation. The proposed algorithm has been evaluated on both computer simulated and real dynamic objects. Results show that the proposed technique is able to demodulate fringe pattern volumes successfully.     

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。     

基于窗口傅里叶变换剪切干涉法波前检测

提出了一种利用二维窗口傅里叶变换从径向剪切干涉条纹中准确得到波前的重建技术。首先对剪切干涉条纹做二维窗口傅里叶变换,设置阈值和频率积分范围后,进行二维窗口傅里叶逆变换,然后对包裹相位做去载频和相位展开处理得到相位差分布,最后使用波前迭代算法从相位差中复原实际波前。模拟计算表明,使用该方法最大相位复原误差为0.82%,均方根值为0.020 9 rad,实验结果验证了该方法的有效性。同时也对窗口傅里叶变换的关键参数,如窗函数的选择、窗口大小的确定以及阈值的选取等进行了简要讨论。与传统傅里叶变换法(FFT)相比,基于窗口傅里叶变换的剪切干涉波前检测法有更高的精度和稳定性,为波前检测提供一种新的处理方法。     

Enhanced wavefront reconstruction by random phase modulation with a phase diffuser

A phase retrieval technique for enhanced wavefront reconstruction using random phase modulation and a phase diffuser is proposed. The speckle field generated is sampled at multiple axially displaced planes and the speckle patterns are used in an iterative algorithm based on the optical wave propagation in free space. The presentation of this technique is carried out using two setups. In the first setup, a diffuser plate is placed at the image plane of a metallic test object. The benefit of randomizing the phase of the object wave is the enhanced intensity recording due to high dynamic range of the diffusely scattered beam. The use of demagnification optics will also allow the investigations of relatively large objects. In the second setup, a transparent object is illuminated using a wavefront with random phase and constant amplitude by positioning the phase diffuser close to the object. The benefit of phase-only modulation is the increased resolution of the phase structures of the transparent test objects.     

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.     

Two-step interferometry by a regularized optical flow algorithm

A two-step phase-shifting method, that can demodulate open- and closed-fringed patterns without local sign ambiguity is presented. The proposed method only requires a constant phase-shift between the two interferograms. This phase-shift does not need to be known and can take any value inside the range (0, 2π), excluding the singular case where it corresponds to π. The proposed method is based on determining first the fringe direction map by a regularized optical flow algorithm. After that, we apply the spiral phase transform (SPT) to one of the fringe patterns and we determine its quadrature signal using the previously determined direction. The proposed technique has been applied to simulated and experimental interferograms obtaining satisfactory results. A complete MATLAB software package is provided in [http://goo.gl/Snnz7].     

Eliminating the zero spectrum in Fourier transform profilometry using a two-dimensional continuous wavelet transform

In this paper, a filtering technique based upon two-dimensional continuous wavelet transform (2D-CWT) is used to eliminate the low frequency components of fringe patterns. The filtered fringe patterns are subsequently demodulated using a standard Fourier transform profilometry (FTP) algorithm. This image pre-filtering stage improves the noise performance of the FTP algorithm and enables the FTP method to demodulate fringe patterns with larger bandwidths. Also, the 2D-CWT technique reduces speckle noise significantly. Moreover, only a single fringe pattern is required in this technique. The 2D-CWT algorithm is capable of separating low frequency terms from the high frequency terms that contain phase-modulated fringe information, even when both interfere, greatly, in the frequency domain. The proposed algorithm is tested, both via computer simulation and using real fringe patterns. This revealed the robustness of this algorithm and also demonstrably enables the demodulation of a wider range of fringe patterns using the FTP technique.     

光载波条纹图的计算机辅助分析——阶梯形虚拟光栅解调法

本文提出一种两维光测条纹图的相位测量技术--阶梯形虚光栅解调算法。此法只需要获取一幅光载波条纹图,由计算机产生两个由N(整数)个象素构成、透射函数呈阶梯形分布、彼此间有一定相位差的两个虚光栅(参考信号),通过在整数域的运算实现对条纹图和虚光栅的相乘型叠加,低通滤波后得到两个相位差已知的叠栅函数,然后从两个相差为已知值的正弦信号中提取相位信息。理论分析和计算机模拟表明,具有相当高的测量精度,计算简便快捷。文中还给出了阶梯虚光栅解调法在投影光栅法三维形貌测量中的应用实例。     

Gerchberg迭代法在三维面形测量中的应用

在基于结构光照明的三维面形测量中,针对有孤立区域物体的条纹图像存在不规则缺陷的问题,提出先对其进行Gerchberg迭代,消除或减少条纹缺陷,获取较完善的迭代条纹,然后再利用傅里叶变换轮廓术(FTP)重建面形。设计了迭代流程,并分析了影响迭代精度的因素,解决了光学加工用具磨盘表面不完善条纹Gerchberg迭代过程中存在的问题,成功地重建了磨盘的三维面形。该工作为表面存在孤立区域的被测物体三维面形测量提供了可供参考的技术方案,也给可实时形变的应力盘三维面形动态测量奠定了基础。     

Study on an automatic processing technique of the circle interference fringe for fine interferometry

The fringe center method (FCM) is an important digital processing technique of fringe patterns analysis for interferometry. In this paper, an improved automatic processing technique based on FCM was presented, which correlated the processing link and the looped feature of the circle fringe pattern. It also integrated several techniques including noise removal, the fringe thinning, the fringe patching, assignment of the fringe orders and wavefront reconstruction and can be executed orderly and automatically. Based on the new the algorithms of the fringe patching and assignment of the fringe orders, the fringe feature information was extracted automatically and the interference wavefront was reconstructed by Zernike polynomial fitting method. With the automatic processing technique, the circle interference fringe of the fine polished aluminum disks surface captured by the Twyman-Green interferometer was processed, and the surface profile and the parameters of the disk were obtained automatically. The experiments show that the improved automatic processing technique was more accurate and fast in measurement than the conventional one. It was convenient to use it in in-situ industry inspection.     

光学扫描全息术研究进展

光学成像技术极大地拓展了人类的视觉极限,提高了人们观察和理解现实世界的能力。越多地获得目标的光学信息,对其的认识越充分。数字全息术是一种可以将样本的三维信息以二维全息图的形式编码记录下来的一种成像技术。通过获得由携带物体信息的物光波和参考光波叠加产生的干涉图案,可以以数字化的方式实现多种重建模态,例如图像恢复、相位成像和切片成像等。光学扫描全息术是一种独特的数字全息成像技术,通过主动式二维化扫描对三维物体进行成像,其完整的波前信息可以被单像素探测器记录,并基于光外差检测进行信号解调,从而恢复出复数全息图。对光学扫描全息术的最新进展进行介绍。首先,基于双光瞳成像系统,通过特殊的硬件和算法设计,提高光学成像系统的性能,如提高空间分辨率、缩短扫描时间。其次,基于计算成像原理,通过改进和优化全息像重建算法,实现高质量的图像恢复,主要涉及切片成像和三维成像等重建模态。第三,介绍光学扫描全息术的其他研究方向,并讨论该领域未来可能的发展方向。     

载波相移全息干涉计量

本文报道了一项称为载波相移全息干涉计量的自动相位估算的新技术。该技术的主要特点是不同相移的条纹图案可用双曝光全息重视。这样即可用来对与时间相关的问题进行自动相位估算。     

Orthogonal projection technique for resolution enhancement of the Fourier transform fringe analysis method

The spatial resolution of the phase map in the Fourier transform fringe analysis method is determined by the size of the filter’s window in frequency domain. This article reports a straightforward technique to improve the method’s resolution by a factor of nearly two. The technique requires capturing a second image with a fringe pattern orthogonal to the first one, therefore using the information from both patterns to eliminate the central component in frequency space. The resulting spectrum supports double sized filter windows for removal of the carrier frequency without leaking into adjacent orders. The overall spatial resolution of the method is thus increased. In the following, the Fourier fringe analysis method is briefly reviewed, the new technique is described and analyzed and the experimental results are shown and discussed.