Noise immune unwrapping based on phase statistics and self-calibration

Unwrapping is an important step for precise phase measurement in an interferometric technique. Due to the effects of noises and speckles, an accurate unwrapping has been quite difficult. To address this issue, a new phase unwrapping method is proposed. The new method uses the wrapped phase statistics together with the limited smoothness characteristics of the interference phase. In this method, statistical parameters of the wrapped phase are firstly obtained. The step is then followed by a self-calibration process to identify and correct corrupted data points to obtain preliminary unwrapped phases. Finally, a phase revision step is taken to remove the effects of the residual errors. A computational testing was carried out to demonstrate the performance of the proposed method at six different levels of noise injection. An experimental test was also carried out using a lateral shearing interferometer. The success and the precision achieved using the proposed algorithm show that the method is quite effective and accurate for phase recovery under the condition of noise contaminations.     

基于自适应加权窗口的相位质量图提取

加权相位解缠算法的解缠精度取决于所提取的质量图的可靠性。目前提取相位质量图的方法大多采用以各个像素为中心的固定窗口法,但当某些像素被噪声严重干扰时,采用固定窗口法提取质量图往往得不到正确的解缠结果。因此,提出了几种自适应加权窗口方法来提取相位质量图,并给出了具体的实现方法和步骤,同时采用加权小波变换相位解缠算法进行相位解缠。实验结果表明,采用自适应加权窗口方法提取相位质量图来确定初始权重系数能获得比较好的解缠效果。     

光学干涉图像处理中基于质量权值的离散余弦变换解包裹相位

为减少噪声对相位恢复过程的影响,快速得到正确的解包裹相位,提出了一种改进的相位解包裹方法——加权离散余弦变换解包裹算法。该方法把离散余弦变换和标识相位数据好坏的质量权值结合起来,兼有速度快和可靠度高的优势。为验证此算法,对模拟和实验得到的包裹相位图添加随机噪声和散粒噪声,同时采用加权与非加权离散余弦变换算法进行处理,所得到的解包裹结果与未加噪声的解包裹相位值进行比较,结果表明,通过加权离散余弦变换算法恢复的相位图比非加权离散余弦变换算法所恢复的相位图更接近于理想值,而且两种算法的运行速度基本相同,这证明提出的算法不仅保证了效率高的优点,而且所恢复的解包裹相位具有较好的噪声免疫能力和可靠度。     

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.     

基于结构光编码的相展开方法

探讨了一种新的基于结构光编码相展开技术。实现方法是先将计算机构造的用于解相的光栅由投影仪投射到物体上 ,再将计算机构造的一系列黑白相间的编码光栅也由投影仪投射到物体上 ,然后将畸变栅线图像由摄像机采集到计算机中 ,用解相光栅进行解相得到折叠在 [-π ,π]区间内的相主值 ,用所述结构光编码方法进行相展开得到相位的周期 ,二者相加得到真实相位值。与传统的相展开方法相比 ,该方法相展开过程变得相对简单 ,不依赖于路径 ,不存在误差的传播 ,对噪声的抗干扰能力强 ,能够得到准确的周期 ,并能够与解相过程有机结合起来。实验证明该方法获取光栅周期快速、准确     

Temporal phase unwrapping using orthographic projection

This paper proposes a novel temporal phase unwrapping method which is a generalization of the three commonly proposed approaches: hierarchical, heterodyne, and number theoretical phase unwrapping. The proposed unwrapping method is based on the orthographic projection of wrapped phases from the measurement space to the space of co-dimension 1. In the space of co-dimension 1 all unknown integer period-order numbers are computed simultaneously using a nearest-neighbor search on a fixed constellation of points. The proposed method offers new key insights about relationship between unwrapping success rate, noise limit, and maximum unwrapping range. We give example how the proposed method may be applied in the multiple frequency phase shifting profilometry.     

Robust wrapping-free phase retrieval method based on weighted least squares method

Phase unwrapping is one of the most challenging processes in many profilometry techniques. To sidestep the phase unwrapping process, Perciante et al. (2015) proposed a wrapping-free method to retrieve the phase based on the direct integration of the spatial derivatives of the fringe patterns. However, this method is only applicable to objects with phase continuity, so it may fail to handle fringe patterns containing complicated singularities such as noise, shadows, shears and surface discontinuities. In the light of this problems, a robust wrapping-free phase retrieval method is proposed that is based on the combined use of Perciante's method and the weighted least squares method. Two partial derivatives of the desired phase are obtained from the fringe patterns, while the carrier is eliminated using the direct phase difference method. The phase singularities are determined using a derivative variance correlation map (DVCM), and the weighting coefficient is obtained from the binary mask of the reverse DVCM. Simulations and experiments are conducted to prove the validity of the proposed method. The results are analyzed and compared with those of Perciante's method demonstrating that in addition to maintaining the advantage of sidestepping the phase unwrapping process, the proposed method is available for measuring objects with some types of singularities sources.     

基于希尔伯特变换的干涉条纹相位解调新算法

提出了一种新的应用希尔伯特变换解调干涉条纹相位的算法,可以从单幅干涉条纹图中解调出全场相位分布.在实际应用中,常借助傅里叶变换实现希尔伯特变换算法,但是会忽略负频率成分,造成相位信息的丢失.对于相位分布非单调变化的干涉条纹,提出了一种判断函数,用来计算相位信息零频率点的分布.利用相位的零频率点分布构造了一个二元模板,使用该模板对本文提出的两次希尔伯特变换法产生的包裹相位图进行修正.对修正后的包裹相位图进行解包裹处理,可以得到连续的全场相位分布.对该方法用计算机模拟进行了验证.     

含噪声包裹相位图的加权最小二乘相位展开算法研究

二维相位展开广泛应用在精密光学测量、自适应光学、合成孔径雷达、图像处理等领域中。为处理含噪声包裹相位图,以预条件共轭斜量法求解权重最小二乘相位展开方程。引入非加权二维离散余弦变换求解泊松方程得到的最小二乘相位解作为共轭斜量法的初始解,从而加快了收敛速度,同时提出一种新质量图确定算法求解过程中的权重项。计算机模拟和试验表明算法计算速度快,能有效地消除传统路径积分法在处理信噪比低包裹相位图时的"拉线"现象,是一种有效的相位展开方法。     

Evaluation of absolute phase for 3D profile measurement using fringe projection

A new method of absolute phase evaluation for three-dimensional (3D) profile measurement using fringe projection is presented, which combines the gray code and the phase shift technique. Two kinds of fringe patterns are projected onto the object surface respectively, one is sinusoidal intensity distribution used for phase demodulation and the other is gray code fringe pattern for unwrapping. These images are acquired by camera and stored into computer. The absolute phase is obtained by analyzing these images. The validity of this method is verified experimentally. The method is superior to other phase unwrapping methods.     

调制度分析在等步长相移法相位展开中的应用

推导了两种常用等步长相移算法的调制度表达式,提出一种新的调制度分析方法。该方法用于等步长相移法中基于加权最小二乘法的相位展开,能够充分利用调制度信息,构造二值和小数权重,从而增强相位展开过程对多种干扰因素的免疫力。实验结果说明了该方法的有效性和实用性。最后比较了二值权重和小数权重在加权最小二乘法的相位展开中的性能表现。     

Micro-phase measuring profilometry: Its sensitivity analysis and phase unwrapping

Global illumination affects shape measurement accuracy, and phase unwrapping is an important problem in phase measuring profilometry. In this paper, a micro-phase measuring profilometry is proposed to reduce the effects of global illumination. The wrapped phase error level of the proposed method is lower than that of the traditional micro-phase shifting method. First, a frequency selection rule is developed in combination with the micro-phase rule to design the frequencies of the proposed phase measuring profilometry. The frequency rule is obtained by analysing the uncertainty of the wrapped phase caused by intensity noise. Then, phase unwrapping is regarded as a congruence problem, and the closed-form robust Chinese remainder theorem algorithm is adopted to determine the correspondence. Finally, the comparative experiments are conducted on a projector-camera system. Experimental results show that the effects of global illumination can be effectively reduced with the proposed phase measuring profilometry, and the proposed frequency selection rule is valid. In addition, the performance of the robust Chinese remainder theorem in addressing the phase error is better than that of traditional Chinese remainder theorem. Furthermore, the unwrapping accuracy can nearly reach 100% if the frequency selection rule is satisfied. Otherwise, the performance degrades.     

A generalized temporal phase unwrapping algorithm for three-dimensional profilometry

A generalized temporal phase unwrapping algorithm is proposed for absolute phase measurement of object surfaces with complex topography. We first make comments on error analysis of various temporal phase unwrapping (TPU) algorithms and point out problems existing in these techniques. We present a generalized TPU algorithm (GTPU), which eliminates some limitations imposed on the fringe sequence for the classical TPU algorithms. So the desired number of fringes can be determined according to practical situation, leading to a flexible method for phase reconstruction. In addition, compared with the classical TPU algorithms, GTPU has better noise immunity and less computational complexity. Theoretical analysis and experiment results are presented to show the validity of the proposed algorithm.     

Phase retrieval in two-wavelength DSSI using a combined filtering method

Phase retrieval in two-wavelength DSSI (digital speckle shearing interferometry) using a combined filtering method is proposed for small deformation derivative measurement. A simultaneous two-wavelength illumination and 3-CCD camera are employed in the experimental setup. The proposed method, which uses a two-wavelength technique does not require the conventional spatial phase unwrapping and has the advantage of good noise suppression for phase retrieval. Experimental results obtained show that using the proposed combined filtering method sensitivity similar to the single wavelength technique can be achieved.     

3-D shape measurement based on complementary Gray-code light

A combination of phase-shift with Gray-code light projection into a three-dimensional (3-D) measurement system has been exploited to digitalize 3-D shape information of a tested object, even with a discontinuous surface. Unfortunately, the phase unwrapping will fall into an error, when an improper value of Gray coding is caused by mistake at the partial boundary of two adjacent binary words. To this end, a new complementary Gray-code method is proposed in this paper as well as the corresponding phase-unwrapping method. This problem of phase unwrapping could be cleverly solved by projecting an additional Gray-code pattern to extend this code and using the different and complementary boundary locations of the traditional and additional codes. The results of computer simulation and experiment confirm that this proposed method based on complementary Gray-code can reliably reconstruct the nature phase distribution of the tested object with only one extra fringe pattern.     

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.     

Surface contouring by phase-shifting digital holography

Surface contouring by phase-shifting digital holography is proposed that provides surface height from a change of reconstructed object phases due to the tilt of object illumination. Surface height from a reference plane is directly obtained from the phase change. Its sensitivity depends on the tilt angle as well as on the initial incident angle. By proper selection of the angles we can derive surface height without phase unwrapping. The sensitivity can be enhanced by increasing the tilt angle. Then we need phase unwrapping that is sensitive to noise due to laser speckles in the reconstructed images. This noise could be suppressed by selecting phase values at points of the maximum product of amplitudes before and after the illumination change in the course of data reduction from 1024×1024 to 512×512 and by selecting paths for phase unwrapping by looking for the intensity maximum. The observed height resolution is 20 μm. Effects of numerical focusing have also been investigated. The present method has the same sensitivity as the fringe projection method, but it has larger measurement depth and is also applicable to the deformation measurement with the same arrangement.     

一种新的快速解相位方法

提出了一种快速可靠的4步相移编码-解相位算法。通过对中心条纹的光强进行摄动,将编码信息加入到基本相移光栅中,使4幅基本相移图不但包含了相位场主值信息,还包含了解相位所需的编码信息。建立了摄动度函数描述相移图的摄动信息进而得到编码信息,解出完整的相位值。对摄动度函数的误差和噪声进行分析,提出方向滤波方法来消除噪声,极大地减少了编码信息的误判情况。仿真和实验证实了本算法的可行性。与传统相移法相比,解相位的速度和可靠性得到明显的提高。     

基于平面估计的三维测量相位展开新方法

工业自动化生产中微米级的三维测量大多采用相位测量轮廓术,但其中现有的包裹相位展开方法容易受图像噪声和相位突变的干扰;在电路板贴片安装的锡膏三维测量中,利用电路板的平面区域包裹相位信息进行平面估计,然后全局相位展开向拟合平面靠拢,根据统计信息确定参数,得到连续相位;利用展开后的相位再进行电路板平面的二次曲面拟合,提高基平面的拟合精度和相对高度;对比实验证明了该方法的鲁棒性和快速性,处理时间短,不受噪声、相位突变、阴影等干扰。     

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.