Study on an improved five-interferogram phase-shifting algorithm

Using traditional five-interferogram algorithm to unwrap phase for length measurement, the phase steps must be equal to π/2 exactly, but it is almost impossible to achieve in nanometer positioning technique.Aiming to overcome this defect of traditional five-interferogram algorithm, an improved five-interferogram algorithm is presented.This improved algorithm not only keeps the high accuracy of traditional five-interferogram algorithm, but also does not need absolute equal step to unwrap phase.Instead, this algorithm only needs measuring phase-shifting.With the numerical simulation, the improved five-interferogram algorithm shows high accuracy, high reliability, and feasibility in practice.It is very valuable for accurate length measurement with Fizeau interferometer and Fabry-Perot interferometer.     

基于主元分析的随机相移算法

将统计理论中的主元分析应用到干涉条纹分析中,提出一种基于主元分析的随机相移算法。该算法先将多帧条纹数据分解成不相关的主元成分,然后从主元成分中提取2维相位信息。数值模拟结果表明:该算法不需要迭代运算就能从4帧完全随机相移干涉图中有效提取相位信息,运算时间少,精度高。实验结果表明主元分析相移算法比现有迭代相移算法更适合于随机相移干涉图分析。     

Profile measurement of a moving object using an improved projection grating phase-shifting profilometry

3-D profile measurement of a moving object using a novel phase-shifting technique is introduced. Digital gratings with two steps phase-shifting are projected periodically onto a measured object surface. The deformed fringe patterns are captured by a frame CCD camera within a short exposure time. By synchronizing the projector and the CCD camera accurately, there is an overlapping part which is the same part of the object among three neighbouring frames. The length of an overlapping part can be controlled as one third of a frame length. Hence the intensity values at the same surface point modulated by three neighbouring gratings can be obtained, and its phase value can be computed by an improved phase-extracting algorithm. The profile of a specimen is detected by the proposed method. Experimental results demonstrate that this method is effective for the profile measurement of a moving object.     

Efficient iterative algorithm for phase-shifting interferometry

This paper presents an efficient iterative least-squares algorithm for phase-shifting interferometry. If the phase shifts contain errors, the residuals (i.e. the differences between the recorded intensities and their recalculated values) of least-squares algorithm are dependent on these errors. Based on this fact, an approach that allows estimating the phase shift errors from these residuals is derived. Using the results, the values of phase shifts are corrected. By iterating the two steps: phase evaluation and phase shift correction, the phase distribution can be accurately reconstructed. Its validity and performances have been investigated by both the numerical simulation and experiment results. The convergence condition with this algorithm is also discussed.     

Discussions about FFT-based two-step phase-shifting algorithm

An FFT-based two-step phase-shifting (TPS) algorithm is described in detail and implemented by use of experimental interferograms. This algorithm has been proposed to solve the TPS problem with random phase shift except π. By comparison with the visibility-function-based TPS algorithm, it proves that the FFT-based algorithm has obvious advantages in phase extracting. Meanwhile, we present a π-phase-shift supplement to the TPS algorithm, which combines the two interferograms and demodulates the phase map by locating the extrema of the combined fringes after removing the respective backgrounds. So combining this method and FFT-based one, one could really implement the TPS with random phase shift. Whereafter, we systematically compare the TPS with single-interferogram analysis algorithm and conventional three-step phase-shifting one. The results demonstrate that the FFT-based TPS algorithm has a satisfactory accuracy. At last, based on the polarizing interferometry, a schematic setup of two-channel TPS interferometer with random phase shift is suggested to implement the simultaneous collection of interferograms.     

一种基于移相误差估计的5步移相算法

移相误差是用移相法进行相位测量的主要误差。本文提出一种 5步移相算法 ,分两步进行相位计算 ,首先估计实际步进移相的线性移相误差 ,然后再利用此移相误差估计值计算相位分布。移相误差估计公式和相位计算公式简洁 ,算法简单易行 ,对线性移相误差和二次谐波的敏感度低 ,可基本消除线性移相误差对解调相位的影响。对本文提出的算法进行了仿真研究 ,同时给出了 Hariharan 5步算法、Surrel 6步最小算法的仿真结果。结果表明 :本算法明显优于以上两种算法 ,可基本消除线性移相误差引起的相位偏移。本算法适用于作等步移相的相位测量或移相的标定。     

优化的两步相移算法在图像加密中的应用研究

优化了此前提出的两步相移算法,仅通过两幅去除背景光强(或抑制直流分量)后的干涉图数据和一个(0,π)区间的相移值,就可以成功再现出原始物波场信息,无需借助于物光光强、参考光光强等其他辅助测量信息.与菲涅耳域的双随机相位编码技术结合,该优化算法可以应用于图像加密方案中,通过计算机仿真实验验证了所提方案的可行性,并对几何密钥的灵敏度进行了测试分析.     

Community detection based on modularity and an improved genetic algorithm

Complex networks are widely applied in every aspect of human society, and community detection is a research hotspot in complex networks. Many algorithms use modularity as the objective function, which can simplify the algorithm. In this paper, a community detection method based on modularity and an improved genetic algorithm (MIGA) is put forward. MIGA takes the modularity Q$Q$ as the objective function, which can simplify the algorithm, and uses prior information (the number of community structures), which makes the algorithm more targeted and improves the stability and accuracy of community detection. Meanwhile, MIGA takes the simulated annealing method as the local search method, which can improve the ability of local search by adjusting the parameters. Compared with the state-of-art algorithms, simulation results on computer-generated and four real-world networks reflect the effectiveness of MIGA.     

Study on a novel phase-recovering algorithm for partial intensity saturation in digital projection grating phase-shifting profilometry

The phase error and its periodic behavior caused by the partial intensity saturation of fringe patterns in the digital projection grating phase-shifting profilometry are studied. A saturation coefficient K is defined to describe the saturation degree of the fringe patterns projected on a measured object. The distribution of the phase error is analyzed through a simulation method. Moreover, a novel phase-recovering algorithm is studied to resolve the phase error issue introduced by the partial saturated fringe patterns. The real phase can be recovered by the unsaturated intensity values. A series of results corresponding to different degrees of saturation defined by K are given to prove the validity of the proposed algorithm.     

一种基于希尔伯特变换实施相移的相位解调算法

相移法因其精度高、运算简单,所以被广泛应用于形貌检测中的相位解调。该方法的弱点是:不仅要采集多幅相移图像,而且不能克服相移器的移相误差。将小波分析与希尔伯特变换结合起来,采用小波分析去除直流背景成分,利用希尔伯特变换方法实现90°相移;利用相移法解调形貌相位,由于是采用软件来实现相移的,因此只需采集一幅变形栅线图。对该方法与传统相移技术进行了模拟比较实验,结果表明,该方法具有较高的精度。     

Analysis of the principal component algorithm in phase-shifting interferometry

We recently presented a new asynchronous demodulation method for phase-sampling interferometry. The method is based in the principal component analysis (PCA) technique. In the former work, the PCA method was derived heuristically. In this work, we present an in-depth analysis of the PCA demodulation method.     

Real-time quantitative phase imaging with a spatial phase-shifting algorithm

This Letter reports on the use of a spatial phase-shifting algorithm in a fast, straightforward method of real-time quantitative phase imaging. The computation time for phase extraction is five times faster than a Fourier transform and twice as fast as a Hilbert transform. The fact that the phase extraction from an interferogram of 512 × 512 pixels takes less than 8.93 ms with a typical desktop computer suggests the proposed method can be readily applied to high-speed dynamic quantitative phase imaging. The proposed method of quantitative phase imaging is effective and sufficiently general for application to the dynamic phenomena of biological samples.     

基于模糊多核学习的改进支持向量机算法研究

针对传统SVM对噪声点和孤立点敏感的问题,以及不能解决样本特征规模大、含有异构信息、在特征空间中分布不平坦的问题,将模糊隶属度融入多核学习中,提出了一种模糊多核学习的方法。通过实验验证了模糊多核学习比传统SVM、模糊支持向量机以及多核学习具有更好的分类效果,从而验证了所提方法能够有效的克服传统SVM对噪声点敏感以及数据分布不平坦的问题。     

Study on the simplified phase-shifting digital holographic microscopy

In this paper, a new simplified technique for effectively eliminating the zero order and the conjugate virtual image in digital holographic microcopy, which makes use of two-step phase-shifting method of just recording two holograms and an intensity image of object wave, is proposed. Meanwhile, combined with the principle of making full use of spatial bandwidth of the CCD sensor by in-line lens-less Fourier holographic recording geometry, the theory and experimental methods to increase the resolution of the reconstructed image in digital holography by using phase-shifting technique are detailedly analyzed. At end, the validity and availability of this technique has been demonstrated through the off-axis and in-line Fourier transform recording geometry. The study provides some theoretical and experimental guidance for the design and operation of a digital holographic microscopy system.     

Study on digital holography with single phase-shifting operation

The digital holography with single phase-shifting operation has been studied. Experimental results and computer-simulated work are presented. The phase-shifting error makes the intensity of primary image decrease and the conjugate image appear in reconstruction. The explicit equation for explaining these effects is given. The calculation of the normalized intercorrelation peak between the input and the reconstruction for different algorithms shows that, when the phase-shifting operation is the main error source, the quality of the image reconstructed from the digital holography with single phase-shifting operation is favorable.     

Generalized phase-shifting algorithm for dynamic phase measurement in electron-wave interferometry

A generalized phase-shifting algorithm is implemented in the electron-wave interferometry with a transmission electron microscope, based on simultaneous measurement of the initial phases of the interferograms. The initial phase of each interferogram that has inherent linear carrier fringes is calculated using the Fourier co-efiicients of the interferogram itself corresponding to the carrier-frequency. Taking advantage of this phase-shifting method in both spatial resolution and precision, the phase distribution of a biological weak phase object is successfully measured. This promises to be one of the most spectacular application fields for this new technology.     

Study on two-dimensional distribution of X-ray image based on improved Elman algorithm

The principle of the X-ray detector which can simultaneously perform the measurement of the exposure rate and 2D (two-dimensional) distribution is described. A commercially available CMOS image sensor has been adopted as the key part to receive X-ray without any scintillators. The correlation between the pixel value (PV) and the absorbed exposure rate of X-ray is studied using the improved Elman neural network. Comparing the optimal adjustment process of the BP (Back Propagation) neural network and the improved Elman neural network, the neural network parameters are selected based on the fitting curve and the error curve. The experiments using the practical production data show that the proposed method achieves high accurate predictions to 10⁻¹⁵, which is consistent with the anticipated value. It is proven that it is possible to detect the exposure rate using the X-ray detector with the improved Elman algorithm for its advantages of fast converges and smooth error curve.     

Application of an improved subpixel registration algorithm on digital speckle correlation measurement

Digital speckle correlation method (DSCM) has been widely used in experimental mechanics to obtain the surface deformation fields. One of the challenges in practical applications is how to obtain the high accuracy with far less computation complexity. To determine the subpixel registration of the DSCM, a high efficient gradient-based algorithm is developed in this paper. The principle is described and four different modes of the algorithm are given. Based on computer-simulated images, the optimal mode of the algorithm is verified through the comparison of computation time, optimal subset-region size and sensitivity of the four modes. The influences of speckle-granule size and speckle-granule density on accuracy are studied and a quantitative estimation of the optimal speckle-granule size range is obtained. As the applications of this method, the practical deformation measurements with the rigid body translation and rotation as well as an experiment on biomechanics are presented to certify the feasibility and the validity of the algorithm.     

用于相移点衍射干涉仪的加权最小二乘相位提取算法

针对现有的相位提取算法只对某些特定的误差不敏感,不能满足高精度光学检测的要求,本文引入一种等间隔多步移相算法—权重待定的加权最小二乘算法。通过在最小二乘算法中添加待定的权重,分析移相点衍射干涉仪中多种误差源对算法的影响,获得多组约束方程,从而确定权重和新算法。对新算法和标准四步算法、Hariharan五步算法进行比对分析,验证了新算法对PZT线性和二阶非线性移相不准、光强的一阶二阶波动和光源频率一阶二阶波动等误差抑制能力远远优于标准四步算法和Hariharan五步算法;新算法对CCD的量化误差、光强噪声、频率噪声的抑制能力也具有一定优势,且对CCD的二阶响应非线性完全不敏感。