Surface normal guided method for two-dimensional phase unwrapping

A novel phase unwraping method has been presented and evaluated in this paper. This method works by first constructing a quality map based on the characteristic of the active triangulation system from the wrapped phase data. The quality map is then used to guide the unwrapping. In order to reduce the execution time of phase unwrapping, we tessellate the whole wrapped phase map into blocks. Blocks with higher confidence will be unwrapped first. Experiment shows that this method can unwrap the wrapped phase map derived from the digital moiré system successfully. In data integration stage, only data with higher confidence will be reserved and used to merge together to form a complete 3D model.     

A fast,accurate phase unwrapping method for wavelet-transform profilometry

A novel phase unwrapping method used in wavelet-transform profilometry is presented to improve the accuracy and speed of the unwrapping process. The wrapped phase of the fringe image is extracted by using wavelet transform. How to establish quality map using scale factor at wavelet ridge is discussed firstly. The proposed method can reflect the reliability of the pixels in fringe image effectively. As the consuming time of traditional flood-fill phase unwrapping algorithm is too long, an improved quality-guided method is used in phase unwrapping process. We divide the wrapped phase map into two levels following the established quality map, and process these two levels using different algorithms. Compared with the traditional flood-fill algorithm, we can get the accurate result while the consuming time of the phase unwrapping process is much less by using the proposed method. Simulation and experiment results verify that the 3D information of the measured object can be obtained rapidly and accurately by using the proposed method. Also the dynamic object can be measured too.     

Complex-amplitude-based phase unwrapping method for digital holographic microscopy

A complex-amplitude-based phase unwrapping approach for digital holographic microscopy is proposed in this paper. A quality map is derived directly from the reconstructed complex amplitude distribution of object wave to evaluate noise influence and phase reliability in the wrapped phase image. Quality-guided phase unwrapping algorithm is then implemented with the quality map to retrieve continuous phase profile. Unwrapping errors caused by unreliable phase data are successfully suppressed. The effectiveness of this method is demonstrated with simulation and experimental results.     

基于分支设置的质量导引相位展开算法

二维相位展开方法是近年来较为活跃、引起关注的一个研究课题,它在许多测量应用中有着重要的作用。尽管掩膜阻断算法在多个领域都有成功应用实例,该算法存在着固有的缺陷。为了克服掩膜阻断算法的缺陷,综合分支阻断方法和质量导引方法的优点,提出一种基于分支设置的质量导引相位展开新算法。它先以一个初始质量图来引导分支的设置,然后把分支对应的相位质量设置为最低,从而产生一个新的质量图,最后按新质量图来引导相位展开,并使用几个包裹相位图来验证此方法的有效性。计算机模拟相位图和实际相位图的相位展开结果表明,在存在复杂轮廓不连续和高噪声的情况下,该算法优于模板阻断算法,能得到较好的相位展开结果。     

Weighted least-squares phase unwrapping algorithm based on derivative variance correlation map

Among different phase unwrapping approaches, the weighted least-squares minimization methods are gaining attention. In these algorithms, weighting coefficient is generated from a quality map. The intrinsic drawbacks of existing quality maps constrain the application of these algorithms. They often fail to handle wrapped phase data contains error sources, such as phase discontinuities, noise and undersampling. In order to deal with those intractable wrapped phase data, a new weighted least-squares phase unwrapping algorithm based on derivative variance correlation map is proposed. In the algorithm, derivative variance correlation map, a novel quality map, can truly reflect wrapped phase quality, ensuring a more reliable unwrapped result. The definition of the derivative variance correlation map and the principle of the proposed algorithm are present in detail. The performance of the new algorithm has been tested by use of a simulated spherical surface wrapped data and an experimental interferometric synthetic aperture radar (IFSAR) wrapped data. Computer simulation and experimental results have verified that the proposed algorithm can work effectively even when a wrapped phase map contains intractable error sources.     

基于图切割的相位展开

剪切散斑干涉术中,普遍采取相移法提取相位,只可得到被包裹的相位信息,进一步量化计算之前,必须展开相位,但是大量的散斑噪音使相位展开变得非常困难.本文提出基于图切割理论的相位展开算法,将相位展开等价于整数的最优估计问题,通过最小化能量函数展开相位,无需对散斑包裹相位图进行滤波,就可以从包含大量散斑噪音的包裹相位图中准确地提取出真实相位,极大程度地保留了相位包裹图中的细节信息.对于同一幅模拟的散斑包裹相位图,传统的质量导向枝切法和最小二乘法的均方根误差分别为11.7076和4.9775,新算法的均方根误差则为0.9459,数值模拟与实验结果均验证了新算法优良的抗噪性能.     

基于图切割的相位展开

剪切散斑干涉术中,普遍采取相移法提取相位,只可得到被包裹的相位信息,进一步量化计算之前,必须展开相位,但是大量的散斑噪音使相位展开变得非常困难.本文提出基于图切割理论的相位展开算法,将相位展开等价于整数的最优估计问题,通过最小化能量函数展开相位,无需对散斑包裹相位图进行滤波,就可以从包含大量散斑噪音的包裹相位图中准确地提取出真实相位,极大程度地保留了相位包裹图中的细节信息.对于同一幅模拟的散斑包裹相位图,传统的质量导向枝切法和最小二乘法的均方根误差分别为11.707 6和4.977 5,新算法的均方根误差则为0.945 9,数值模拟与实验结果均验证了新算法优良的抗噪性能.     

A new quality map for quality-guided phase unwrapping

A new quality map for quality-guided phase unwrapping is presented. The quality map is derived from the wrapped phase map directly and can reflect phase quality accurately. It is demonstrated that the proposed quality map is a good phase-quality indicator, with which the quality-guided unwrapping algorithm can retrieve a reliable phase profile.     

Fringe contrast-based 3D profilometry using fringe projection

Quality-guided algorithm is a widely used method in phase unwrapping. This paper shows an accurate quality map based on fringe contrast for 3D shape measurement. Phase-shifted fringe patterns are projected onto an object surface by a programmable liquid crystal projector and recorded by a CCD camera. A wrapped phase map and a fringe contrast map are extracted from the deformed fringe patterns by the phase-shifting technique. Guided by the contrast map, the quality-guided unwrapping algorithm minimizes unwanted shadow and non-uniform surface reflectance effects and is able to retrieve a correct surface profile. Validity of the proposed method is tested on a fish model and a cutting tool specimen.     

最小二乘相位解包络方法

介绍一种最小二乘解相位包络的方法 ,该法的优点在于把图像作为一个整体处理 ,图像上每一个像素点的值由方程唯一确定 ,而且解得的相位图与原包裹的相位图偏差平方加权最小 ,具有局部解相法所不具有的优点。实验证明 ,它能够处理局部处理方法难以解决的相位图 ,并给出几幅实际相位图的处理结果     

Removal of carrier frequency in phase-shifting techniques

The existence of carrier frequency is unavoidable in many phase-shifting techniques. It makes the phase-unwrapping procedure more difficult, especially when speckle-like noise exists in the wrapped phase map. In this paper, it is shown that the carrier frequency is approximately equal to the average of the first difference of the phase. To remove the carrier frequency, we compute the first difference of the phase before attaining the phase map, subtract the average of the first difference, and integrate to get the phase map without carrier frequency. Computer simulation and experimental results show this method as being profitable for phase unwrapping.     

基于方向图变换的快速不连续相位展开

几何突变导致的相位不连续一直是相位展开中具有挑战的问题.针对这一问题,提出基于方向与变换的快速不连续相位展开算法.在提出的算法中,利用图像的结构张量估计包裹相位图的方向,将方向图进行变换和差分计算得到的可靠的权重系数图作为加权最小二乘法的权重,并使用预处理共轭梯度法迭代求解.该算法可以快速地找出不连续位置,并在不连续分...     

Reliability-guided phase unwrapping algorithm following noncontinuous path based on color fringe projection

The intrinsic drawbacks of existing reliability-based algorithms, they often fail to handle wrapped phase data contains error sources, such as phase discontinuities, noise and undersampling. These algorithms often calculate the reliability only relying on the recorded pixel intensity or wrapped phase value, but the intensity of pixel always exist many noises. In this paper, we present a new method to define the reliability of pixel and path of phase unwrapping, the pixel's intensity and color are employed in fringe analysis simultaneously. The reliability function is calculated based on modulation, second difference of wrapped phase, and second difference of modulation, then we present the concept of smoothness of path, the reliability of path is calculated based on reliability of pixel and smoothness of path. Experiment results validate our proposed algorithm is more accurate than many previous algorithms. The proposed algorithm can be used to unwrap the complex phase map with discontinuous jump, and can be implemented with high efficiency without any manual interface.     

小波变换轮廓术中用小波脊系数幅值引导相位展开的研究

为了减少小波变换轮廓术中相位展开过程的误差传递,从小波变换的相关实质出发,提出了在小波变换轮廓术中利用以前被忽略的小波脊系数幅值作为可靠度判据指导相位展开的方法.该方法选择最大幅值的小波脊系数所在位置作为相位展开起始点,根据小波脊系数幅值的大小,确定一条由大幅值到小幅值的最优化的展开路径,最大限度减少了相位展开过程中的误差传递.由于充分利用了小波变换系数的幅值信息,最大限度减小了相位展开过程中的误差传递.计算机模拟和实验验证了基于小波脊系数幅值的相位展开方法的正确性.     

Phase map retrieval in digital holography: avoiding the undersampling effect by a lateral shear approach

In digital holography (DH) the numerical reconstruction of the whole wavefront allows one to extract the wrapped phase map mod, 2 pi. It can occur that the reconstructed wrapped phase map in the image plane is undersampled because of the limited pixel size in that plane. In such a case the phase distribution cannot be retrieved correctly by the usual unwrapping procedures. We show that the use of the digital lateral-shearing interferometry approach in DH provides the correct reconstruction of the phase map in the image plane, even in extreme cases where the phase profile changes very rapidly. We demonstrate the effectiveness of the method in a particular case where the profile of a highly curved silicon microelectromechanical system membrane has to be reconstructed.     

相位解码的时-空重建算法

基于相位映射的三维传感技术对几何形状和拓扑结构复杂或表面梯度很大的物体进行绝对相位测量及相位重建仍然是一个困难的问题。近年来国际上提出了一种时间维度相位重建算法可以对此提供一种解决方案。然而,该算法对结构光照明系统提出了很高的要求,当系统无法满足算法要求时,重建结果存在严重的噪声。针对这一问题,提出了一种利用分段函数构造的相位解码的时空重建算法。该算法在相位重建过程中同时考虑时间维度和空间维度相位的相对关系,使得空间频率非严格按指数增长的条纹序列可以得到正确的重建,消除了跳变边界的相位模糊问题,从而可以更加有效地解决深度表面不连续和存在相互孤立物表面拓扑结构的景物相位重建问题。实验结果证明了此算法的可行性和有效性。     

A simple method for phase wraps elimination or reduction in spatial fringe patterns

In this paper, we propose a simple method for processing a 2D wrapped phase map that contains a spatial carrier signal in order to completely eliminate, or greatly reduce, the number of phase wraps in the image. The 2D Fourier transform of the wrapped phase map is calculated. Then the spectrum is shifted to the origin in frequency space. After that, the inverse 2D Fourier transform is computed. Finally, a four-quadrant arctangent function is used to calculate the angle of the complex array that was produced by the inverse 2D Fourier transform. This produces a phase map with a smaller number of 2π phase jumps than the original phase map. In some cases, all of the phase wraps are eliminated and there is therefore no need to unwrap the resultant phase map. The reduction of the number of 2π phase jumps can reduce the execution time and improve the noise performance of some phase unwrapping algorithms such as the Flynn method. The validation of the proposed algorithm is demonstrated experimentally and also via computer-simulation.     

欠采样包裹相位图的恢复方法

针对非球面光学元件面形检测中的欠采样问题,提出了一种欠采样包裹相位图的恢复方法.首先,将原始欠采样包裹相位图在水平和竖直两个方向进行一个像素的错位相减,得到两个包裹相位差图.其次,对这两个包裹相位差图进行解包裹运算,得到两个解包裹相位差图.最后,应用傅里叶变换和最小二乘法恢复出连续的相位分布.模拟结果表明该方法可以高精...     

相位编码条纹投影轮廓术的相位展开误差校正方法

相位编码法是条纹投影技术中常用的一种相位展开方法。然而,受到随机噪声、图像采样、系统离焦等因素的影响,条纹阶次与包裹相位的对应关系容易被破坏,从而引入相位展开误差。根据相位展开误差的分布特点,提出一种附加二值条纹的相位展开误差校正方法。引入的二值条纹与相位编码条纹的码字存在半周期错位,使得计算出的2组条纹阶次值具有互补性,利用两者的互补性可以有效地消除相位展开误差。仿真和真实实验均表明,该方法能够准确地恢复出被测物体的绝对相位,具有较高的可靠性。     

Minute displacement and strain analysis using lensless Fourier transformed holographic interferometry

An optical system for lensless Fourier transformed holographic interferometry is constructed to enable the measurement of minute displacements from nanometers to micrometers scale and to obtain corresponding strain distributions using a CCD camera with poor spatial resolution. Since a Fourier spectrum of an object beam is recorded on a hologram in this technique, the image reconstruction is easily performed with a single pass of 2-D fast Fourier transformation. Then, the map of the phase difference over the whole field is obtained by comparing two images before and after deformation. A suitable and effective unwrapping process is, however, inevitably required since the phase difference distribution is wrapped from −π to π in this technique. For phase unwrapping, the maximum spanning tree method is adopted here, which seeks a spanning tree that maximizes overall edge weights given by the cross amplitude. In-plane and out-of-plane displacements are obtained separately from the phase difference distributions at one's request. Moreover, in-plain strain is easily calculated from the in-plane displacement distribution.