On art and science in curve-fitting vibrational spectra
On art and science in curve-fitting vibrational spectra
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DOI：
10.1016/j.vibspec.2005.03.003
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发表时间：
2005-10-31
影响因子：
2.5
通讯作者：
Meier, RJ
中科院分区：
文献类型：
--
作者：
Meier, RJ
在本文中，我们对曲线拟合振动谱中一些似乎并不总是受到重视的关键问题进行了评论。大多数情况下，在工业应用中，当然也在部分学术研究中，分析结果的量化是必不可少的。这可以从污染物的浓度变化到聚合物基体中组分的分数，例如，共聚单体的含量或复合材料中某一相的分数。对于某些分析技术，定量比其他分析技术更直接。在中红外和拉曼光谱中，单个波段的重叠是常见的现象。量化可以通过多种方式完成，最合适的方式取决于感兴趣的光谱范围内光谱的整体形状。当我们有良好隔离的波段时，基本上没有问题，甚至使用尺子的传统峰高测量也足以确定来自不同样品的光谱之间的相对量（这确实是过去正确完成的方式）。当频带重叠时，问题就出现了。在这种情况下，曲线拟合是一种揭示实际的、个别的振动带的技术。曲线拟合也可称为建模，因为模型应构成一系列曲线与实际光谱拟合的基础。曲线拟合是从一组规定的单个条带开始寻找重叠条带剖面的最佳拟合。有时，曲线拟合被称为反褶积的一种特殊形式。然而，这在形式上是不太正确的。在振动光谱学中，反褶积通常是从光谱中去除仪器效应的过程。由于实谱是两个函数（即真实的物理线形和仪器展宽）的卷积，即乘积，反卷积步骤消除了导致真实物理线形的仪器展宽。在本文中，我们将重点讨论曲线拟合的一些方面，因为它是一种合适的方法，它经常被使用，许多光谱软件包包含允许曲线拟合的工具。然而，在许多报道的案例中，线形和曲线拟合的不正确应用很可能是由于对基本的潜在物理学认识不足造成的。这一问题正是本文的主题。复杂波段剖面的曲线拟合，虽然人们可能认为这是一个众所周知的过程，但往往似乎没有以适当的，即科学合理的方式应用。最引人注目的是，使用高斯-洛伦兹求和函数的形式
In this note we comment on some crucial issues in curvefitting vibrational spectra that do not always seem respected. Most often in industrial applications, but certainly also in part of the academic studies, quantification of analytical results is essential. This may vary from the concentration of a pollutant to the fraction of a constituent in a polymer matrix, eg, comonomer content or the fraction of a certain phase in a complex material. For some analytical techniques quantification is more straightforward than for others. In mid-infrared and Raman spectra, overlapping of individual bands is a common phenomenon. Quantification can be accomplished in various ways, with the most appropriate way depending on the overall shape of the spectrum in the spectral range of interest. When we have well-isolated bands, there is essentially no problem, and even traditional peak height measurement using a ruler may suffice to determine relative amounts between spectra originating from different samples (which was really the way it was done, appropriately, in the past). Problems arise when there is band overlap. In that case curve fitting is a technique to unravel the actual, individual, vibrational bands. Curve fitting may also be called modelling, as a model should form the basis of the fitting of a series of curves to the actual spectrum. Curve fitting is finding the best fit to an overlapping band profile starting from a prescribed set of individual bands. Sometimes curve fitting is said to be a particular form of deconvolution. This, however, is formally less correct. In vibrational spectroscopy, deconvolution is generally the process in which instrumental effects are removed from a spectrum. With the real spectrum being the convolution, that is the product, of two functions, namely the true physical line-shape and the instrumental broadening, the deconvolution step removes the instrumental broadening leading to the true physical line-shape. In this note we will focus on some aspects of curve fitting as it is an appropriate method, it is frequently used, and many spectroscopic software packages contain tools allowing for curve fitting. The incorrect application of line-shapes and curve fitting in a number of reported cases, however, is most likely caused by insufficient appreciation of the essential underlying physics. It is this issue that is the subject of the present contribution. Curve fitting of complex band profiles, although one might expect this to be a well-known procedure, often does not seem to be applied in an appropriate, ie, scientifically justifiable, way. Most strikingly, the use of a Gauss–Lorentz sum function of the form