Voigt函数法的误差分析

对Voigt函数法进行了系统的误差分析,得到了误差的规律,同时以公式和图象的形式对其进行了描述,并指出Voigt函数法的可靠性区域。 关键词：     

基于Voigt函数的拉曼成像插值方法

拉曼成像是拉曼光谱技术非常重要的一个环节,通过生成光谱数据的伪彩图像,可以得到采集区域中某物质组分的浓度和位置分布信息,当前,拉曼成像技术已经逐渐成为监测生物活性以及物质组分的最优解之一.为了得到清晰的成像效果,采集过程中的数据量不宜过小,否则成像效果差、锯齿感较重,从而导致视觉效果不好.但是,数据量的增加虽然可以得到...     

Voigt线型函数及其最大值的研究

研究了多普勒和洛伦兹线型函数卷积形式的Voigt线型函数, 给出了它的最大值.结果表明, Voigt线型函数是关于中心频率的对称函数, Voigt线型函数的最大值由多普勒和洛伦兹线型函数的半宽度决定, 与中心频率无关, 且比洛伦兹和多普勒线型函数的最大值都小.提出了利用Voigt线型函数最大值和半宽度获得多普勒线型函数和洛伦兹线型函数的方法, 并利用Monte Carlo方法进行了验证. 关键词： Voigt线型函数 半宽度 最大值 傅里叶变换     

基于Voigt函数拟合的离子激发发光光谱分峰方法

离子激发发光(IBIL)分析作为一种实时原位的光谱分析技术,由于其对样品内部结构的敏感性,给我们分析样品光谱谱峰信息带来了一定的困难。为了准确地对离子激发发光能谱进行分峰以便更加清晰地判断材料内部不同缺陷的发光中心,提出了一种利用Voigt函数,通过L-M（levenberg-marquardt）非线性最小二乘算法对100和200 K温度时ZnO的IBIL能谱中深能级发射（DBE）峰进行分峰的方法。通过对比Gauss函数和Voigt函数对能谱拟合后峰位随注量的波动情况,发现使用Voigt函数拟合得到的峰位更加稳定,并且收敛速度更快。同时通过对使用Voigt函数拟合后得到的峰中心位于1.75, 1.95和2.10 eV三个子峰的高斯函数半高宽与洛伦兹函数半高宽比较,发现洛伦兹函数半高宽约为高斯函数半高宽的1/10,而且100 K时的1.95 eV峰,200 K时1.75和1.95 eV峰,其洛伦兹峰半高宽数值为10-10量级以下,说明其中非均匀展宽（高斯展宽）仍然是谱峰展宽的主要机制;而电子与声子散射作用是洛伦兹展宽的主要机制。对于涉及导带中大量电子的2.10 eV子峰,其在200 K时洛伦兹函数半高宽明显大于100 K时,由于在温度较高时,由于晶格热振动加剧,且电子热运动加强,增大了散射概率,导致电子与声子的散射作用加强,从而对洛伦兹谱线进一步展宽。而峰中心位于1.75 eV的红光,其主要与V_Zn相关,在100 K时其子峰的洛伦兹半高宽为0.02 eV, 但在200 K时变得极小,这可能是由于100 K时V_Zn束缚的电子或激子在200 K获得足够的热动能摆脱了V_Zn束缚,减弱了与周围的晶格的散射作用,从而使得洛伦兹展宽变得极弱。实验结果表明Voigt函数更加适用于IBIL能谱拟合分峰,这也为以后IBIL技术应用于其他材料内部结构能谱分析提供了可借鉴的依据。     

蜡样芽孢杆菌的二阶导数红外光谱研究

采用傅里叶变换红外光谱非破坏性地分析了蜡样芽孢杆菌,在获得完整全细胞组分的红外光谱信息基础上,进行了二阶导数光谱转换。结果表明,根据二阶导数光谱特征吸收峰可区分蜡样芽孢杆菌细胞的荚膜、芽孢、贮能物质等特殊结果物质。以1 654 cm-1附近的α-螺旋结构的蛋白酰胺带吸收峰与在1 601和1 403 cm-1附近显示的强羧基伸缩振动吸收峰可探测到细胞荚膜结构;根据1 617,1 372和1 569 cm-1附近的吡啶二羧酸(DPA)的吸收峰可认定细胞内芽孢的存在;此外,可在二阶导数红外谱图中同时找到多聚β-羟基丁酸(PHB)细胞粒、荚膜、芽孢的吸收峰。由二阶导数红外光谱可分辨重叠光谱来探测细胞多种结构物质,为从分子生物学与细胞生物学角度,为研究蜡样芽孢杆菌提供参考信息。     

δ函数导数在电磁学中的一些应用

本文说明理想电偶极子、电四极子的电荷分布可分别用δ函数的一阶、二阶导数来表示．在此基础上，运用δ函数导数的计算公式。可以直观、简便地得出理想电多极子的静电势和辐射场标势的表达式     

函数的H-导数和分形动力学

 给出了函数的Hausdorff测度与H-导数。从而，为开展自给的分形动力学提供了解析的数学工具。同时，给出了分形动力学的演化方程组并做了初步讨论与分析。     

基于样条法的米兰X射线衍射二阶导数指纹图谱

利用3次样条法编写了由X射线衍射指纹图谱的二阶导数图谱的Matlab程序,利用该程序分别获得了标准样品SiO2和米兰的二阶导数指纹图谱,结果表明该方法能有效解决植物类药材弥散型X射线衍射指纹图谱解析问题,放大功能显著,值得推广.     

二维图象中二阶导数滤波器边缘定位误差的理论分析

本文从理论上讨论了低通滤波后二维图象中弯曲边缘的定位误差问题.边缘位置通常由二阶导数算子的零交叉点定义.研究表明:梯度方向上的二阶导数算子(secondderivativein gradient direction SDGD)产生向心的、可预测的边缘偏移;而线性拉普拉斯算子(Laplacian Operator)产生相反方向(离心)的可预测位置偏移.由此可推断:两者之和——称之为PLUS,将产生比其组成成份(SDGD 和 Laplace)更为精确的边缘定位算子.文章讨论了常用的低通滤波器(如 Gaussian 滤波器及 Tepee 滤波器)对边缘定位精度的影响.     

二阶导数光度法测定豆奶粉中微量铜

在含有乳化剂OP(聚乙二醇辛基苯基醚)的pH值为9.2的磷酸氢二钠缓冲溶液中,以1-(2-吡啶偶氮)-2-萘酚(PAN)为显色剂,在566nm波长处用二阶导数分光光度法测定铜,可消除锌、镉的干扰.校准曲线回归方程A=0.0976C 0.0038,线性范围0.025-2.1μg/mL,相关系数r=0.9992.检出限为5.5×10-6g/L,相对标准偏差RSD为2.37%,测定豆奶粉中铜的回收率在95%-102%之间,结果令人满意.     

Rapid and accurate calculation of the Voigt function

Two general techniques significantly improve both the accuracy and speed of spectral line shapes that use only the complex Voigt function. Such line shape functions include the Voigt line profile, which is closely related to the real part of this function. The first technique is a new algorithm, which trades a small amount of RAM (at most 1.49 megabytes) for a considerable gain in speed and accuracy. The accuracy is one part in 10⁶ of the function itself. In addition, the derivatives of the function with respect to x and y are returned with an accuracy of 0.5%. The algorithm is up to nine times faster than the Drayson or Humlí?ek algorithms and about two orders of magnitude more accurate. A second independent improvement is a set of simple criteria to decide when an evaluation is required and when a value of zero can be assumed. This section alone can reduce the computation time by three orders of magnitude or more and it can be applied to algorithms using any Voigt approximation.     

Rapidly convergent series for high-accuracy calculation of the Voigt function

A rapidly convergent series, based on Fourier expansion of the exponential multiplier, is presented for highly accurate approximation of the Voigt function (VF). The corresponding algorithm enables the rapid calculation, required for its implementation as a subprogram in an interpolation approach. The numerical analysis of this VF approximation suggests that it may be more accurate than 10⁻⁹ in the Humlí?ek regions 3 and 4.     

A new procedure for obtaining the Voigt function dependent upon the complex error function

This work proposes a new method for obtaining the differential equation of the Voigt function and, from this equation, expressing the Voigt function as dependent upon the complex error function. In addition, the integral expression of the successive derivatives of the Voigt function is given, and from this a method is generalized which permits the representation, also, of other functions depending on the complex error function. This enables us to simplify other functions which are the convolution of a Gaussian function with rational polynomial functions. Moreover, the relationship between the Lorentzian (w_L), Gaussian (w_G) and Voigt (w_V) widths at half maximum for the function is given, which is of great interest in diverse branches of physics, such as plasma spectroscopy, astrophysics, nuclear magnetic resonance, etc.     

Determination of nonlinear optical properties using the Voigt function: Stochastic considerations

In this work, the absorptive and dispersive profiles of a molecular system have been calculated through a methodology based on the averaging of the coherence obtained by the resolution of the optical stochastic Bloch equations. To this aim, a generalized Lorentzian approximation to the Voigt function has been used as a probability distribution, which allows a more generalized analysis of the interactions between the solvent and the molecule. This has been modeled with the parameters of the standard organic dye Green Malaquite, which exhibits a nonlinear behavior under the interaction with a high intensity electric field.     

Generalized Voigt functions and their derivatives

This paper deals with a special class of functions called generalized Voigt functions H⁽ⁿ⁾(x,a) and G⁽ⁿ⁾(x,a) and their partial derivatives, which are useful in the theory of polarized spectral line formation in stochastic media. For n=0 they reduce to the usual Voigt and Faraday-Voigt functions H(x,a) and G(x,a). A detailed study is made of these new functions. Simple recurrence relations are established and employed for the calculation of the functions themselves and of their partial derivatives. Asymptotic expansions are given for large values of x and a. They are used to examine the range of applicability of the recurrence relations and to construct a numerical algorithm for the calculation of the generalized Voigt functions and of their derivatives valid in a large (x,a) domain. It is also shown that the partial derivatives of the usual H(x,a) and G(x,a) can be expressed in terms of H⁽ⁿ⁾(x,a) and G⁽ⁿ⁾(x,a).     

Comment on “A new procedure for obtaining the Voigt function dependent upon the complex error function”

The numerical solution of Eq. (1) relating the Voigt, Lorentzian, and Gaussian full-widths at half-maximum, as shown in Fig. 2 of the article A new procedure for obtaining the Voigt function dependent upon the complex error function by Luque, Calzada and Saez (JQSRT 2005; 94:151-161), is not valid in some parts of the computational domain. The problem resides within a physical domain that is of current spectroscopic interest for the diagnostics of low temperature (∼300 K), high pressure (∼1 atm) dielectric barrier discharge plasmas. The purpose here is to identify the deficiency and to demonstrate a well-conditioned numerical approach for this domain of interest.     

佛克脱反常色散原子滤光器工作机理研究

对佛克脱（Voigt)型反常色散原子滤光器的工作机理和各种性能进行讨论,该种滤光器的实现研究表明理论与实验结果符合得好。滤光器在外加磁场为0．02T、汽室温度为110℃的单峰带宽为0．8GHz,比相同条件下的法拉第型反常色散原子滤光器小0．5Hz,并且工程化实现比法拉第型反常色散原子滤光器容易。佛克脱型反常色散原子滤光器在卫星光通信领域有潜在的极大应用前景。