Physics-based multiplicative scatter correction approaches for improving the performance of calibration models

Light scattering effects pose a major problem in the estimation of chemical properties of particulate systems such as blood, tissue, and pharmaceutical solids. Recently, Martens et al. proposed an extended multiplicative signal correction (EMSC) approach where light-scattering effects were taken into account in an empirical manner. It is possible to include causal, first-principles mathematical models based on the physics of light scattering into the EMSC framework. This could lead to significant improvements in the separation of absorption and scattering effects. A preconditioning step prior to application of EMSC, whereby a transformation based on the physics of light scattering is used to convert the spectra into a form where the absorption and scattering effects are separable (an underlying assumption of EMSC), is proposed. Results indicate that the transformation followed by EMSC gives better calibration models than the direct application of EMSC to the absorbance spectra.     

Extracting chemical information from spectral data with multiplicative light scattering effects by optical path-length estimation and correction

When analyzing complex mixtures that exhibit sample-to-sample variability using spectroscopic instrumentation, the variation in the optical path length, resulting from the physical variations inherent within the individual samples, will result in significant multiplicative light scattering perturbations. Although a number of algorithms have been proposed to address the effect of multiplicative light scattering, each has associated with it a number of underlying assumptions, which necessitates additional information relating to the spectra being attained. This information is difficult to obtain in practice and frequently is not available. Thus, with a view to removing the need for the attainment of additional information, a new algorithm, optical path-length estimation and correction (OPLEC), is proposed. The methodology is applied to two near-infrared transmittance spectral data sets (powder mixture data and wheat kernel data), and the results are compared with the extended multiplicative signal correction (EMSC) and extended inverted signal correction (EISC) algorithms. Within the study, it is concluded that the EMSC algorithm cannot be applied to the wheat kernel data set due to core information for the implementation of the algorithm not being available, while the analysis of the powder mixture data using EISC resulted in incorrect conclusions being drawn and hence a calibration model whose performance was unacceptable. In contrast, OPLEC was observed to effectively mitigate the detrimental effects of physical light scattering and significantly improve the prediction accuracy of the calibration models for the two spectral data sets investigated without any additional information pertaining to the calibration samples being required.     

Raman spectra of biological samples: A study of preprocessing methods

In this study preprocessing of Raman spectra of different biological samples has been studied, and their effect on the ability to extract robust and quantitative information has been evaluated. Four data sets of Raman spectra were chosen in order to cover different aspects of biological Raman spectra, and the samples constituted salmon oils, juice samples, salmon meat, and mixtures of fat, protein, and water. A range of frequently used preprocessing methods, as well as combinations of different methods, was evaluated. Different aspects of regression results obtained from partial least squares regression (PLSR) were used as indicators for comparing the effect of different preprocessing methods. The results, as expected, suggest that baseline correction methods should be performed in advance of normalization methods. By performing total intensity normalization after adequate baseline correction, robust calibration models were obtained for all data sets. Combination methods like standard normal variate (SNV), multiplicative signal correction (MSC), and extended multiplicative signal correction (EMSC) in their basic form were not able to handle the baseline features present in several of the data sets, and these methods thus provide no additional benefits compared to the approach of baseline correction in advance of total intensity normalization. EMSC provides additional possibilities that require further investigation.     

Estimating and correcting mie scattering in synchrotron-based microscopic fourier transform infrared spectra by extended multiplicative signal correction

We present an approach for estimating and correcting Mie scattering occurring in infrared spectra of single cells, at diffraction limited probe size, as in synchrotron based microscopy. The Mie scattering is modeled by extended multiplicative signal correction (EMSC) and subtracted from the vibrational absorption. Because the Mie scattering depends non-linearly on alpha, the product of the radius and the refractive index of the medium/sphere causing it, a new method was developed for estimating the Mie scattering by EMSC for unknown radius and refractive index of the Mie scatterer. The theoretically expected Mie contributions for a range of different alpha values were computed according to the formulae developed by Van de Hulst (1957). The many simulated spectra were then summarized by a six-dimensional subspace model by principal component analysis (PCA). This subspace model was used in EMSC to estimate and correct for Mie scattering, as well as other additive and multiplicative interference effects. The approach was applied to a set of Fourier transform infrared (FT-IR) absorbance spectra measured for individual lung cancer cells in order to remove unwanted interferences and to estimate ranges of important alpha values for each spectrum. The results indicate that several cell components may contribute to the Mie scattering.     

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.     

New indicator for optimal preprocessing and wavelength selection of near-infrared spectra

Preprocessing of near-infrared spectra to remove unwanted, i.e., non-related spectral variation and selection of informative wavelengths is considered to be a crucial step prior to the construction of a quantitative calibration model. The standard methodology when comparing various preprocessing techniques and selecting different wavelengths is to compare prediction statistics computed with an independent set of data not used to make the actual calibration model. When the errors of reference value are large, no such values are available at all, or only a limited number of samples are available, other methods exist to evaluate the preprocessing method and wavelength selection. In this work we present a new indicator (SE) that only requires blank sample spectra, i.e., spectra of samples that are mixtures of the interfering constituents (everything except the analyte), a pure analyte spectrum, or alternatively, a sample spectrum where the analyte is present. The indicator is based on computing the net analyte signal of the analyte and the total error, i.e., instrumental noise and bias. By comparing the indicator values when different preprocessing techniques and wavelength selections are applied to the spectra, the optimal preprocessing technique and the optimal wavelength selection can be determined without knowledge of reference values, i.e., it minimizes the non-related spectral variation. The SE indicator is compared to two other indicators that also use net analyte signal computations. To demonstrate the feasibility of the SE indicator, two near-infrared spectral data sets from the pharmaceutical industry were used, i.e., diffuse reflectance spectra of powder samples and transmission spectra of tablets. Especially in pharmaceutical spectroscopic applications, it is expected beforehand that the non-related spectral variation is rather large and it is important to remove it. The indicator gave excellent results with respect to wavelength selection and optimal preprocessing. The SE indicator performs better than the two other indicators, and it is also applicable to other situations where the Beer-Lambert law is valid.     

近红外光谱法测定茶多酚中总儿茶素含量

以高效液相色谱(HPLC)分析结果为参考值,建立了快速测量茶多酚中总儿茶素含量的近红外光谱定标模型.将48份茶多酚样品组成定标样品集,在1000～2500nm(4000～10000cm-1)的近红外漫反射光谱为定标波长范围内,光谱经一阶导数(Firstderivative)、二阶导数(Secondderivative)、标准归一化(Stan-dardnormalvariate,SNV)和多元散射校正(multiplicativesignalcorrection,MSC)处理后结合偏最小二乘回归(PLS)定标.经内部交叉验证表明,光谱经SNV处理后建模结果最佳.模型的相关系数Corr.Coeff=0.997,校正均方根RMSEC=1.71%.比较了经典最小二乘法(CLS)、偏最小二乘法(PLS)和主成分回归(PCR)等方法建模结果,以偏最小二乘回归建模效果最好.     

Extended multiplicative signal correction as a tool for separation and characterization of physical and chemical information in Fourier transform infrared microscopy images of cryo-sections of beef loin

Extended multiplicative signal correction (EMSC) is used to separate and to characterize physical and chemical information in spectra from Fourier transform infrared (FT-IR) microscopy. This appears especially useful for applications in infrared spectroscopy where the scatter variance in spectra changes with the chemical variance in the sample set. In these cases the chemical information of specific bands that are assigned to functional groups is easier to interpret when the scatter information is removed from the spectra. We show that scatter (physical) information in FT-IR spectra of heat-treated beef loin is related to chemical changes due to heat treatment. This information is caused by textural changes induced by the heat treatment and expressed by physical effects as the optical path length. The chemical absorbance changes introduced in the FT-IR spectra due to heat treatment are shifts in the protein region of the infrared spectrum caused by changes in the secondary structure of the proteins. If the scatter and the chemical information is not separated properly, scatter information may erroneously be interpreted as chemical information.     

Calibration of multiplexed fiber-optic spectroscopy

Large-scale commercial bioprocesses that manufacture biopharmaceutical products such as monoclonal antibodies generally involve multiple bioreactors operated in parallel. Spectra recorded during in situ monitoring of multiple bioreactors by multiplexed fiber-optic spectroscopies contain not only spectral information of the chemical constituents but also contributions resulting from differences in the optical properties of the probes. Spectra with variations induced by probe differences cannot be efficiently modeled by the commonly used multivariate linear calibration models or effectively removed by popular empirical preprocessing methods. In this study, for the first time, a calibration model is proposed for the analysis of complex spectral data sets arising from multiplexed probes. In the proposed calibration model, the spectral variations introduced by probe differences are explicitly modeled by introducing a multiplicative parameter for each optical probe, and then their detrimental effects are effectively mitigated through a "dual calibration" strategy. The performance of the proposed multiplex calibration model has been tested on two multiplexed spectral data sets (i.e., MIR data of ternary mixtures and NIR data of bioprocesses). Experimental results suggest that the proposed calibration model can effectively mitigate the detrimental effects of probe differences and hence provide much more accurate predictions than commonly used multivariate linear calibration models (such as PLS) with and without empirical data preprocessing methods such as orthogonal signal correction, standard normal variate, or multiplicative signal correction.     

PARTICLE SIZE DISTRIBUTION STUDY OF LANTHANUM-DOPED YTTRIA POWDERS BY SEM-IMAGE ANALYSIS AND LASER LIGHT-SCATTERING METHODS

Particle size analysis of lanthana-doped yttria powders by automatic image analysis (IA) has been used to improve the quality of sizing data obtained using classical laser light scattering methods. A calibration test using monomodal, standard polystyrene spheres confirmed that the IA method provides a narrower distribution and improved size resolution compared to that obtained by light scattering. To ensure that the light-scattering distributions obtained in a study of lanthana-doped yttria powders were accurate, image analysis methods were used to obtain particle size distribution data from which corrected parameters for data reduction of the light-scattering data were obtained. In one case, a bimodal distribution obtained by light-scattering data was found to be artifactural when compared to the distribution obtained from IA measurements. It is concluded that direct particle size distribution analysis by image analysis can be successfully applied in light-scattering studies of yttria powders and can be extended to sizing studies of other powder types.     

Extraction of chemical information of suspensions using radiative transfer theory to remove multiple scattering effects: application to a model multicomponent system

The effectiveness of a scatter correction approach based on decoupling absorption and scattering effects through the use of the radiative transfer theory to invert a suitable set of measurements is studied by considering a model multicomponent suspension. The method was used in conjunction with partial least-squares regression to build calibration models for estimating the concentration of two types of analytes: an absorbing (nonscattering) species and a particulate (absorbing and scattering) species. The performances of the models built by this approach were compared with those obtained by applying empirical scatter correction approaches to diffuse reflectance, diffuse transmittance, and collimated transmittance measurements. It was found that the method provided appreciable improvement in model performance for the prediction of both types of analytes. The study indicates that, as long as the bulk absorption spectra are accurately extracted, no further empirical preprocessing to remove light scattering effects is required.     

Multivariate sensitivity for the interpretation of the effect of spectral pretreatment methods on near-infrared calibration model predictions

Predictions obtained from a multivariate calibration model are sensitive to variations in the spectra such as baseline shifts, multiplicative effects, etc. Many spectral pretreatment methods have been developed to reduce these distortions, and the best method is usually the one that minimizes the prediction error for an independent test set. This paper shows how multivariate sensitivity can be used to interpret spectral pretreatment results. Understanding why a particular pretreatment method gives good or bad results is important for ruling out chance effects in the conventional process of "trial and error", thus obtaining more confidence in the finally selected model. The principles are exemplified using the transmission near-infrared spectroscopic prediction of oxygenates in ampules of the standard reference material gasoline. The pretreatment methods compared are the multiplicative signal correction, first-derivative method, and second-derivative method. It is shown that for this application the first- and second-derivative methods are successful in removing the background. However, differentiating the spectra substantially reduces multivariate net analyte signal (in the worst case by a factor of 21). Consequently, a significantly smaller multivariate sensitivity is obtained which leads to increased spectral error propagation resulting in a larger uncertainty in the regression vector estimate and larger prediction errors. Differentiating spectra also increases the spectral noise (each time by a factor 2(1/2)) but this effect, which is well-known, is of minor importance for the current application.     

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.     

Near-infrared spectra of Penicillium camemberti strains separated by extended multiplicative signal correction improved prediction of physical and chemical variations

Different methods for spectral preprocessing were compared in relation to the ability to distinguish between fungal isolates and growth stages for Penicillium camemberti grown on cheese substrate. The best classification results were obtained by temperatureand wavelength-extended multivariate signal correction (TWEMSC) preprocessing, whereby three patterns of variation in nearinfrared (NIR) log(1/R) spectra of fungal colonies could be separated mathematically: (1) physical light scattering and its wavelength dependency, (2) differences in light absorption of water due to varying sample temperature, etc., and (3) differences in light absorption between different fungal isolates. With this preprocessing, discriminant partial least squares (PLS) regression yielded 100% correct classification of three isolates, both within the cross-validated calibration set and in two independent test sets of samples.     

Advanced calibration strategy for in situ quantitative monitoring of phase transition processes in suspensions using FT-Raman spectroscopy

There is an increasing interest in using Raman spectroscopy to identify polymorphic forms and monitor phase changes in pharmaceutical products for quality control. Compared with other analytical techniques for the identification of polymorphs such as X-ray powder diffractometry and infrared spectroscopy, FT-Raman spectroscopy has the advantages of enabling fast, in situ, and nondestructive measurements of complex systems such as suspension samples. However, for suspension samples, Raman intensities depend on the analyte concentrations as well as the particle size, overall solid content, and homogeneity of the solid phase in the mixtures, which makes quantitative Raman analysis rather difficult. In this contribution, an advanced model has been derived to explicitly account for the confounding effects of a sample's physical properties on Raman intensities. On the basis of this model, a unique calibration strategy called multiplicative effects correction (MEC) was proposed to separate the Raman contributions due to changes in analyte concentration from those caused by the multiplicative confounding effects of the sample's physical properties. MEC has been applied to predict the anhydrate concentrations from in situ FT-Raman measurements made during the crystallization and phase transition processes of citric acid in water. The experimental results show that MEC can effectively correct for the confounding effects of the particle size and overall solid content of the solid phase on Raman intensities and, therefore, provide much more accurate in situ quantitative predictions of anhydrate concentration during crystallization and phase transition processes than traditional PLS calibration methods.     

Liquid waveguide-based evanescent wave sensor that uses two light sources with different wavelengths

We demonstrate a prototypic optofluidic evanescent wave sensor made of poly(dimethylsiloxane) (PDMS) elastomer in which two light sources with different wavelengths are coupled into an optofluidic liquid-core/liquid-cladding (L(2)) waveguide. The exponentially decaying evanescent wave interacts with analyte molecules dissolved in the cladding fluids or products formed by in situ reactions at the core-cladding interface. The analyte molecules exhibit distinctly different light absorbance at the two wavelengths during the light-analyte interaction. Therefore, by using the normalized absorbance calculated from the intensity ratio of the two wavelengths instead of the absolute magnitude of either signal, unwanted effects from omnipresent external noise sources can be reduced. In addition, the differential absorption of the two beams by the analyte solutions can be used to enhance the resolution of sample analysis. The evanescent wave sensor based on a liquid waveguide can also be used for real-time monitoring of chemical reactions, because the core and cladding fluids in the L(2) waveguide are slightly miscible at the core-cladding interface due to the diffusional mixing.     

Correction of inner filter effect in mirror coating cells for trace level fluorescence measurements

The sensitivity of the spectrofluorometric technique can be improved by a factor of about 3.6 using a mirror coating cell. In the case of a large working range, the nonlinear relationship due to the absorbance of solutions between concentration of the analyte of interest and fluorescence intensity (called inner filter effect) must be corrected. This paper suggests a universal inner filter correction equation based on the physical absorbance phenomenon of a mirror coating cell that only depends on the solution absorbance spectra and the cell parameters. These parameters are determined with rhodamine b standard solutions and a simplex method-based mathematical fitting. The methodology has been successfully applied to the correction of classical and synchronous spectra in absorbent media. The partial least squares (PLS) quantification of a mixture of trace levels (approximately 1-10 microg L(-1)) of six polycyclic aromatic hydrocarbons (PAHs) by synchronous fluorescence is possible, even in an absorbent matrix. This simple method allows extension of the analytical field of fluorescence quantification to a large working range in absorbent solutions.     

Comparison of two multiplicative signal correction strategies for calibration transfer without standards

Two multiplicative signal correction (MSC) algorithms are compared for the standardization of data from two near-infrared (NIR) spectrometers. Absorbance spectra were measured from 1000-2200 nm for a set of 45 jet fuel samples. Data from one instrument were standardized to match data from a second instrument using windowed MSC (W-MSC) and moving window MSC (MW-MSC). For W-MSC user-defined windows were selected and for MW-MSC the window size was optimized based on a two-step procedure: 1) assigning a cut off window to avoid over-processing and 2) selection of a specific window size based on sample leverage. For reproducibility studies performed over time on a single instrument, data extending through the last day of the study (63 days outside the calibration) required no preprocessing except a peak alignment correction on day 58. For analysis between the two instruments, successful results were obtained using a sub-region of the data from 1000–1700 nm processed by MW-MSC using a 441 point window. A method of selecting an appropriate window size is proposed based on statistical significance testing.     

Multivariate curve resolution applied to infrared reflection measurements of soil contaminated with an organophosphorus analyte

Multivariate curve resolution (MCR) is a powerful technique for extracting chemical information from measured spectra of complex mixtures. A modified MCR technique that utilized both measured and second-derivative spectra to account for observed sample-to-sample variability attributable to changes in soil reflectivity was used to estimate the spectrum of dibutyl phosphate (DBP) adsorbed on two different soil types. This algorithm was applied directly to measurements of reflection spectra of soils coated with analyte without resorting to soil preparations such as grinding or dilution in potassium bromide. The results provided interpretable spectra that can be used to guide strategies for detection and classification of organic analytes adsorbed on soil. Comparisons to the neat DBP liquid spectrum showed that the recovered analyte spectra from both soils showed spectral features from methyl, methylene, hydroxyl, and P=O functional groups, but most conspicuous was the absence of the strong PO-(CH2)3CH3 stretch absorption at 1033 cm(-1). These results are consistent with those obtained previously using extended multiplicative scatter correction.     

光谱预处理对棉涤混纺面料近红外定量模型的影响

以46个棉涤混纺面料样品为研究对象,采集样品的近红外漫反射光谱,光谱范围为12 000~4 000 cm-1,利用偏最小二乘法建立定量校正模型,并用交叉检验法对模型进行检验,以交叉验证均方差RMSECV和决定系数R2作为判断模型优劣的标准.对利用无光谱预处理、一阶导数法、二阶导数法、多元散射校正和矢量归一化五种不同预处理方法所建的模型进行了比较,发现对光谱进行矢量归一化预处理所建模型最优;此外还分析了建立纺织布料的近红外光谱定量分析模型时主要的误差来源及近红外光谱分析技术用于纺织面料定量分析的可行性.