InP/InGaAsP多量子阱自发辐射谱的解析函数

利用洛伦兹线型函数、高斯线型函数和Sech线型函数对InP/InGaAsP多量子阱自发辐射谱进行拟合,采用莱文贝格-马夸特算法,得到上述三种函数的解析表达式.研究结果表明:高斯线型光谱拟合函数的中心波长为1548.651nm,谱线半极大全宽度为61.42 nm,功率补偿为0.00212 mW,拟合优度为0.99191,残差平方和为2.26505×10~(-6).高斯线型拟合的拟合优度最大,残差平方和最小,且各数据点的残差值分布在±0.0001之间,分布比较均匀.高斯线型函数具有较高拟合度.     

腔衰荡光谱技术中衰荡时间的准确快速提取

对NO₃腔衰荡光谱(cavity ring-down spectroscopy,CRDS)探测系统中衰荡时间的准确提取方法进行了研究。对衰荡时间有效快速的提取可以提高CRDS测量的精度和速度。选取了五种常用的提取衰荡时间的拟合方法,分别为快速傅里叶变换法、离散傅里叶变换法、线性回归总和法、列文伯格-马夸尔特算法和最小二乘法。采用以上五种算法对带有不同大小白噪声的模拟衰荡信号进行拟合,并从受噪声影响情况、拟合准确性和精度、拟合速率,三个方面对五种算法的拟合结果进行对比和分析,结果表明列文伯格-马夸尔特算法和线性回归总和法准确度高、抗噪能力强,但列文伯格-马夸尔特算法拟合速率相对较慢。选取衰荡时间的5～10倍为衰荡信号的最佳拟合波形长度,此时五种算法拟合结果的标准偏差最小。采用外部调制二极管激光器及高反腔搭建CRDS探测系统,针对0.2%噪声的实验条件,选取线性回归总和法和列文伯格-马夸尔特算法对实际测量的实验数据进行处理。实验表明,线性回归总和法拟合准确度和精度与列文伯格-马夸尔特算法相似,但拟合速率比列文伯格-马夸尔特算法快约5倍。实验结果与模拟分析相吻合,表明线性回归总和法为适合我们实验条件的最佳拟合方法。     

Advanced diffusion models in head and neck squamous cell carcinoma patients: Goodness of fit,relationships among diffusion parameters and comparison with dynamic contrast-enhanced perfusion

PurposeWe assessed advanced fitting models of diffusion weighted imaging (DWI) in head/neck squamous cell carcinoma (HNSCC) patients to determine the best goodness of fit and correlations among diffusion parameters. We compared these results with those of dynamic contrast-enhanced (DCE) perfusion parameters.Materials and methodsWe retrospectively evaluated 32 HNSCC patients (12 sinonasal, 20 pharynx/oral cavity). The DWI acquisition used single-shot spin-echo echo-planar imaging (EPI) with 12 b-values (0 − 2000). We calculated 14 DWI parameters using mono-exponential, bi-exponential, and tri-exponential models, stretched exponential model (SEM) and diffusion kurtosis imaging (DKI) models. We compared each model's goodness of fit using the residual sum of squares (RSS), Akaike Information Criterion (AIC) and Bayesian information criterion (BIC) value. We determined the correlation between each pair of DWI parameters and between each DWI parameter and DCE perfusion parameter.ResultsThe tri-exponential fit's RSS, AIC and BIC values were significantly smaller than those for bi-exponential fit. The RSS, AIC and BIC values of the SEM fit and DKI fit were significantly smaller than mono-exponential model. Significant correlations were observed in 30 pairs (sinonasal cavity) and 31 (sinonasal cavity group) among 91 DWI parameter combinations. Significant correlations were also observed in nine pairs (both sinonasal cavity and pharynx/oral cavity group) among 64 DWI/DCE perfusion parameter pairs, in particular, high positive correlations between the tri-exponential model's intermediate diffusion fraction (f₂) and the volume of the extracellular extravascular space per unit volume of tissue (v_e) were observed in both patient groups.ConclusionWe identified several correlations between DWI parameters by advanced fitting models and correlations between DWI and DCE parameters. These will help determine HNSCC patients' detailed tissue structures.     

基于DE算法和NURBS曲线的ICP-AES光谱基线校正方法研究

电感耦合等离子体原子发射光谱(ICP-AES)分析法是一种常用的溶液元素浓度分析方法,但在ICP-AES测量过程中,由于温度漂移、杂散光和仪器暗电流等原因,光谱往往会存在一定程度的基线漂移,导致元素光谱强度值的测量结果存在误差,进而影响元素浓度的定量分析结果,因此基线校正是ICP-AES分析法中的必要环节之一。对传统光谱基线校正方法进行简要分析,在此基础上设计了一种基于非均匀B样条曲线和差分进化算法的ICP-AES光谱基线漂移校正方法;首先验证了光谱信号中噪声的概率密度分布服从高斯分布,然后对原始光谱进行预处理,通过高斯滤波对光谱信号去噪;然后以光谱基线校正过程中极小值序列的标准偏差作为评价指标,以非均匀B样条曲线作为基线模型,以曲线的控制点序列C和内接点序列T作为评价函数特征参数,建立ICP-AES光谱基线校正评价函数,将光谱基线校正问题转换为求解评价函数特征参数全局最优解的问题;最后简要介绍了差分进化算法的流程,通过差分进化算法求解使得评价函数取得最小值时的特征参数的全局最优解,即非均匀B样条曲线的控制点序列C与内接点序列T的取值,并以此拟合相应的非均匀B样条曲线作为光谱基线,实现...     

Visualization of coalescence behavior of two bubbles with smoothness constraint

A new method based on 2D contour curve fitting and 3D rotation surface generation to visualize the coalescence phenomenon of two bubbles in static water is presented. First, some contour points are extracted from key frame images in different coalescence stages of two bubbles. Second, those points are fitted using a new approach combining piecewise curve fitting with a smoothing constraint. Third, a family of transition functions is proposed to deal with continuous changes of contour curves in the process of coalescence. Finally, we use those contours to generate dynamical 3D rotation surfaces and achieve the continuous deformation visualization of two-bubble coalescence.     

大米拉曼光谱不同预处理方法的相近产地鉴别研究

用相近产地的大米代替独有的地理因素形成的地域品牌大米,消费者难以辨别。基于拉曼光谱技术,试验对比不同预处理方法包括一阶导数+平移平滑、二阶导数+平移平滑,小波变换+去除基线三种常用的预处理方法,另外提出一种改进的分段多项式拟合+去除基线共四种预处理方法,分别结合偏最小二乘法实现相近产地大米的鉴别分析,提出一种最佳的鉴别相近产地大米的预处理方法。首先用拉曼光谱仪采集了黑龙江省依安县3个相近产地大米的150个拉曼位移为200～3 100 cm-1的大米光谱样本,再对原始拉曼光谱分别用一阶导数+平移平滑、二阶导数+平移平滑、小波变换+去除基线、分段多项式拟合+去除基线进行光谱预处理。分别从每个产地选取33个样本进行训练,并对未知的51个样本建立了基于偏最小二乘法的鉴别分析模型,在训练集中一阶导数+平移平滑的预处理方法相关系数值最大、均方误差和均方根误差最小,小波变换+去除基线的预处理方法相关系数值最小、均方误差和均方根误差最大;在测试集中采用3点2次拟合+去除基线的预处理方法的相关系数值最大、均方误差和均方根误差最小,二阶导数+平移平滑的预处理方法最差。最后再通过PLS建模结果得知,在训练集中,采用四类九种预处理的方法对三个产地大米的总识别率均为100%;在测试集中,采用3点2次拟合+去除基线对三个产地大米总识别率为100%,采用5点2次拟合+去除基线对三个产地大米总识别率为52.9%,其他分段多项式拟合介于二者之间;采用一阶导数+平移平滑、二阶导数+平移平滑和小波变换的总识别率分别为88.2%,86.2%和96.1%;从中发现,分段式多项式拟合中的3点2次拟合+去除基线的优势明显,与其相关系数、均方误差、均方根误差结果吻合,总体识别率高,鉴别效果稳定。     

The Use of the Levenberg–Marquardt and Variable Projection Curve-Fitting Algorithm in Intravoxel Incoherent Motion Method for DW-MRI Data Analysis

The objective of this study was to evaluate the performances of different algorithms for diffusion parameters estimation in intravoxel incoherent motion method for diffusion-weighted magnetic resonance imaging (DW-MRI) data analysis. Traditionally, the method of non-linear least squares analysis by means of Levenberg–Marquardt algorithms has been used to estimate the parameters obtained from exponential decay data. In this study, we evaluated the Variable Projection curve-fitting algorithm and the performance of two non-linear regression methods when single and multiple starting points were used. Analysis was done on simulation data to which different amounts of Gaussian noise had been added. The performance of two non-linear regression methods was compared using the residual sum of squares and the number of failures in data fitting. We conclude that the VarPro algorithm is superior to the LM algorithm for curve fitting in intravoxel incoherent motion method for DW-MRI data analysis.     

计算全息检测离轴非球面的离散相位拟合

为了计算补偿用计算全息图的刻线位置,需要对光线追迹得到的离散相位数据进行拟合。为此详细推导了均匀三次B样条和非均匀三次B样条的基函数,介绍了各自对应的曲面拟合方法。以一块抛物型离轴非球面数据为例,对其非对称的离散相位分布进行了三次B样条曲面拟合。拟合结果表明,三次B样条曲面拟合能使拟合面经过所有数据点,保证拟合精度,且得到的连续的相位补偿函数表达式结构简单（最高次数只有3次）, 还能根据实际情况优化采样点数量,控制计算量。     

一种面向土壤重金属含量检测的X射线荧光光谱预处理方法研究

土壤重金属的污染影响着农作物的产量和质量。传统的土壤重金属检测方法步骤繁琐、检测费用高且速度慢。利用X射线荧光光谱(XRF)分析技术检测土壤中重金属含量，具有处理简单、现场、快速、无损等优点。由于土壤背景复杂，包含大量噪声和无关信息，建立XRF校正模型前，对光谱的预处理能有效的去除不相干信息，保留有用信息，对XRF预测模型的精度有重要影响。主要研究光谱预处理方法对重金属含量预测模型精度的影响。首先，采用向前间隔偏最小二乘(FiPLS)作为校正模型，对比了无预处理、去趋势处理(DT)、标准正态变量变换(SNV)、多元散射校正(MSC)、小波去噪(WT)、SNV+DT、卷积平滑(SG)+一阶导数、卷积平滑(SG)+二阶导数等7种不同预处理条件下的土壤重金属模型的检测精度。初步结果表明，多元散射校正预处理方法效果较好，与原始光谱相比，相关系数r从原始的0.988提高到0.990，预测均方根误差RMSEP、相对误差平均从原来的20.809和0.166分别降低到19.051和0.121。其次，在多元散射校正预处理方法的基础上，针对多元散射校正方法以线性表达式描述非线性关系的局限性，提出了局部加权线性回归多元散射校正(LWLRMSC)和偏最小二乘多元散射校正(PLSMSC)，并比较了它们的建模效果。LWLRMSC是基于加权思想，在预测一个点的值时，选择适当的核函数和权重分配策略进行预测点的线性回归，来解决简单线性回归的欠拟合状况；PLSMSC是基于PLS建模思想，考虑了自变量和因变量的最大相关性，来减少拟合误差及失真问题。结果表明，PLSMSC具有最佳的预处理效果，五种重金属Cu，Zn，As，Pb，Cr预测值和实际值的R分别为0.989，0.973，0.991，0.989和0.986，RMSEP分别为8.805，58.360，7.671，12.549和20.851，相比于传统的MSC方法不仅在精度方面有大幅度的提升，且具有更好的泛化性能，能消除光谱噪声，提升有效信息贡献度，为土壤重金属含量预测模型选取合适的预处理方法提供了理论支撑。     

The use of cubic splines in vibration-rotation problems of diatomic molecules

Vibration-rotation energies of diatomic molecules are computed in a basis of cubic splines using a series expansion of the centrifugal potential instead of its fitting representation. The vibrational continuum wavefunctions can be evaluated in a mixed basis set, as the spline fitting technique previously used for the electronic potential makes the analytical integration of the new functions possible. The same fitting algorithm suggests a fast method for defining approximately the best locations of the knots to be used in the least squares spline representation of the potential.     

相对误差最小二乘法的TDLAS气体浓度标定曲线拟合

可调谐半导体激光光谱技术（TDLAS）是光谱检测技术的一个分支,具有高灵敏度、高分辨率、实时监测、便携性好、小型化等优点,在工业环保、医疗检测、气象监测等领域得到了广泛应用。TDLAS气体传感器的测量精度与标定曲线密切相关,标定时,常用最小二乘法对标定曲线进行多项式拟合,但最小二乘法是以绝对误差的最小平方和作为评价标准,无法对相对误差进行约束,在低浓度量程下TDLAS气体传感器的标定曲线相对误差偏大,限制了标定量程。推导了光强透射率对数与气体浓度关系式作为目标函数,提出了基于相对误差意义下的最小二乘法,迭代方法采用高斯-牛顿迭代法（Gauss-Newton iteration method）,实验以雅士林DHS-100恒温恒湿箱来产生大量程范围的水汽标定浓度,Vaisala HMT337在线湿度检测仪的测量值作为标定浓度,自主研发的TDLAS湿度传感器选择波数为7 306.752 1 cm-1的水汽吸收峰,气室的光路长为50 mm,对1%~50%VOL的水汽浓度进行了拟合标定,对比了最小二乘法与相对误差最小二乘法的标定拟合结果。实验结果表明：采用最小二乘法拟合时,在低浓度量程下会出现较大的相对误差,高浓度量程下相对误差逐渐减小,无法保证整个大量程下测量精度要求;采用相对误差最小二乘法拟合时,在整个大量程范围下的相对误差波动比较小,相对误差分布曲线比较平稳,最大相对误差和相对误差标准差都远小于最小二乘法的拟合结果;以Ratio-C关系式作为目标函数,采用相对误差最小二乘法进行拟合标定时,最大相对误差为0.049 4,相对误差标准差为0.023 7,远优于最小二乘法的拟合结果,符合TDLAS传感器测量精度要求,验证了相对误差最小二乘法的标定算法可靠性,提高了TDLAS气体传感器的测量精度。     

基于迭代拟合的集装箱角件边缘检测算法

噪声通常是影响集装箱角件图像中低层次语义信息提取精度的重要因素,传统的边缘检测算法通常通过改进滤波器和阈值来消除图像中的物理噪声和环境噪声,但是却无法去除边缘检测后的噪声,为解决这一问题,提出了一种基于迭代拟合的边缘检测算法。首先,对角件图像进行一系列预处理操作获取边缘点集,其次,使用拟合算法处理点集并且得到函数表达式,然后定义偏差值度量并计算,用于衡量目标点集到拟合或者检测结果的偏差,最后,去除定义下距离拟合结果最远的指定数量的点,如此迭代拟合直至评价函数收敛。实验结果与分析表明,该算法可以有效地去除边缘点集中的非真实边缘点,相比于传统的边缘检测算法更能去除特殊噪声,算法具有收敛速度快、准确率较高、灵活性好等特点。     

辐射源定标红外焦平面阵列非均匀性校正算法研究

针对红外成像系统工程应用的实际要求,对辐射源定标红外焦平面阵列非均匀性校正的数学方法进行了研究,揭示了该实际工程问题属于函数插值或函数拟合的数学原理,并据此导出了三次样条插值、B样条最小二乘拟合及多项式最小二乘拟合等非均匀性校正算法.实验表明,该算法能有效适应红外焦平面阵列响应特性的大动态范围和非线性,校正准确度高,计算速度快.     

An analysis of error propagation in Abel inversions of spectral emission-absorption data

This paper investigates the effects of several influences upon the accuracy of Abel inversions which are performed upon spectral emission-absorption data that are obtained from axisymmetric sources of radiation.The influences that are investigated are the numerical step size that is used in the inversion, uncertainty in source diameter, and Gaussian noise superimposed upon the data. The effects of graphical and numerical data smoothing upon inversion results that are obtained with noisy data are also investigated. Graphical smoothing is found to be superior to quadratic curve fitting.     

A weighted least squares method for circle fitting to frequency response data

Despite the recent development of powerful multi-degree of freedom curve fitting programs the advent of the microcomputer has meant that there is still scope for improvement of simpler single degree of freedom models. A weighted least squares curves fitting method, based on a well known conformal mapping, is described. This method is shown to have important theoretical advantages over some established methods.     

摄像机镜头畸变的一种非量测校正方法

为了减少噪声对摄像机镜头畸变的校正结果带来的影响,提出了一种校正摄像机镜头畸变的非量测方法.先找出由直线畸变而成的曲线,再用直线段连接每条曲线的两个端点形成一些闭合曲线.把它们的面积平方和定义为畸变测度,并用遗传算法搜索畸变测度的最小值.以此得到畸变参量.计算表明,该畸变测度具有较好的抗噪声能力,而遗传算法能避免收敛于局部极小值,减少了矫正图像的均方根误差.实验表明,对多幅图像分别和联合校正,相应矫正图像之间的均方根误差较小,计算和实验郜表明该校正方法具有良好的稳健性.     

可见光/近红外光谱技术快速测定橙汁柠檬酸含量

为了快速无损测定橙汁的柠檬酸含量,提出了一种用可见光/近红外光谱技术进行检测的新方法。选用高效液相色谱法作为光谱柠檬酸测定的标定方法。采用平滑点数为5的移动平滑法对原始光谱进行预处理消除噪声。由于采集的光谱数据量非常大,为了减少建模时间,建模之前采用小波变换对经过预处理的大量光谱数据进行降维压缩,并在Matlab7.01中通过自编程序实现此变换。利用光谱专用分析软件Unscrambler 9.5,对压缩后的新变量进行分析,建立偏最小二乘(PLS)校正模型。考虑到不同小波基及分解尺度对数据压缩的影响,采用预测平方和PRESS值最小的评价标准,选择最佳的小波基Db4及分解尺度5。用于本实验的样本总数为40,其中30个样本进行建模,10个用于预测。用校正集相关系数(r)和标准偏差(SEC)作为校正模型的评价指标,预测结果采用预测相关系数(r)和预测标准偏差(SEP)来评定。文章将基于小波变换的PLS模型与直接建立的PLS模型进行了比较,偏最小二乘法结合小波变换的模型预测相关系数为r=0.901, 预测标准偏差SEP=0.937;而由PLS建立的模型其预测相关系数r=0.849,预测标准偏差SEP=1.662。由此可见,由偏最小二乘法结合小波变换所得模型效果优于单独使用偏最小二乘法的结果。     

Accurate estimation of Brillouin frequency shift in Brillouin optical time domain analysis sensors using cross correlation

Current methods of estimating the Brillouin frequency shift in Brillouin optical time domain analysis sensors are based on curve-fitting techniques. These techniques apply the same weight to all portions of the curve and dutifully fit into the peak and noisy ends of the curve. This makes them very sensitive to noise, initialization of fitting parameters, symmetry, and start and stop frequencies. We introduce a method based on the cross-correlation technique to estimate the central frequency of noisy Lorentzian curves, which is more robust to noise and free from initial settings of fitting parameters.     

多参考组态相互作用方法计算研究XOn(X=S,Cl；n=0,±1)的解析势能函数和光谱常数

采用从头计算的多参考组态相互作用方法和含扩散基的3个基组aug-cc-PVXZ (X=D,T,Q) 计算了SO和ClO分子及其分子离子的势能曲线，确定了平衡几何结构、离解能，并采用Feller拟合递推方法得到了基函数为无穷大计算水平值. 确定了SO^－，ClO⁺，ClO^-分子离子的基态. 通过Murrell-Sorbie势能函数和最小二乘法拟合得到了解析势能函数. 基于所得的势能函数，通过解核运动的薛定谔方程得到振 关键词： 多参考组态相互作用 势能曲线 解析势能函数 光谱常数     

Least square fitting of low resolution gamma ray spectra with cubic B-spline basis functions

In this paper, the least square fitting method with the cubic B-spline basis lunctions is derived to reduce the influence of statistical fluctuations in the gamma ray spectra. The derived procedure is simple and automatic. The results show that this method is better than the convolution method with a sufficient reduction of statistical fluctuation.