An Improvement of Spatial Carrier Phase-shifting Method

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Volume quantification by fuzzy logic modelling in freehand ultrasound imaging

Introduction

Many algorithms exist for 3D reconstruction of data from freehand 2D ultrasound slices. These methods are based on interpolation techniques to fill the voxels from the pixels. For quantification purposes, segmentation is involved to delineate the structure of interest. However, speckle and partial volume effect errors can affect quantification.

Objective

This study aimed to assess the effect of the combination of a fuzzy model and 3D reconstruction algorithms of freehand ultrasound images on these errors.

Methods

We introduced a fuzzification step to correct the initial segmentation, by weighting the pixels by a distribution function, taking into account the local gray levels, the orientation of the local gradient, and the local contrast-to-noise ratio. We then used two of the most wide-spread reconstruction algorithms (pixel nearest neighbour (PNN) and voxel nearest neighbour (VNN)) to interpolate and create the volume of the structure. Finally, defuzzification was used to estimate the optimal volume.

Validation

B-scans were acquired using 5 MHz and 8 MHz ultrasound probes on ultrasound tissue-mimicking phantoms. Quantitative evaluation of the reconstructed structures was done by comparing the method output to the real volumes. Comparison was also done with classical PNN and VNN algorithms.

Results

With the fuzzy model quantification errors were less than 4.3%, whereas with classical algorithms, errors were larger (10.3% using PNN, 17.2% using VNN). Furthermore, for very small structures (0.5 cm³), errors reached 24.3% using the classical VNN algorithm, while they were about 9.6% with the fuzzy VNN model.

Conclusion

These experiments prove that the fuzzy model allows volumes to be determined with better accuracy and reproducibility, especially for small structures (<3 cm³).     

基于相位展开及拼接算法的一种高精度大量程宽光谱干涉显微术

宽光谱干涉显微术广泛应用于高精密检测领域,它测量样品形貌通常采用垂直扫描干涉术对亚微米至毫米级特征进行测量,以及相移干涉术对纳米级特征进行测量。其中,相移干涉术精度可达纳米级,但量程有限,高度变化对应的相位需限制在区间内。采用包裹相位展开算法可以扩展相移干涉术的量程,也仅适用于平滑表面,当高度起伏超出焦深或者光源相干长度的限定范围时,干涉条纹模糊或对比度丧失,所解算的结果将产生较大误差甚至错误。提出一种基于相位展开及拼接算法的高精度、大量程宽光谱干涉显微测量方法,以干涉条纹调制度量化条纹质量,条纹对比度高、成像清晰的区域对应调制度较高,定义当前焦面条纹调制度高于阈值的区域为理想区域,定义焦面条纹调制度低于阈值的区域为问题区域。以相位展开算法获得理想区域中的样品相位分布,问题区域的包裹相位不进行展开。使用微位移结构纵向移动物镜焦平面,选择合理的步长,使相邻焦面位置理想区域展开后的真实相位保持部分区域重合,根据重合区域的相位值均差可以实现不同焦面位置的高精度相位拼接,最终获得扩展量程的高精度真实相位结果,进而可以恢复样品完整的表面形貌分布。该算法通过对理想区域的筛选,避免了相位在问题区域展...     

Beam steering approach for high-precision spatial light modulators

Steering accuracy is limited by the quantized phase modulation values and the number of phase pixels for spatial light modulators （SLMs）.Conventional methods of beam steering lack optimum precision.In this letter,a beam steering approach based on horizontally moving phase steps is proposed.Compared with the conventional methods,this novel method is able to reduce the maximum normalized steering error in SLM significantly by a factor proportional to the number of pixels.In addition,steering errors of high steering angles can be drastically reduced by a factor proportional to the product of the number of pixels and the quantized phase levels; the number of high-precision steering angles increases with the number of pixels or the quantized phase levels increasing.     

Improved accuracy phase retrieval in spatial phase-shifting interferometry

Algorithms for phase retrieval in spatial phase-shifting interferometry are examined. It is noticed that the classical Carré technique based on four neighbor pixels may introduce shaped phase residuals that affect the accuracy of the reconstruction. A variant of the technique is proposed, taking into consideration five pixels and steering the phase retrieval algorithm to the appropriate subset so that residuals are free of underlying errors. Computational results are presented illustrating the approach and demonstrating the accuracy improvement in a case study.     

Non-iterative spot center location algorithm based on Gaussian for fish-eye imaging laser warning system

The directional accuracy of threaten laser is highly dependent on the laser spot center location accuracy for the laser warning system. On the basis of analyzing the spot features on wide field of view (FOV) fish-eye imaging laser warning system, a refinement of existing methodology based on fitting a 2D Gaussian distribution for estimating the center of the spot is developed. The proposed procedure is using a linear least squares based algorithm to determine the best-fitting parameters of the Gaussian. However, in contrast to the standard Gaussian Fitting procedure, this new scheme gives rise to equations that are rigorously linear in the transformed unknown parameters which can be solved easily by linear least squares estimators. To validate the accuracy of the proposed algorithms, experimental approaches with a type of laser warning detector and simulated threaten laser in laboratory are used to quantify its performance. The experimental results show that this method outperforms significantly the commonly used location technique. It is less susceptible to the non-100% fill ratio of CMOS and large unsymmetrical optical aberration of fish-eye lens. The positioning precision in paraxial region and 80° incident angle region are 1/60 pixels, 1/30 pixels respectively. The biggest error is less than 1/20 pixels. The proposed method is suitable for wide FOV laser warning system for high accuracy and low computational complexity.     

高精度六面体垂直度误差测量的一种新方法

介绍了一种利用波面干涉仪和精度为0.2″的端齿盘组合测量六面体相邻两面垂直度误差的新方法,建立了基于最小二乘算法的评定垂直度误差分布的数学模型,介绍了测量装置及测量实验步骤。该方法不但测量精度高,而且能够获得两个面之间垂直度误差分布数据,可用于六面体面体形位误差的高精度修形加工。针对精度为2″的标准直角棱镜的测量实验表明该方法测量结果可信,精度优于0.5″。可推广到其他多面体类零件形位误差的高精度测量。     

基于选择采样的高效迭代相位提取算法

在光学精密测量中,相移干涉法应用广泛。常用的相移器件容易出现相移误差,采用等步距相位提取算法会产生测量误差。基于最小二乘的迭代相位提取算法可以有效消除该类相位提取误差,提高测量精度,但是其迭代过程运行时间长,效率低。提出了一种基于选择采样的迭代相位提取算法,先对干涉图像进行等间隔抽样,降低计算量;再根据对比度滤除干涉图像中低质量像素点,防止误差增大,进行最小二乘迭代求解相位。仿真实验对算法进行了分析和验证,在抽样间隔为2时的选择采样方法与所有像素点全部代入计算相比,运行时间从6.687 s降为0.725 s,均方根误差仅为0.032 9。实验结果证明:选择采样的迭代相位提取算法运算时间短、误差小,非常适合高速相移干涉测量应用。     

基于一阶泰勒展开式的迭代最小二乘相移新算法

提出了一种新的最小二乘迭代算法 ,能有效消除因相移器存在导向误差面使相移平面倾斜从而导致的相移误差。当相移器存在的相移误差包括位移误差与倾斜误差时 ,同一幅干涉图诸像素点的相移并不同步 ,但其相移量在同一平面上。求解此平面 ,即可消除相移误差。通过求解由一阶泰勒展开式得到的线性方程组 ,避免了为求解此平面而求解非线性方程组最小二乘解的过程 ,使算法简化。利用迭代法 ,保证求解的精度。并通过数值模拟 ,验证了这种算法在消除较大的相移器倾斜及位移误差影响上具有良好的效果。     

Phase Measurement Algorithm without Phase unwrapping Problem for Phase stepping interferometry

１ＩｎｔｒｏｄｕｃｔｉｏｎＰｈａｓｅｓｔｅｐｐｉｎｇｉｎｔｅｒｆｅｒｏｍｅｔｒｙｈａｓｂｅｅｎｅｘｔｅｎｓｉｖｅｌｙａｐｐｌｉｅｄｉｎｍａｎｙａｓｐｅｃｔｓ．Ｃｏｎｖｅｎｔｉｏｎａｌｐｈａｓｅｕｎｗｒａｐｐｉｎｇｉｓｉｍｐｌｅｍｅｎｔｅｄｂｙｔｈ...     

基于高斯拟合的激光光斑中心定位算法

激光光斑中心定位是光学测量中的关键技术之一。通过对常用定位算法的分析,给出利用光斑图像中的不饱和点对光斑进行高斯拟合,并以拟合函数的幅值点作为光斑中心的方法。利用人工光斑对该算法进行验证,结果表明该算法误差远小于0.1 像素;利用一维高精度电动平移台、CCD相机、激光器等搭建测试系统,由计算机自动采集激光光斑图像并对其进行分析,实验结果表明该算法与理论分析结果的均方根误差仅为0.1 像素。     

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.     

分振幅型全Stokes同时偏振成像系统波片相位延迟误差分析

分振幅型全Stokes同时偏振成像仪具有实时性好、空间分辨率高、精度高等优点,有很高的应用价值.分振幅型全Stokes同时偏振成像系统利用偏振分束器、1/2波片和1/4波片将入射光Stokes矢量调制在4幅图像中,可解析入射光Stokes矢量. 1/2波片和1/4波片的相位延迟误差对Stokes矢量测量精度有着不可忽略的影响.建立了包含上述两种误差的Stokes矢量测量误差方程,分析了1/2波片和1/4波片相位延迟耦合误差对自然光、0°/45°线偏光、左旋圆偏光等典型基态入射光的Stokes矢量测量误差的影响,推导了任意偏振态的Stokes矢量测量误差的表征方法.在邦加球球面和球内选取不同偏振度的Stokes矢量作为入射光进行仿真.结果表明, Stokes矢量测量误差和偏振度测量误差均随着入射光偏振度的增大而增大.选取入射光偏振度为1时的偏振测量精度评估系统.为满足2%的偏振测量精度, 1/2波片相位延迟误差应在±1.6°内, 1/4波片相位延迟误差应在±0.5°内.这对提高系统的偏振测量精度具有重要意义,为系统设计和研制提供了重要的理论指导.     

一种基于电光调制光频梳光谱干涉的绝对测距方法

提出了一种基于电光调制光学频率梳的光谱干涉测距方法.理论分析了电光调制光学频率梳的数学模型和光谱扩展原理,并分析得出了光谱干涉测距方法的非模糊范围和分辨力的影响因素.在实验中,使用三只级联的电光相位调制器调制单频连续波激光生成了40多阶高功率梳齿状边带,并通过单模光纤和高非线性光纤对电光调制器输出的激光进行光谱扩展,得到重复频率为10 GHz,光谱宽度达30 nm的光学频率梳.将该光频梳作为光谱干涉测距装置的光源,可以实现无"死区"的绝对距离测量.另外,使用等频率间隔重采样和二次方程脉冲峰值拟合算法对测量结果进行数据处理,可以修正系统误差,提升测距精度.实验结果表明,在1 m的测量范围内,使用该装置可以在任意位置达到±15μm以内的绝对测距精度.     

拼接式编码器测角误差分析及试验

根据望远镜测角系统的精度需求,分析了影响拼接式编码器测角精度的误差源,以及多读数头测角消差原理,确定了采用相位相差90°的4读数头的测角方式。在某望远镜方位轴系转台进行了逆时针和顺时针方向的测角试验,通过对测角数据进行谐波分析并补偿后,得到两组实验测角误差RMS分别为0.34"、0.38"。实验表明,相位相差90°的均布4读数头的测角方式消除了由轴系误差、编码器安装位置误差和钢带安装盘部分圆度误差对测角精度的影响,实现了亚角秒级测角的目的。研究结果可用于大口径望远镜设计阶段的误差分析与分配、预估测角精度,为降低设计和加工误差提供参考。     

光栅投影三维测量系统标定技术研究

相机与投影仪的标定是影响光栅投影三维测量系统精度的因素之一,且标定所得参数的精度直接影响系统的测量精度。分析标志点边缘成像时的退化模型,提出了基于高斯曲线拟合与边缘局部区域效应相结合的亚像素边缘检测方法,获取高精度边缘,提高标志点检测精度;使用基于透视变换图像矫正的标志点快速排序匹配方法,进行相机快速高精度标定。分析投影仪标定时的相位误差,提出了一种基于径向基的线性插值方式,提高标志点圆心相位获取精度。实验验证,使用上述亚像素边缘检测方式,标志点的边缘残差为0.0871,对比基于高斯曲线的拟合方式,精度提高了41%,相机标定重投影误差均值为0.0524像素;使用上述相位插值方式,投影仪标定重投影误差均值为0.1203像素,对比使用双线性插值方式,标定精度提高23.9%。     

利用相邻相关像素进行噪音抑制的模糊小目标检测算法

提出了一种利用相邻相关像素对红外数字图像中的可疑小目标进行检测的算法.该算法首先利用自适应全局阈值检测图像中的亮像素,并借助相邻相关像素信息滤除结果中的亮噪音点;然后依据亮像素的相关性,对剩余的亮像素进行加强,并再次抑制噪音,获得可观的信噪比增益.相对于传统的Top-Hat变换,该算法能够在有效提高待检测目标信号强度的同时很好地抑制噪音,有效地保留了目标图像的边缘细节.     

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.     

利用相邻相关像素进行噪音抑制的模糊小目标检测算法

提出了一种利用相邻相关像素对红外数字图像中的可疑小目标进行检测的算法. 该算法首先利用自适应全局阈值检测图像中的亮像素,并借助相邻相关像素信息滤除结果中的亮噪音点;然后依据亮像素的相关性,对剩余的亮像素进行加强,并再次抑制噪音,获得可观的信噪比增益.相对于传统的Top-Hat变换,该算法能够在有效提高待检测目标信号强度的同时很好地抑制噪音,有效地保留了目标图像的边缘细节.     

Comparison of eight unwrapping algorithms applied to Fourier-transform profilometry

Phase unwrapping is a task common to many applications like interferometry imaging, medical magnetic resonance imaging, solid-state physics, etc. Fourier transform profilometry (FTP) values the height distribution of object, elaborating the interference between a plane reference grating and a deformed object grating. Since the height information is extracted from the phase of a complex function, the phase unwrapping is a critical step of the process. Several unwrapping algorithms are proposed in literature, but applied to measurement technologies different from FTP. The purpose of this paper is to define the performances of eight different unwrapping algorithms applied to FTP optical scan method and to define the best one. The algorithms chosen are: Goldstein's algorithm, quality guided path following method, Mask cut method, Flynn's method, multi-grid method, weighted multi-grid method, preconditioned conjugate gradient method and minimum L_p-norm method. The methods were tested on real images acquired by a FTP scanner developed and calibrated for these experiments. The objects used vary from simple geometries, like planes and cylinders, to complex shapes of common use objects. Algorithms were qualified considering the phase unwrapping errors, execution time and accuracy of the shape of objects obtained from the scan method in comparison with real ones. The results show that quality guided algorithm best fits in FTP application.