Procedures for Wavelength Calibration and Spectral Response Correction of CCD Array Spectrometers

This work describes a procedure for acquiring a spectrum of an analyte over an extended range of wavelengths and validating the wavelength and intensity assignments. To acquire a spectrum over an extended range of wavelengths with a spectrometer with a charge coupled device (CCD) array detector, it is necessary to acquire many partial spectra, each at a different angular position of the grating, and splice the partial spectra into a single extended spectrum. The splicing procedure exposes instrument dependent artifacts. It is demonstrated that by taking a spectrum of a reference irradiance source and making spectral correction, the artifacts exposed by the splicing are removed from the analyte spectrum. This is because the irradiance reference spectrum contains the same artifacts as the analyte spectrum. The artifacts exposed by the splicing depend on the wavelength of the splice; therefore it is important to measure the irradiance reference spectrum for the same range of wavelengths used to measure the spectrum of the analyte solution. In other words, there is no general spectral correction factor which is applicable to spectra taken for different range of wavelengths. The wavelength calibration is also carried out by splicing many partial spectra from a source like a krypton lamp. However the wavelength assignments are not sensitive to the splicing procedure and the same wavelength calibration can be used for spectra acquired over different extended wavelength ranges. The wavelength calibration checks the validity of the setting of the grating angular position, and the assignment of wavelengths to individual pixels on the CCD array detector. The procedure is illustrated by measuring the spectrum of an orange glass and the spectrum of a suspension of microalgae.     

Assessment of pareto calibration, stability, and wavelength selection

Recent work has shown that ridge regression (RR) is Pareto to partial least squares (PLS) and principal component regression (PCR) when the variance indicator Euclidian norm of the regression coefficients, //p//, is plotted against the bias indicator root mean square error of calibration (RMSEC). Simplex optimization demonstrates that RR is Pareto for several other spectral data sets when //p// is used with RMSEC and the root mean square error of evaluation (RMSEE) as optimization criteria. From this investigation, it was observed that while RR is Pareto optimal, PLS and PCR harmonious models are near equivalent to harmonious RR models. Additionally, it was found that RR is Pareto robust, i.e., models formed at one temperature were then used to predict samples at another temperature. Wavelength selection is commonly performed to improve analysis results such that bias indicators RMSEC, RMSEE, root mean square error of validation, or root mean square error of cross-validation decrease using a subset of wavelengths. Just as critical to an analysis of selected wavelengths is an assessment of variance. Using wavelengths deemed optimal in a previous study, this paper reports on the variance/bias tradeoff. An approach that forms the Pareto model with a Pareto wavelength subset is suggested.     

Removal of analyte-irrelevant variations in near-infrared tissue spectra

This paper describes mathematical techniques to correct for analyte-irrelevant optical variability in tissue spectra by combining multiple preprocessing techniques to address variability in spectral properties of tissue overlying and within the muscle. A mathematical preprocessing method called principal component analysis (PCA) loading correction is discussed for removal of inter-subject, analyte-irrelevant variations in muscle scattering from continuous-wave diffuse reflectance near-infrared (NIR) spectra. The correction is completed by orthogonalizing spectra to a set of loading vectors of the principal components obtained from principal component analysis of spectra with the same analyte value, across different subjects in the calibration set. Once the loading vectors are obtained, no knowledge of analyte values is required for future spectral correction. The method was tested on tissue-like, three-layer phantoms using partial least squares (PLS) regression to predict the absorber concentration in the phantom muscle layer from the NIR spectra. Two other mathematical methods, short-distance correction to remove spectral interference from skin and fat layers and standard normal variate scaling, were also applied and/or combined with the proposed method prior to the PLS analysis. Each of the preprocessing methods improved model prediction and/or reduced model complexity. The combination of the three preprocessing methods provided the most accurate prediction results. We also performed a preliminary validation on in vivo human tissue spectra.     

Spectral multivariate calibration with wavelength selection using variants of Tikhonov regularization

Tikhonov regularization (TR) is a general method that can be used to form a multivariate calibration model and numerous variants of it exist, including ridge regression (RR). This paper reports on the unique flexibility of TR to form a model using full wavelengths (RR), individually selected wavelengths, or multiple bands of selected wavelengths. Of these three TR variants, the one based on selection of wavelength bands is found to produce lower prediction errors. As with most wavelength selection algorithms, the model vector magnitude indicates that this error reduction comes with a potential increase in prediction uncertainty. Results are presented for near-infrared, ultraviolet-visible, and synthetic spectral data sets. While the focus of this paper is wavelength selection, the TR methods are generic and applicable to other variable-selection situations.     

Alternative statistical methods for spectral data processing: applications to laser-induced breakdown spectroscopy of gaseous and aerosol systems

A new spectral data processing scheme based on the standard deviation of collected spectra is compared with the traditional ensemble-averaging of laser-induced breakdown spectroscopy (LIBS)-based spectral data for homogenous (i.e., pure gas phase) systems and with a LIBS-based traditional conditional spectral analysis scheme for non-homogenous (e.g., aerosol system) analyte systems under discrete particle loadings. The range of conditions enables quantitative assessment of the analytical approaches under carefully controlled experimental conditions. In the homogeneous system with gaseous carbon dioxide producing the carbon atomic emission signal, the standard deviation method provided a suitable metric that is directly proportional to the analyte signal and compares favorably with a traditional ensemble averaging scheme. In contrast, the applicability of the standard deviation method for analysis of non-homogenous analyte systems (e.g., aerosol systems) must be carefully considered. It was shown both experimentally and via Monte Carlo simulations that the standard deviation approach can produce an analyte response that is monotonic with analyte concentration up to a point at which the analyte signal starts to transition from a non-homogeneous system to a homogeneous systems (i.e., around a 50% sampling point for aerosol particles). In addition, the standard deviation spectrum is capable of revealing spectral locations of non-homogeneously dispersed analyte species without a priori knowledge.     

Surface plasmon spectral fingerprinting of adsorbed magnesium phthalocyanine by angle and wavelength modulation

A novel instrumental method for angle and wavelength modulated surface plasmon resonance (SPR) spectroscopy is applied to the problem of spectral selectivity in SPR experiments. For transparent analytes, SPR reflectivity data are reduced to a two-dimensional (2D) spectrum of resonance wavelength versus incident angle, lambdaSPR(theta). This spectrum encodes the refractive index (RI) dispersion of the analyte and illustrates the increased SPR spectral shift per unit RI change at longer wavelengths (lower angle). For the absorbing analyte magnesium phthalocyanine (MgPc), the 2D data reduction method is complicated by the way the SPR and MgPc-based spectral peaks mix. Fresnel reflectivity models support experimental observations of spectral branching and qualitative fingerprints in the form of branched spectra, and difference reflectivity deltaR(lambda, theta) contour plots are presented.     

In vivo near-infrared spectroscopy of rat skin tissue with varying blood glucose levels

We have performed in vivo measurements of near-infrared rat skin absorption in the 4000-5000-cm(-1) spectral range (2.0-2.5-microm wavelength) during a glucose clamp experiment in order to identify the presence of glucose-specific spectral information. Spectra were collected during an initial 3-h period where the animal's blood glucose concentration was held at its normal value. The blood glucose level was then increased above 30 mM by venous infusion of glucose and held for 2 h, after which it was allowed to return to normal. Spectra were recorded continuously during the procedure and are analyzed to identify spectral changes associated with changes in glucose concentration. Because the change in absorbance due to an increase in glucose concentration is small compared to changes due to other variations (e.g., the thickness of the skin sample), a simple subtraction of absorbance spectra from the hyperglycemic and euglycemic phases is not instructive. Instead, a set of principal components is established from the euglycemic period where the glucose concentration is constant. We then examine the change in absorbance during the hyperglycemic period that is orthogonal to these principal components. We find that there are significant similarities between these orthogonal variations and the net analyte signal of glucose, which suggests that glucose spectral information is present. The analysis described here provides a procedure by which the analytical significance of a multivariate calibration can be evaluated.     

Wavelength selection for multivariate calibration using tikhonov regularization

Prediction of sample properties using spectroscopic data with multivariate calibration is often enhanced by wavelength selection. This paper reports on a built-in wavelength selection method in which the estimated regression vector contains zero to near-zero coefficients for undesirable wavelengths. The method is based on Tikhonov regularization with the model 1-norm (TR1) and is applied to simulated and near-infrared (NIR) spectral data. Models are also formed from wavelength subsets determined by the standard method of stepwise regression (SWR). Harmonious (bias/variance tradeoff) and parsimonious considerations are compared with and without wavelength selection for principal component regression (PCR), ridge regression (RR), partial least squares (PLS), and multiple linear regression (MLR). Results show that TR1 models generally contain large baseline regions of near-zero coefficients, thereby essentially achieving built-in wavelength selection. For example, wavelengths with spectral interferences and/or poor signal-to-noise ratios obtain near zero regression coefficients. Results often improve with TR1 models, compared to full wavelength PCR, RR, and PLS models. The SWR subset results are similar to those for the TR1 models using the NIR data and worse with the simulated spectral situations. In general, wavelength selection improves prediction accuracy at a sacrifice to a potential increase in variance and the parsimony remains nearly equivalent compared to full wavelength models. New insights gained from the reported studies provide useful guidelines on when to use full wavelengths or use wavelength selection methods. Specifically, when a small number of large wavelength effects (good sensitivity and selectivity) exist, subset selection by SWR (with caution) and TR1 do well. With a small to moderate number of large to moderate sized wavelength effects, TR1 is better. Lastly, when a large number of small effects are present, full wavelengths with the methods of PCR, RR, or PLS are best.     

Application of Mueller polarimetry in conical diffraction for critical dimension measurements in microelectronics

Fast and efficient metrology tools are required in microelectronics for control of ever-decreasing feature sizes. Optical techniques such as spectroscopic ellipsometry (SE) and normal incidence reflectometry are widely used for this task. In this work we investigate the potential of spectral Mueller polarimetry in conical diffraction for the characterization of 1D gratings, with particular emphasis on small critical dimensions (CDs). Mueller matrix spectra were taken in the visible (450-700 nm) wavelength range on a photoresist grating on a Si substrate with 70/240 nm CD/period nominal values, set at nine different azimuthal angles. These spectra were fitted with a rigorous coupled-wave analysis (RCWA) algorithm by using different models for the grating profile (rectangular and trapezoidal, with or without rounded corners). A detailed study of the stability and consistency of the optimal CD values, together with the variation of the merit function (the mean square deviation D2) around these values, clearly showed that for a given wavelength range, this technique can decouple some critical parameters (e.g., top and bottom CDs, left and right sidewall projections) much more efficiently than the usual SE.     

Efficient computation of net analyte signal vector in inverse multivariate calibration models

The net analyte signal vector has been defined by Lorber as the part of a mixture spectrum that is unique for the analyte of interest; i.e., it is orthogonal to the spectra of the interferences. It plays a key role in the development of multivariate analytical figures of merit. Applications have been reported that imply its utility for spectroscopic wavelength selection as well as calibration method comparison. Currently available methods for computing the net analyte signal vector in inverse multivariate calibration models are based on the evaluation of projection matrices. Due to the size of these matrices (p × p, with p the number of wavelengths) the computation may be highly memory- and time-consuming. This paper shows that the net analyte signal vector can be obtained in a highly efficient manner by a suitable scaling of the regression vector. Computing the scaling factor only requires the evaluation of an inner product (p multiplications and additions). The mathematical form of the newly derived expression is discussed, and the generalization to multiway calibration models is briefly outlined.     

A variable selection method based on uninformative variable elimination for multivariate calibration of near-infrared spectra

Variable (or wavelength) selection plays an important role in the quantitative analysis of near-infrared (NIR) spectra. A modified method of uninformative variable elimination (UVE) was proposed for variable selection in NIR spectral modeling based on the principle of Monte Carlo (MC) and UVE. The method builds a large number of models with randomly selected calibration samples at first, and then each variable is evaluated with a stability of the corresponding coefficients in these models. Variables with poor stability are known as uninformative variable and eliminated. The performance of the proposed method is compared with UVE-PLS and conventional PLS for modeling the NIR data sets of tobacco samples. Results show that the proposed method is able to select important wavelengths from the NIR spectra, and makes the prediction more robust and accurate in quantitative analysis. Furthermore, if wavelet compression is combined with the method, more parsimonious and efficient model can be obtained.     

Temperature-insensitive near-infrared method for determination of protein concentration during protein crystal growth

A temperature-insensitive method for measuring protein concentration in aqueous solutions using near-infrared spectroscopy is described. The method, which is based on identification of the net analyte signal of single-beam spectra, can be calibrated using a single protein absorbance measurement and is thus well suited for crystallization monitoring where the quantity of protein is limited. The method is applied to measurements of glucose-isomerase concentration in a sodium phosphate buffer that is actively varied over the temperature range of 4-24 degrees C. The standard error of prediction using the optimized spectral range of 4670-4595 cm(-1) is 0.12 mg/mL with no systematic trend in the residuals with solution temperature. The method is also applied to previously collected spectra of hen egg-white lysozyme and yields a standard error of prediction of 0.14 mg/mL. Spectra sampled at discrete wavelengths can also be used for calibration and prediction with performance comparable to that obtained with spectral bands. A set of four wavelengths are identified that can be used to predict concentrations of both proteins with a standard error less than 0.14 mg/mL.     

基于紫外/可见光谱技术的李子硬度无损检测

目的探究采用紫外/可见光谱技术结合化学计量学预测李子硬度的可行性。方法以“红”李子和“青”李子为研究对象,采用光谱采集系统获取李子样本的平均光谱;采用标准正态变换对原始光谱数据进行预处理,并利用连续投影算法(SPA)和竞争性自适应重加权算法(CARS)从全光谱的1024个波长中分别提取2个(513.04 nm和636.72 nm)和10个(230.01,244.67,274.71,287.66,290.90,300.59,311.78,423.08,515.39,631.31 nm)特征波长;分别建立基于全光谱和提取的特征波长预测李子硬度的误差反向传播(BP)网络模型。结果将采用SPA和CARS特征波长选择方法提取的特征变量作为BP网络输入,明显提升了BP网络模型的运行效率,且SPA-BP网络模型具有相对较好的李子硬度预测能力(rp=0.695,预测样本集均方根误差为1.610 kg/cm2)。结论采用紫外/可见光谱技术结合特征波长提取方法可实现李子硬度的快速无损检测。     

Adaptable multivariate calibration models for spectral applications

Multivariate calibration techniques have been used in a wide variety of spectroscopic situations. In many of these situations, spectral variation can be partitioned into separate classes. For example, suppose that multiple spectra are obtained from each of a number of different objects wherein the level of the analyte of interest varies within each object over time. In such situations, the total spectral variation observed across all measurements has two distinct general sources of variation: intraobject and interobject. One might want to develop a global multivariate calibration model that predicts the analyte of interest accurately both within and across objects, including new objects not involved in developing the calibration model. However, this goal might be hard to realize if the interobject spectral variation is complex and difficult to model. If the intraobject spectral variation is consistent across objects, an effective alternative approach might be to develop a generic intraobject model that can be adapted to each object separately. This paper contains recommendations for experimental protocols and data analysis in such situations. The approach is illustrated with an example involving the noninvasive measurement of glucose using near-infrared reflectance spectroscopy. Extensions to calibration maintenance and calibration transfer are discussed.     

Conditional data processing for single-shot spectral analysis by use of laser-induced breakdown spectroscopy

Schemes of conditional data processing are evaluated based on either the peak-to-base ratio or the signal-to-noise ratio as a metric for analyte detection in single-shot laser-induced breakdown spectra. The analyte signal investigated is the 288.1-nm Si I emission line provided by an aerosol stream of monodisperse 2.5-microm-sized silica microspheres. Both the Si emission line and a spectral region corresponding to continuum emission are used to evaluate the statistical distribution of spectral noise. The probability of false hits is determined by evaluating various conditional processing thresholds. As the detection threshold increases, the rate of detected silica particle hits decreases along with the expected fraction of false-particle hits (i.e., spectral noise). For all threshold values the signal-to-noise ratio is found to provide a more robust metric for single-shot analyte detection compared with the peak-to-base ratio.     

Identification of chemical substances by their near-infrared spectra

Salamin, P.A., Cornelis, Y. and Bartels, H., 1988. Identification of chemical substances by their near-infrared spectra. Chemometrics and Intelligent Laboratory Systems, 3: 329–333.Near-infrared spectra show a large variability due to physical parameters such as particle size. This makes the identification of chemical substances by spectral comparison difficult. This article reviews an earlier method of identification of chemical substances by near-infrared spectra based on the Mahalanobis distance and introduces a new method based on the multiplicative scatter correction. This new method can to a great extent eliminate the spectral variation due to physical parameters and allows a plain comparison of two complete spectra.     

Broadband absorption spectroscopy in turbid media by combined frequency-domain and steady-state methods

A technique for measuring broadband near-infrared absorption spectra of turbid media that uses a combination of frequency-domain (FD) and steady-state (SS) reflectance methods is presented. Most of the wavelength coverage is provided by a white-light SS measurement, whereas the FD data are acquired at a few selected wavelengths. Coefficients of absorption (mu(a)) and reduced scattering (mu(s)') derived from the FD data are used to calibrate the intensity of the SS measurements and to estimate mu(s)' at all wavelengths in the spectral window of interest. After these steps are performed, one can determine mu(a) by comparing the SS reflectance values with the predictions of diffusion theory, wavelength by wavelength. Absorption spectra of a turbid phantom and of human breast tissue in vivo, derived with the combined SSFD technique, agree well with expected reference values. All measurements can be performed at a single source-detector separation distance, reducing the variations in sampling volume that exist in multidistance methods. The technique uses relatively inexpensive light sources and detectors and is easily implemented on an existing multiwavelength FD system.     

Spectral Emissivity of Surface Blackbody Calibrators

The normal spectral emissivity of commercial infrared calibrators is compared with measurements of anodized aluminum samples and grooved aluminum surfaces coated with Pyromark. Measurements performed by FTIR spectroscopy in the wavelength interval from 2 to 20 μm and at temperatures between 5 and 550°C are presented with absolute uncertainties from 0.25% to 1% in spectral regions with sufficient signal and no significant atmospheric gas absorption. A large variation in emissivity with wavelength is observed for some surfaces, i.e., from 1% to 3% to more than 10%. The variation in emissivity using similar materials can be reduced to 0.5–1% by optimizing the coating process and the surface geometry. Results are discussed and an equation for calculation of the equivalent blackbody surface temperature from FTIR spectra is presented, including reflected ambient radiation. It is in most cases necessary to correct temperature calibration results for calibrators calibrated at 8–14 μm to obtain absolute accuracies of 0.1–1°C in other spectral regions depending on the temperature. Uncertainties are discussed and equations are given for the correction of measured radiation temperatures.     

基于可见/近红外光谱分析技术的水性油墨黏度预测模型

针对水性油墨黏度测量方法存在操作复杂、主观性强等问题,利用可见/近红外光谱分析技术结合化学计量学方法,建立水性油墨黏度预测模型,实现水性油墨黏度的快速无损检测。首先,利用微型光纤光谱仪采集水性油墨样本的反射光谱;再通过比较不同预处理方法对原始光谱数据的预处理效果,分别基于原始全光谱及预处理后的光谱数据构建水性油墨黏度的偏最小二乘回归(PLSR)和主成分回归(PCR)预测模型;最后,将预处理后的光谱数据采用连续投影算法(SPA)和竞争性自适应重加权算法(CARS)提取特征波长,并基于特征波长的光谱数据建立水性油墨黏度的PLS预测回归模型。结果表明,采用SPA算法从全光谱中只提取了4个特征波长,不仅显著简化了模型,提升了模型的运算效率,建立的SNV-SPA-PLS模型还具有最佳的预测性能(R_p²=0.9992,RMSEP=0.0732)。该研究结果表明应用光谱分析技术实现对水性油墨黏度检测是有效可行的,为进一步通过光谱分析技术进行水性油墨在线黏度检测提供了新方法,为提高印刷品质量稳定性提供了技术基础。     

Correction of photoresponse nonuniformity for matrix detectors based on prior compensation for their nonlinear behavior

What we believe to be a novel procedure to correct the nonuniformity that is inherent in all matrix detectors has been developed and experimentally validated. This correction method, unlike other nonuniformity-correction algorithms, consists of two steps that separate two of the usual problems that affect characterization of matrix detectors, i.e., nonlinearity and the relative variation of the pixels' responsivity across the array. The correction of the nonlinear behavior remains valid for any illumination wavelength employed, as long as the nonlinearity is not due to power dependence of the internal quantum efficiency. This method of correction of nonuniformity permits the immediate calculation of the correction factor for any given power level and for any illuminant that has a known spectral content once the nonuniform behavior has been characterized for a sufficient number of wavelengths. This procedure has a significant advantage compared with other traditional calibration-based methods, which require that a full characterization be carried out for each spectral distribution pattern of the incident optical radiation. The experimental application of this novel method has achieved a 20-fold increase in the uniformity of a CCD array for response levels close to saturation.