Least-squares Calibration Research Articles

A Novel Low-Order Method for Recovery of the Corneal Shape

To describe a novel low-order method for the recovery of the corneal height from videokeratographically obtained images. The method uses an iterative cubic approach with implicit continuous curvature. Convergence is easily established for a particular videokeratograph. The effect of skew rays is treated in a postprocessing step. Four simulated model corneas are tested: (1) an asphere; (2) an ellipsoid; (3) a radially keratotomized cornea; and (4) a simulation of photorefractive keratectomy (PRK). The corneal height, slope, and tilt are compared against theory and a 2nd order Taylor series method using root mean square error measures. The effect of lateral and axial shifts (up to 0.1 mm) is examined. The two methods are tested (experimentally) on an 8-mm spherical calibration ball, in which the image data are processed using a least-squares calibration procedure. The lowest height errors are found for the asphere and PRK models (4.5 x 10 microm and 3.6 x 10 microm). The maximum height error is 0.38 microm (ellipsoid), with 0.14 microm average overall error and 0.45 microm error for the 8-mm calibration ball. The comparison method has an average error of 0.92 microm, with maximum error of 1.5 microm (PRK) and 0.55 microm error for the 8-mm calibration ball. Shift induces larger (approximately 200 microm/mm) height errors than axial shift (approximately 2 microm/mm), but the errors are similar between methods. A demonstration on additional ellipsoids suggests the new algorithm (without skew ray compensation) is not as effective as the comparison method for increasingly nonspherical surfaces. The method has a short completion time of 2.3 s in seven iterations using MATLAB version 5.0 (The MathWorks, Inc., Natick, MA), running on a Pentium III 667-MHz processor with 128 MB RAM, and running the Windows 2000 operating system (Microsoft, Redmond, WA). An accurate, simple, robust, iteratively stable and fast method for estimating the corneal shape is described. A recovery with continuous curvature and skew ray compensation suggests a potential improvement within the context of current standard corneal shape recovery algorithms.

Monitoring and control of Gluconacetobacter xylinus fed-batch cultures using in situ mid-IR spectroscopy

A partial least-squares calibration model, relating mid-infrared spectral features with fructose, ethanol, acetate, gluconacetan, phosphate and ammonium concentrations has been designed to monitor and control cultivations of Gluconacetobacter xylinus and production of gluconacetan, a food grade exopolysaccharide (EPS). Only synthetic solutions containing a mixture of the major components of culture media have been used to calibrate the spectrometer. A factorial design has been applied to determine the composition and concentration in the calibration matrix. This approach guarantees a complete and intelligent scan of the calibration space using only 55 standards. This calibration model allowed standard errors of validation (SEV) for fructose, ethanol, acetate, gluconacetan, ammonium and phosphate concentrations of 1.16 g/l, 0.36 g/l, 0.22 g/l, 1.54 g/l, 0.24 g/l and 0.18 g/l, respectively. With G. xylinus, ethanol is directly oxidized to acetate, which is subsequently metabolized to form biomass. However, residual ethanol in the culture medium prevents bacterial growth. On-line spectroscopic data were implemented in a closed-loop control strategy for fed-batch fermentation. Acetate concentration was controlled at a constant value by feeding ethanol into the bioreactor. The designed fed-batch process allowed biomass production on ethanol. This was not possible in a batch process due to ethanol inhibition of bacterial growth. In this way, the productivity of gluconacetan was increased from 1.8 × 10 −3 [C-mol/C-mol substrate/h] in the batch process to 2.9 × 10 −3 [C-mol/C-mol substrate/h] in the fed-batch process described in this study.

Carbon nanotube-chitosan system for electrochemical sensing based on dehydrogenase enzymes.

Multiwalled carbon nanotubes (CNT) were solubilized in aqueous solutions of a biopolymer chitosan (CHIT). The CHIT-induced solubilization of CNT facilitated their manipulations, including the modification of electrode surfaces for sensor and biosensor development. The colloidal solutions of CNT-CHIT were placed on the surface of glassy carbon (GC) electrodes to form robust CNT-CHIT films, which facilitated the electrooxidation of NADH. The GC/CNT-CHIT sensor for NADH required approximately 0.3 V less overpotential than the GC electrode. The susceptibility of CHIT to chemical modifications was explored in order to covalently immobilize glucose dehydrogenase (GDH) in the CNT-CHIT films using glutaric dialdehyde (GDI). The stability and sensitivity of the GC/CNT-CHIT-GDI-GDH biosensor allowed for the interference-free determination of glucose in the physiological matrix (urine). In pH 7.40 phosphate buffer solutions, linear least-squares calibration plots over the range 5-300 microM glucose (10 points) had slopes 80 mA M(-1) cm(-2) and a correlation coefficient 0.996. The detection limit was 3 microM glucose (S/N = 3). The CNT-CHIT system represents a simple and functional approach to the integration of dehydrogenases and electrodes, which can provide analytical access to a large group of enzymes for wide range of bioelectrochemical applications including biosensors and biofuel cells.

Simultaneous spectrophotometric determination of carbamazepine and phenytoin in serum by PLS regression and comparison with HPLC

Carbamazepine (CBZ) and phenytoin (PHT) are two antiepileptic drugs which are used simultaneously. In this paper a partial least-squares (PLS) calibration method is described for the simultaneous spectrophotometric determination of CBZ and PHT in plasma. Standard binary mixtures of CBZ and PHT have been resolved by application of PLS-1 to their UV spectra. Then, the binary standard solutions, spiked to plasma, were prepared and after the extraction of the drugs, their corresponding UV spectrum were analyzed by PLS regression to calculate the concentration of drugs in unknown plasma. A leave one out cross-validation procedure was employed to find the optimum numbers of latent variables using PRESS. A HPLC method was also applied for simultaneous determination of two drugs in the plasma and in methanol. The mean recoveries obtained by PLS were 98.4 and 98.2 for CBZ and PHT and those obtained by HPLC were 100.1 and 101.7, respectively. Although, the HPLC method showed better performance than PLS, it was found that the results obtained by PLS were comparable with those obtained by HPLC method.

Determination of Lubricant Base Oil Properties by near Infrared Spectroscopy Using Different Sample and Variable Selection Methods

The use of near infrared (NIR) spectroscopy and chemometrics for the prediction of seven lubricant base oil properties was studied. The partial least-squares calibration models were developed using spectra acquired on an acousto-optic tunable filter (AOTF)-NIR spectrophotometer equipped with a fibre-optic probe in the 1100–1700 nm region. In this work, 88 samples obtained from three Brazilian refineries over a period of two years were employed. Different variable selection and sample selection methods were also investigated. The partial least squares regression (PLSR) models thus obtained showed good correlation coefficients for the properties studied and the calculated root mean square errors of prediction (relative density = 0.0005 g cm−3; molecular weight = 12 g mol−1; flash point = 7°C; temperature 50% recovered = 6.5°C; aromatic carbon assay = 0.5%; naftenic carbon assay = 1.0% and parafinic carbon assay = 1.4%) were lower than half the reproducibility values defined by the ASTM methods, except for the relative density. These results indicate, therefore, the potential of the NIR spectroscopy and chemometric techniques for on-line lubricant oil production process control.

The detection and quantification of adulteration in olive oil by near-infrared spectroscopy and chemometrics.

A new procedure has been developed for the classification and quantification of the adulteration of pure olive oil by soya oil, sun flower oil, corn oil, walnut oil and hazelnut oil. The study was based on a chemometric analysis of the near-infrared (NIR) spectra of olive-oil mixtures containing different adulterants. The adulteration of olive oil was carefully carried out gravimetrically in a 4 mm quartz cuvette, starting with pure olive oil in the cuvette first. NIR spectra of the 525 adulterated mixtures were measured in the region of 12,000-4000 cm(-1). The spectra were subjected batch wise to multiplicative signal correction (MSC) before calculating the principal component (PCA) models. The MSC-corrected data were subjected to Savitzky-Golay smoothing and a mean normalization procedure before developing partial least-squares calibration (PLS) models. The results revealed that the models predicted the adulterants, corn oil, sun flower oil, soya oil, walnut oil and hazelnut oil involved in olive oil with error limits +/-0.57, +/-1.32, +/-0.96, +/-0.56 and +/-0.57% weight/weight, respectively. Furthermore, the PCA developed models were able to classify unknown adulterated olive oil mixtures with almost 100% certainty. Quantification of the adulterants was carried out using their respective PLS models within the same error limits as mentioned above.

Fast spectrophotometric determination of fluoride in ground waters by flow injection using partial least-squares calibration

The presence of sulphate constitutes a serious interference in the usual zirconium lake-based spectrophotometric method for the determination of fluoride in water. In this report, full spectral data have been recorded for the zirconium lake of 2-(parasulfophenylazo)-1,8-dihydroxy-3,6-naphthalene-disulfonate (SPADNS) in the simultaneous presence of fluoride and sulphate, as obtained with a flow injection system with a diode-array detector. The information has been processed with partial least-squares (PLS) multivariate calibration. Adequate modeling using a sixteen-sample calibration set allows fluoride to be determined in ground waters by the automated flow injection method, even in the presence of sulphate in concentrations up to 1000 mg l −1. In the calibration range 0–1.50 mg l −1 for fluoride, the limit of detection is 0.1 mg l −1. The fluoride contents in real samples, as determined with the present method, were satisfactorily compared with those provided by ion selective potentiometry.

Pure component selectivity analysis of multivariate calibration models from near-infrared spectra.

A novel procedure is proposed as a method to characterize the chemical basis of selectivity for multivariate calibration models. This procedure involves submitting pure component spectra of both the target analyte and suspected interferences to the calibration model in question. The resulting model output is analyzed and interpreted in terms of the relative contribution of each component to the predicted analyte concentration. The utility of this method is illustrated by an analysis of calibration models for glucose, sucrose, and maltose. Near-infrared spectra are collected over the 5000-4000-cm(-)(1) spectral range for a set of ternary mixtures of these sugars. Partial least-squares (PLS) calibration models are generated for each component, and these models provide selective responses for the targeted analytes with standard errors of prediction ranging from 0.2 to 0.7 mM over the concentration range of 0.5-50 mM. The concept of the proposed pure component selectivity analysis is illustrated with these models. Results indicate that the net analyte signal is solely responsible for the selectivity of each individual model. Despite strong spectral overlap for these simple carbohydrates, calibration models based on the PLS algorithm provide sufficient selectivity to distinguish these commonly used sugars. The proposed procedure demonstrates conclusively that no component of the sucrose or maltose spectrum contributes to the selective measurement of glucose. Analogous conclusions are possible for the sucrose and maltose calibration models.

Minimum value assured by a method to determine gold in alloys by using laser-induced breakdown spectroscopy and partial least-squares calibration model

A procedure for estimating the minimum value assured by an analytical method has been developed. It is applied to the determination of gold in jewellery alloys by means of a recently proposed spectroscopy technique. The laser-induced breakdown spectroscopic data of 17 gold alloys, with gold concentration ranging between 50 and 100% were used as calibration set for carrying out the partial least-squares regression (PLS). Ninety alloys, with known gold concentration, were used to evaluate the method’s accuracy. Finally, the minimum guaranteed value of the gold content was analysed, taking into account the values for gold hallmark in Spanish regulations.

Fluorescence spectroscopy for monitoring extra virgin olive oil deterioration upon heating

Fluorescence spectroscopy is a reliable and fast method for determining the deterioration of extra virgin olive oil (EVOO). EVOO was analysed by HPLC for determining antioxidant changes in EVOO due to heating at 170°C for 3 h. This thermal oxidation caused a significant exponential decrease in hydroxytyrosol (OH-Tyr) and vitamin E (vitE), while the reduction in the tyrosol content was relatively small. Hydroperoxydes were analysed by an indirect colorimetric method. Their content decreased exponentially during the heating process. Fluorescence excitation spectra with emission wavelength at 330 nm were recorded to monitor the evolution of polyphenols and vitE, while fluorescence excitation spectra with emission at 450 nm were used to monitor the evolution of hydroperoxydes. Results of partial least-square calibration models (PLS) show that the degradation of polyphenols, vitE and hydroperoxide, as well as formation of fluorescent components derivatives can be quantified with fluorescence spectroscopy. Application of chemometrical data analysis allows to optimise the extraction of the information contained in the data. Fluorescence can therefore be used as a rapid technique for evaluating the quality of heat-treated EVOO.

Examination of spectral pretreatments for partial least-squares calibrations for chemical and physical properties of wheat.

Use of near-infrared (NIR) diffuse reflectance on ground wheat meal for prediction of protein content is a well-accepted practice. Although protein content has a strong bearing on the suitability of wheat (Triticum aestivum L.) for processed foods, wheat quality, as largely influenced by the configuration and conformation of the monomeric and polymeric endosperm storage proteins, is also of great importance to the food industry. The measurement of quality by NIR, however, has been much less successful. The present study examines the effects and trends of applying mathematical transformations (pretreatments) to NIR spectral data before partial least-squares (PLS) regression. Running mean smooths, Savitzky-Golay second derivatives, multiplicative scatter correction, and standard normal variate transformation, with and without detrending, were systematically applied to an extensive set of hard red winter wheat and hard white wheat grown over two seasons. The studied properties were protein content, sodium dodecyl sulfate (SDS) sedimentation volume, number of hours during grain fill at temperature <24 degrees C, and number of hours during grain fill at temperature >32 degrees C. The size of the convolution window used to perform a smooth or second derivative was also examined. The results indicate that for easily modeled properties such as protein content, the importance of pretreatment was lessened, whereas for the more difficult-to-model properties, such as SDS sedimentation volume, wide-window (>20 points) smooth or derivative convolutions were important in maximizing calibration performance. By averaging 30 PLS cross-validation trial statistics (standard error) for each property, we were able to ascertain the inherent modeling ability of each wheat property.

Variations in the ability of adsorbed fibrinogen to mediate platelet adhesion to polystyrene-based materials: a multivariate statistical analysis of antibody binding to the platelet binding sites of fibrinogen.

Platelet adhesion to the surfaces of biomaterials preadsorbed with plasma previously has been shown to be mediated exclusively by surface-bound fibrinogen and does not seem to involve the other adhesion proteins in plasma (Tsai et al., J Biomed Mater Res 2002;60:348-359). In this study, the influence of surface-bound fibrinogen on platelet adhesion to five different types of polystyrene-based microtiter plates preadsorbed with plasma was analyzed relative to the amount of adsorbed fibrinogen and monoclonal antibody binding to the adsorbed fibrinogen. There was no significant correlation between platelet adhesion and the absolute amount of adsorbed fibrinogen. However, platelet adhesion was positively correlated to the ability of the adsorbed fibrinogen to bind three types of monoclonal antibodies. The antibodies used bound to the sites on fibrinogen thought to be involved in platelet binding (the two gamma chain C-terminal dodecapeptides and the RGDF and RGDS sequences in each of the Aalpha chains). A partial least-squares calibration model was used to analyze the relative importance of these binding sites in fibrinogen to platelet adhesion. The gamma chain C-terminal dodecapeptide was shown to be the most important site in adsorbed fibrinogen in mediating platelet adhesion.

The use of Fourier-transform infrared spectroscopy for the quantitative determination of glucose concentration in whole blood

Fourier-transform infrared transmission spectroscopy has been used for the determination of glucose concentration in whole blood samples from 28 patients. A 4-vector partial least-squares calibration model, using the spectral range 950–1200 cm−1, yielded a standard-error-of-prediction of 0.59 mM for an independent test set. For blood samples from a single patient, we found that the glucose concentration was proportional to the difference between the values of the second derivative spectrum at 1082 cm−1 and 1093 cm−1. This indicates that spectroscopy at these two specific wavenumbers alone could be used to determine the glucose concentration in blood plasma samples from a single patient, with a prediction error of 0.95 mM.

A flow-through fluorimetric sensing device for determination of α- and β-naphthol mixtures using a partial least-squares multivariate calibration approach

A single flow-through optosensor spectrofluorimetric system is proposed for the resolution of mixtures of α- and β-naphthol at μg l −1 levels using a partial least-squares (PLS) calibration approach. The sensor was developed in conjunction with a monochannel flow-injection analysis system with fluorimetric detection using Sephadex QAE A-25 resin as an active sorbent substrate in the flow cell and the second derivative of the native synchronous fluorescence spectra of analytes as analytical signal. In the manifold, the solutions of naphthol (at pH 10.0) were injected in a carrier stream of KCl (0.15 M)/NaOH (10 −2 M). Because of the strong spectral overlap, the mixture could not be resolved by conventional spectrofluorimetry. The non-additive behaviour of the fluorescence signals revealed an interaction in the system, which was not found by working in the solution only (without the sorbent support). This interaction, probably due to the environment of the analytes on the solid phase, made impossible their simultaneous determination. So, the use of synchronous fluorescence spectroscopy or even its derivative signal could not resolve satisfactorily the mixture. The simultaneous determination of both naphthol has been carried out by recording the signal of the second-derivative synchronous fluorescence (Δ λ=170 nm) spectra between 200 and 450 nm and a PLS multivariate calibration treatment. The optimum number of factors was selected by using the cross-validation method. After validating the proposed method, it was applied to the determination of these compounds in natural waters with different amounts of each chemical.

Comparison of indices and multivariate models to non-destructively predict the fruit chlorophyll by means of visible spectrometry in apple fruit

Non-destructive, rapid, instrumental tools in fruit production are required for predicting the optimum harvest window and monitoring fruit quality during shelf life. The degree of chlorophyll degradation is a sensitive indicator for fruit maturation and ageing. Adequate indices for chlorophyll prediction by means of non-destructive spectral analysis have been studied in the fields of photosynthesis research and remote sensing developments. However, an evaluation of these indices and multivariate linear regression models does not exist so far for predicting the fruit chlorophyll content. Spectral transmittance recordings in the visible wavelength range were carried out on apple fruit Malus domestica Borkh. ‘Elstar’ ( n=99) and ‘Jonagold’ ( n=117). The fruit chlorophyll a content of ‘Elstar’ apples was measured wet-chemically and predicted by means of the specific indices: NDVI, Tr 698/Tr 760, red-edge, TrII on Tr′( λ), TrII, and RVSI with the correlation coefficients of determination R 2=0.84, 0.81, 0.75, 0.81, 0.15, and 0.67, respectively. Partial least-squares (PLS) calibration models were built using calibrated spectra (630–730 nm), first derivative of spectra and second derivative of spectra yielding multivariate correlation coefficients of determination R 2=0.81, 0.86, and 0.92, respectively. Similar results were found for ‘Jonagold’ apple fruit. Linear regression of indices and PLS calibration models were empirically tested on the chlorophyll a content of apple fruit measuring the same cultivars grown in a different seasons and growing locations. In the case of ‘Elstar’ apple fruit, correlation coefficients of fruit chlorophyll a content analysed wet-chemically as well as fruit maturation measured as calendar weeks were similar to those in the calibration experiment. Application of linear regression equations of indices and PLS models on spectra of ‘Jonagold’ apple fruit led to less accurate results for those methods, which use wavelengths above 720 nm as indicative range.

Fourier-transform infrared spectroscopy for quantification of hydrogen fluoride in sulfur hexafluoride decomposed by partial discharges and sparks

Hydrogen fluoride has been measured by infrared spectroscopy after SF 6 decomposition by either electric partial discharges or sparking. Reference standard spectra necessary for quantification were calculated using the HITRAN96 data base. It is shown that the pressure broadening functions as tabulated for atmospheric conditions, are also applicable for SF 6 as matrix gas. Since a strong J-quantum number dependence exists for pressure broadening of the individual HF-lines, the folding effects for the spectra based on a sinc 2-instrumental line shape function of the FT-IR-spectrometer as used in this study lead to significantly different line dependent deviations from the desired linear Beer law approach. The linearity range of the maximum line absorbances in dependence of the trace volume mixing ratio was studied for a spectral resolution of 0.5 cm −1, which is much larger than the true line halfwidths found for an SF 6 pressure close to 100 kPa. Quantitative results are reported for spectra obtained at optical pathlength of 10 cm and partial HF pressures up to 40 Pa using least-squares fitting and several HITRAN96-derived standard spectra. Furthermore, results from multivariate partial least-squares calibration are presented with a standard error of prediction of 0.2 Pa.

Simultaneous Spectrophotometric Determination of Iron, Titanium, and Aluminum by Partial Least-Squares Calibration Method in Micellar Medium

Simultaneous spectrophotometric determination of iron, titanium and aluminum was carried out using their morin (3,5,7,2′,4′-penta hydroxy flavone) complexes in Triton X-100 micellar medium. Partial least-squares regression was employed for the resolution of ternary mixtures of Fe, Ti, and Al. The presence of Triton X-100 micellar system avoids the solvent extraction step necessary for the formation of soluble morin complexes. The limits of detection obtained for Fe (III), Ti (IV), and for Al (III) were 0.03, 0.04, and 0.02 µg mL−1, respectively. The relative standard error for applying the method to the analysis of 20 synthetic samples in the concentration ranges of 0.03 to 1.0 µg mL−1 Al (III), 0.06 to 1.6 µg mL−1 Ti (IV), and 0.04 to 1.5 µg mL−1 Fe (III) was 5%. Analysis of synthetic and artificial mixtures of solutions of several alloys was successfully performed by the method.

Comparison of UV derivative-spectrophotometry and partial least-squares (PLS-1) calibration for determination of methotrexate and leucovorin in biological fluids.

Binary mixtures of methotrexate (MTX) and leucovorin (LV) have been resolved by application of first-derivative spectrophotometry and partial least squares calibration (PLS-1). By measuring the first-derivative signals of MTX and LV at 354 and 300 nm, respectively, simultaneous determination was possible. The mean recoveries for urine samples were 91 and 96% for MTX and LV, respectively. Partial least squares (PLS-1) multivariate calibration has been applied to the determination of these compounds in serum and in urine without pretreatment of the samples. The absorption spectra of serum or urine samples spiked with methotrexate and/or leucovorin, were used to optimize the calibration matrixes by the PLS-1 method. The sensitivity and selectivity of the proposed procedures were calculated. Mean recoveries were 101 and 97% for MTX and LV, respectively, for serum samples, and 101 and 98% for MTX and LV, respectively, for urine samples.

Calibration Standardization Algorithm for Partial Least-Squares Regression: Application to the Determination of Physiological Levels of Glucose by Near-Infrared Spectroscopy

Calibration standardization methodology for near-infrared (near-IR) spectroscopy is described for updating a partial least-squares calibration model to take into account changes in instrumental response. The guided model reoptimization (GMR) algorithm uses a transfer set of eight samples to characterize the new response and a database of previously acquired spectra used to develop the original calibration model. The samples in the transfer set need not have been measured under the old instrumental conditions, making the algorithm compatible with samples that change over time. The spectra comprising the transfer set are used to guide an iterative optimization procedure that (1) finds an optimal subset of samples from the original database to use in computing the updated model and (2) finds an optimal set of weights to apply to the spectral resolution elements in order to minimize the effects of instrumental changes on the computed model. The optimization relies on an alternating grid search and stepwise addition/deletion steps. The algorithm is evaluated through the use of combination region near-IR spectra to determine physiological levels of glucose in a synthetic biological matrix containing bovine serum albumin and triacetin in phosphate buffer. The ability to update a calibration to account for changes in the response of a Fourier transform spectrometer over four to six years is examined in this study. Separate spectral databases collected in 1994 and 1996 are used with a transfer set and separate test set of spectra collected in 2000. With the 1994 database, the standardization algorithm achieves a standard error of prediction (SEP) of 0.69 mM for the 2000 test set. This compares favorably to SEP values > 2 mM when the original 1994 calibration model is used without standardization. A similar improvement in the prediction performance of the 2000 test set is obtained after standardization with the 1996 database (SEP = 0.70 mM).

Multivariate calibration models for lysozyme from near-infrared transmission spectra in scattering solutions of monodisperse microspheres.

The ability to quantify lysozyme is demonstrated for a series of aqueous samples with different degrees of scattering. Near-infrared spectra are collected for two sets of lysozyme/scattering solutions. In both sets of samples, the solutions are composed of lysozyme dissolved in acetate buffer with suspended monodisperse latex microspheres of polystyrene. The diameter of the microspheres is 6.4 microm for the first set and 0.6 microm for the second. For each set, the amount of microspheres range from 0.005 to 0.998 wt %, the lysozyme concentrations range from 0.834 to 28.6 mg/mL, and solution compositions are designed to minimize correlations between the concentration of lysozyme and percentage of microspheres. Near-infrared spectra are collected individually for each set of solutions. Single-beam spectra are collected over the combination spectral range (5000-4000 cm(-1), 2.0-2.5 microm) by transmitting the incident radiation through a 1.5-mm-thick sample that is maintained at 21 degrees C. Partial least-squares calibration models are evaluated individually for each data set both with and without wavelength optimization. Results indicate that models from raw, nonmodified, single-beam spectra are incapable of extracting lysozyme concentration from these highly scattering solutions. Accurate concentration measurements are possible, however, by implementing either a multiplicative scatter correction to the single-beam spectra or by taking the ratio of these single-beam spectra to an appropriate reference spectrum. In addition, digital Fourier filtering of these spectra enhances model performance. The best calibration model in the presence of 6.4-microm microspheres is obtained from multiplicative scatter corrected single-beam spectra over the 4550-4190-cm(-1) spectral range. The mean percent error of prediction (MPEP) and standard error of prediction (SEP) for this model are 2.2% and 0.28 mg/mL, respectively. Likewise, the multiplicative scatter corrected spectra with wavelength optimization provided the best calibration model for the 0.6-microm data set. In this case, the MPEP and SEP are 2.3% and 0.44 mg/mL, respectively. In addition, the ability to predict lysozyme concentrations is evaluated for the situation where the degree of scattering is greater in the predication samples compared to the calibration samples. Differences in the prediction ability are noted between the 6.4- and 0.6-microm data sets.