The correction of baseline drift is an important step in data preprocessing. An interval linear fitting method based on automatic critical-point-seeking was improved, which made it possible for the baseline to drift automatically. Experimental data were acquired from the sulfamic acid catalytic reaction of the aspirin system, which consisted of different proportions of aspirin.  A simulated baseline with different interval values of moving average smoothing determined setting parameters in this method. After baseline drifts caused by fluorescence were removed, the differences of characteristic aspirin peaks proved the efficiency of this method.

Raman spectroscopy is used worldwide in materials characterization for its ability to obtain information on vibrations from samples. It can also be used for on-line monitoring using a fiber-optic Raman probe (1,2). The Raman spectra show the characteristics for species in sharp and dense peaks. However, during the application of Raman spectroscopy, fluorescence of organic compounds in the samples, which are sometimes several orders of magnitude more intense than the weak Raman scatter, can interfere with the Raman signals (3). A phenomenon of baseline drift shows up, making the resolution and analysis of Raman spectra impractical. 

Both instrumental (4) and mathematical methods have been developed to reduce the drifted baseline caused by fluorescence. The use of laser excitation wavelengths such as 785–1064 nm, which does not eliminate fluorescence (5), is the most traditional instrumental method. Raman scattering is directly proportional to the fourth power of frequency; as the excitation wavelength increases, the sensitivity of the Raman becomes severely reduced. The use of anti-Stokes Raman spectroscopy is another method, based on theory (6). Mathematical methods (7–10) include the first- and second-order derivatives, wavelet transform, median filter, and manual polynomial fitting. These methods are useful in certain situations, but still have some limitations. For example, derivatives are effective, but as a result the shape of the Raman spectrum is changed; wavelet transform can be differentiable in the high- and low-frequency components of the signals; however, it is difficult to choose a decomposition method. Manual polynomial fittings require the user to identify the "non-Raman" locations manually (11), and afterwards the baseline curve is formed by fitting these locations. Consequently, the result involves the inevitable subjective factors and, in addition, the workload is always heavy. Therefore, it is important to choose an optimal decomposition method. 

Piecewise linear fitting based on critical-point-seeking was proposed in this study. The method determines an optimum corrected spectrum by correlation analysis, which can conquer these limitations. A Raman spectrum from the sulfamic acid catalytic reaction of an aspirin system was used as a study subject. By using this method, the Raman spectrum drifted baseline was automatically eliminated, leaving only the corrected spectrum.  

Basis of Qualitative and Quantitative Raman Analysis

 is a plot of the intensity of Raman scattered radiation as a function of its frequency difference from the incident radiation (usually in units of wavenumbers, cm

which is the basis of qualitative analysis (12). The intensity or power of a normal Raman peak depends in a complex way upon the polarizability of the molecule, the intensity of the source, and the concentration of the active group. The power of Raman emission increases with the fourth power of the frequency of the source. Raman intensities are usually directly proportional to the concentration of the active species, which is the basis of quantitative analysis (13,14). Equation 1 shows the factors that determine the Raman scattering cross section: 

 is the frequency of scattered radiation; 

 is the intensity of the incident radiation; 

 is the concentration of the sample. The 

  term dominates if the other terms do not differ appreciably, and a higher frequency laser beam yields a stronger Raman signal. 

We used smoothing to preprocess the data for Raman spectroscopy with frequency shifts and high  sensitivity. Moving average smoothing can effectively lower the frequency and sensitivity as shown in equation 2: 

where ω is the interval number of the moving average smoothing window, which must be an odd number. 

 + δ) where the derivative of the function is defined and is not 0. If 

) the derivative is positive, whereas if 

) is minimum. After finding the local minimum, we can  get a set of minimal critical points λ

) can be fitted in a linear equation as shown in equation 3: 

) was acquired after the fitting baseline was removed from the original spectrum.  

A correlation analysis method was conducted between the original spectrum 

Figure 1: The process of interval linear fitting baseline correction.  			

A laser with the wavelength of 785 nm was used as the excitation light source (Laser-785, Ocean Optics), and a Raman spectrometer (Scientific-grade QE65000, Ocean Optics) was used for the detector. The Raman information was obtained using a fiber-optic probe (BAC100-785-OEM, Ocean Optics), with Spectrasuite spectroscopy software (Ocean Optics); the 

 axis on the workstation menu was selected to be Raman shift, and the selected integral time was 1/s to obtain the Raman spectrum for the 0–2000 cm

We saved the Raman spectrum of acetylsalicylic acid (AR, Tianjin Guangfu Fine Chemical Research Institute) first. According to the literature (15), we precisely weighed acetic anhydride to 41.0 g (AR, ChengDu KeLong Chemical Co.,Ltd.), salicylic acid to 27.7 g (AR, Tianjin Guangfu Fine Chemical Research Institute), and sulfamic acid to 0.5 g (AR, ShanTou XiLong chemical factory). The acetic anhydride, salicylic acid, and sulfamic acid were transferred sequentially to a 100-mL, three-necked, round- bottomed flask that was maintained at a temperature of 81 °C in a water bath. The reaction lasted for 18 min with magnetic stirring, as shown in Figure 2.  

Figure 2: The Raman spectrum sampling device.			

Raman spectra were saved every 3 min during the scanning reaction system. They are shown in Figure 3. 

Figure 3: Original Raman spectra of samples.			

Because of the intense fluorescence, the Raman signals of the reactive solution show an obvious baseline slope (from 100 cm

). With increasing reaction time, the baseline drifted much more seriously, which increased the difficulty in identifying characteristic peaks.   

All functionalities including input, critical-point-seeking, interval linear fitting, and output were integrated into a function based on Scilab 5.4.0 (

In this approach, the interval number of moving average smoothing is the primary parameter. A suitable interval for a simulated baseline is chosen. If a strong baseline slope exists in the Raman spectrum, another regulating parameter must be set, the derivative start point. The Raman spectrum obtained at the 18-min mark, with the maximum baseline drift, was selected for setting parameters. 

The baseline (red) was eliminated without both smoothing and setting of the derivative start point. The corrected spectrum is shown in Figure 4. Many Raman peaks (from 300 cm

) of components in the reaction system were removed as the baseline because of the frequency shift and high sensitivity. An inverse peak (0–100 cm

) exists because of the high slope in the estimated baseline (0–240 cm

Figure 4: Correction without setting parameters.			

With the setting of the derivative start point at 60, the original spectrum of object was handled with the selected interval values of 5, 15, 25, and 35, respectively. They are shown in Figures 5a–d. 

Figure 5: Correction with the derivative start point setting at 60 and interval numbers at (a) 5, (b) 15, (c) 25, and (d) 35. 			

) because of the derivative start point setting, which increased matching with the original spectrum. When the interval value was 5 (Figure 5a), useful information (250–1000 cm

) about the reaction components was removed as baseline, and when the interval values were 25 and 35 (Figures 5c and 5d), the corrected spectral region from 500 cm

  was distorted. Especially when the interval value was 35, the simulated baseline had a region over the original spectrum from 1000 cm

. Comparing those selected values, we see that an interval number of 15 (Figure 5b) is suitable for spectrum correction.  

Correlation measurement is a good comparison method for a full spectrum. The correlation coefficient is a measure of the relationship, which is obtained with equation 5. To subtract the fluorescence background and maximize character matching between the calibration spectrum and the original spectrum, a group of correlation coefficients was used consisting of a hit list from the corrected spectrum in the range of selected interval values from 3 to 35 (with the derivative start point setting at 60). The hit list is shown in Figure 6.   

Figure 6: Hit list in the range of interval numbers.			

Because the original spectra are composed of the Raman scattering of the measured object and the fluorescence background, and the baseline slope was eliminated, all correlation coefficients between the original spectrum and corrected spectra were less than 1. The correlation coefficients were less than 0.7 in the range of interval value from 3 to 7 because the Raman scattering of the measured object was removed. When the interval number was in the range from 9 to 21, the corrected spectra matched favorably with the original spectra. Although the correlation coefficient increased in the range from 29 to 35, the corrected spectra were distorted as shown in Figure 5d. 

Determining the range of the interval values is the most important step. In the program, the range of interval values from 9 to 21 is favorable, as seen in Figure 6. The correction spectrum was obtained respectively for every interval value in the setting range after correlation analyses were conducted and between the original spectrum and every corrected spectrum we obtained a hit list of correlation coefficients. When correlation coefficients on the list were closest to 1, the corrected spectrum was optimum. 

Articles

Peer-Reviewed Articles

Piecewise linear fitting based on critical-point-seeking is proposed in this study.

Baseline Correction for Raman Spectra Based on Piecewise Linear Fitting

The data show that different units of measurement have different relationships to the spectral values, for reasons having nothing to do with the spectroscopy. This finding disproves the unstated, but near-universal, assumption that different measures of concentration are equivalent except, perhaps, for a constant scaling factor.

Over the course of these "Chemometrics in Spectroscopy" columns we have introduced or explained various concepts related to multivariate calibration and assessment using mostly near-infrared (NIR) spectroscopy, but also delineating concepts that are applicable to other molecular spectroscopy techniques. One of the elusive problems associated with quantitative analysis using these techniques is the unexplained error in analysis, and the use of reference techniques to calibrate spectroscopic methods relegates them to being referred to as "secondary techniques." Recent installments of this column have introduced a subject that has mystified analysts over the past several decades (1–11).  

For as long as we've been working with NIR (since 1976 for one of us), we've recognized that modern NIR analysis is subject to a near-universal, but widely ignored problem. In the early days everybody knew that. Since then, the application of chemometrics has covered up the problem and enabled calibration models that "worked." Even though these applications are valuable, they represent game-playing, not science. Newcomers accept the paradigms used without much thought given to what is happening "under the hood." Experienced practitioners of NIR think that something is wrong, however, and the methodology is sensed as not being part of the universe of science. Many characteristics of NIR appear to fly in the face of conventional science, constituting a set of symptoms: 					

the apparent need for, and use of, more variables in calibrations than can reasonably be justified

algebra dictates that no more equations should be needed than variables

difficulty in reproducing calibrations for the same constituents in the same type of samples;

inability to reproduce wavelength sets (for multiple linear regression [MLR] models)

difficulty or inability to relate wavelengths chosen (for MLR) or prominent bands (for principal components regression [PCR] or partial least squares [PLS]) to spectral features

standard error of calibration (SEC) should drop precipitously to the noise level

unexpected and unexplained (or unexplainable) "outliers"

SEC and standard error of prediction (SEP) should drop precipitously when the number of wavelengths or factors equals the number of variations in the samples (in general that doesn't happen)

spectroscopic measurements should be accurate over the entire range of concentrations, not only dilute solutions or a small range of values

calibrations should be extrapolatable, with a calculated reduced accuracy at the extremes of the range, and

calibration transfer should be as easily and readily performed as comparing two mid-IR spectra.

Taken together, these discrepancies from all previous knowledge of chemistry, spectroscopy, physics, and mathematics constitute a set of "mysteries" that nobody in the affected fields had been able to explain. 

These various symptoms of an unknown problem have been attributed to a variety of causes, such as optical scatter effects, reference laboratory error, instrument noise, instrumental nonlinearities, stray light, detector saturation, calibration issues, the "wrong" transforms of spectral data, the "wrong" calibration algorithm, incorrect calibration parameters, an unknown reflectance relation between spectrum and composition, and sample inhomogeneity. 

To be sure, all of these effects exist and affect the spectral readings and the nature of the calibration models achieved. However, they failed to satisfy.While attempts to mitigate these effects "worked" to some greater or lesser extent in individual situations, they failed to improve calibration performance as often as they succeeded in that attempt, and a "shotgun" approach to trying different corrections was often needed. Here again, the reasons for that behavior were unknown, and it was impossible to use the knowledge to predict, for a new calibration situation, whether any given "fix" would succeed. Therefore, while the various methods developed to address the symptoms allowed NIR to enjoy the widespread success it had achieved, the lack of understanding of the underlying problem prevented solving that problem in the scientific sense, and the net result was simply to replace one set of mysteries with another. Something was missing. 

The recent discovery about the effect of using different units for the reference values, which we've described over the course of a number previous column installments (1–11), seemed to have the right properties to explain these mysteries. This approach basically required a different kind of data transform, which differed in two key respects from previous data transforms used in conjunction with NIR data:  					

It was a transform of the concentration values. 

It was based on known physical chemistry. 

The experimental finding that electromagnetic spectroscopy is sensitive to the volume percent (or, strictly speaking, the volume fraction) of materials in a sample is the resulting conclusion. There are a variety of measurement errors because of variation in sample presentation and instrumentation, as described above, but fundamentally the spectroscopy is relating to volume fraction and not weight percent (despite the overwhelming use of weight percent as the most common units used for expressing analyte "concentration" in a majority of analytical situations, nor volume irrespective of density and mixture or solvation issues). Understanding the ramifications of this volume effect may lead to an improved understanding of quantitative measurement errors and, eventually, to changing multivariate spectroscopic techniques into primary analytical methods. 

This column and the next few installments are intended to constitute a discussion on the ramifications of the new findings. We base our discussions on the previously reported results (1–11). 

To review the findings until now, in our previous column (11) we examined the behavior and performance of nearly ideal samples (clear liquid mixtures) using a nearly ideal calibration algorithm (classical least squares [CLS]) and found several characteristics of our data set that indicate that volume fractions are the operative physical variable that spectroscopy is sensitive to. First, we noticed that the values from the CLS analysis of the spectral data from the second laboratory had values that corresponded to the values that represented the target values in the original experimental design: 0%, 25%, 50%, 75%, and 100%. We also noted that in the samples for the second laboratory, those values corresponded to the volume fractions of the various components. 

We then applied the scientific method to our microcosm and formulated the hypothesis that when Beer's law holds, the absorbance spectra of clear solutions are in fact sensitive to the volume fractions of the components in the mixture. Continuing the application of the scientific method, we verified the hypothesis by applying it to the data from the first laboratory, which had not previously been analyzed this way, and found that indeed the performance of the CLS method was much improved when the CLS values were compared to the volume fractions, rather than any of the other concentration units that had been used previously.  

This was ascertained by comparing individual values of the concentrations as determined by the various methods. A more robust comparison can be obtained by calculating a statistical figure of merit, similarly to the way accuracy measures are obtained for other quantitative calibration algorithms. There are both graphical methods available and numeric methods. It made sense to use both approaches for the comparison, if for no other reason than that is standard procedure when performing calibrations with the other algorithms, and we decided to examine our CLS results as closely as is normally done. We started with the numeric approach, and computed the root mean square differences and correlation coefficients between the concentration values from the CLS method and the concentration values obtained using other units. The calculations were taken over all 15 of the samples, going from 0% to 100% of each component in accordance with the experimental design used (see Figure 1 in reference 5).				

Figure 1: Plots of CLS values versus weight percent and volume percent, for toluene: (a) weight percent versus CLS values; (b) volume percent versus CLS values.			

As we saw, the data from the second laboratory were somewhat erratic, a characteristic that was explained by David Heaps, the scientist who performed the data collection in that laboratory, as being caused by fact that the sample cell used was not large enough to encompass the entire beam from the spectrometer. This caused small variations in the position of the cell, which ordinarily would be negligible, and had inordinately large effects on the readings. We also previously noted the erratic nature of the data from the second laboratory in reference 9. Therefore, we present only the results from the first laboratory in Table I. 

Table I: Comparison of performance statistics for different units of concentration			

Table I makes it abundantly clear that for all sample components, the comparison of the CLS values with the volume fraction, overall, is much better than with any of the other units. Indeed, the values of these statistical tests are competitive with what is usually expected for "typical" calibrations using other chemometric calibration algorithms (such as PCR or PLS) 

CLS calculations, done the way described in the previous columns, have several interesting and useful characteristics of their own. 

 It's the nearest thing we have to an "absolute" analytical method, and therefore, the analytical results can be obtained without ever doing a conventional "calibration" of the sort we usually think of. 

				Because results can be obtained without a conventional calibration, you don't have to worry about laboratory error; there's no "lab error" because there are no laboratory values to deal with (except for validation).		

				CLS values are linear with the known concentrations (as long as they are expressed in appropriate units) over the range 0–100% (or, strictly speaking, volume fractions in the range 0–1).			

Because of this linearity, a conventional calibration based on volume fractions (or one of the scaled variants) should be extrapolatable.

Given that these CLS values are obtained without any reference laboratory values, and using zero PLS or PCR factors (which also means they can't be overfit), the results for the statistical values for performance of volume fractions in Table I are pretty impressive. 

We can further confirm the nature of the agreements by plotting the CLS values for each sample versus the concentration expressed in the two different key units of interest. Figures 1–3 show this view of the data for each of the three different components. The plots for the three components versus weight percents (Figures 1a, 2a, and 3a) show varying amounts of scatter. In Figure 1a, the plot for the CLS values for weight percent of toluene does not show any curvature in the plot to the naked eye. Figures 1a and 3a show a considerable amount of scatter, although Figure 2a does not. 

Figure 2: Plots of CLS values versus weight percent and volume percent, for dichloromethane: (a) weight percent versus CLS values; (b) volume percent versus CLS values.			

The other three plots of CLS values versus volume fractions (Figures 1b, 2b, and 3b), show decreased amounts of scatter (except for the dichloromethane). Figures 1–3 present a graphical comparison that provides a convenient "eyeball" comparison method. Figures 1a, 2a, and 3a show that the reference values are constant, at each level of the analyte, at the value specified by the experimental design. Figures 1b, 2b, and 3b show that all three exhibit linear relations between the CLS and volume fractions over the range 0–100%. Neither do any of the plots of CLS values versus volume fractions show appreciable amounts of scatter; indeed, the use of volume fractions as the unit for the reference values has caused all the data points to fall on a line that is visibly straight, for all three components. 

Figure 3: Plots of CLS values versus weight percent and volume percent, for n-heptane: (a) weight percent versus CLS values; (b) volume percent versus CLS values.			

But we would also like to be able to apply a more objective, mathematical comparison method. Therefore, we also applied a statistical linearity test (described in reference 12) to the results. This test computes a 

-value against the null hypothesis so that there is no nonlinearity in the relationship between paired data points. A statistically significant value for the computed 

-value indicates that there is enough nonlinearity to be definitely detected by an objective criterion, while a value that is too small to be statistically significant means that any nonlinearity, if present, is too small to be detected. Table II shows the 

-values for the comparisons when comparing the CLS values against other units. 

Table II: t-values from linearity test, spectroscopy versus indicated units			

-values in Table II, for the comparison of the spectroscopic results with the gravimetric values, indicate highly significant amounts of curvature in the relationship between the CLS values and the known weight percents for dichloromethane, in agreements with our visual observation. The corresponding 

-values obtained when the spectroscopic results were compared to the volumetric values indicate no detectable nonlinearity for this comparison. These statistics agree with what we infer from Figure 2.  

-heptane exhibit statistically significant 

-values for either nonlinearity test. Whereas Figure 1a appears to be adequately straight, Figure 3a visually shows what appears to be a curvature of the relationship for the 

-heptane; both ends of the relationship appear to bend upward from a line that follows the rest of the data. Table II, however, shows that the 

-value for this case is only 3.25, a marginally significant value at best. In the cases of toluene and 

-heptane, the large amount of scatter seen in this plot is masking any systematic effect that might actually be present and prevent us from demonstrating that the systematic portion is more than the large amount of scatter could account for, giving us a nonsignificant result. 	

An interesting side note here: Both the graphical and numerical results show that volume fraction provides a spectroscopic method that is substantially linear over the range 0–100% (when Beer's law holds, of course) and accommodates the variations in the "matrix" — that is, the rest of the sample. Those properties would not disappear if the concentration values expressed in volume fraction were multiplied by a constant. Convenient constants would be ones like density, moles per unit volume, or similar implicit properties of the analyte. Suitable constants would be constants that are measures of a property per unit volume (as the density and moles per unit volume themselves are). Multiplying one of these constants by the volume fraction (or volume ratio) results in canceling the volume term in the numerator of the volume fraction, and thereby replacing the numerator term in the volume fraction expression by the alternate unit (that is, mass if density is the constant, or moles if moles per unit volume were the constant). The resulting values would then be concentration measures on a volume basis (density, molarity, and so on), which arguably are more familiar to chemists. These other quantities would not necessarily satisfy the more stringent requirements of the CLS algorithm, but would be expected to be linearly related to the volume concentration, and therefore provide a satisfactory basis for expressing the analyte concentration for the more common calibration algorithms that do indeed require the concentration for the calculations. 

This is what the data show. The important question now is what it means. 

In the first pair of columns in the previous subseries (1,2) we looked at the CLS analysis of water–methanol–acetic acid mixtures and found that the values computed using the CLS algorithm did not agree with the known amounts of the mixture components introduced in the mixtures. In that experiment, we also found that the reconstruction of the mixture spectrum from the spectra of the pure components was rather poor. Based on the poor reconstructions of the mixture spectra, we attributed the inaccurate analytical results obtained to the known changes in hydrogen bonding because of intermolecular interactions between the three components, interactions that distorted their spectra.  

Therefore, starting with part III of the previous subseries (3), we redid the experiment using hydrocarbons that would not interact as the materials in the previous experiment did because the materials used for the second experiment did not contain any –OH in their structure. With these mixture components we found that indeed, we were able to reproduce the spectra of the mixtures fairly well. 

Chemometrics in Spectroscopy

The data show that different units of measurement have different relationships to the spectral values, for reasons having nothing to do with the spectroscopy. This finding disproves the assumption that different measures of concentration are equivalent except, perhaps, for a constant scaling factor.

Units of Measure in Spectroscopy, Part I: It's the Volume, Folks!

Raman Spectroscopy To Be Used in European Mission to Mars

Madrid-based National Institute for Aerospace Technology, a public research organization specializing in aerospace research and technology development, will contribute to the ExoMars mission to Mars in 2018, with an instrument that uses Raman spectroscopy. The mission is led by the European Space Agency with contributions from Russia. Its objectives are to detect possible evidence of past or present life on Mars and to garner insights into the history of water on the planet.  

After the ExoMars rover is on Mars' surface, a drill in the rover will collect samples up to 2 m beneath the Martian surface. The samples will be crushed into a fine powder and studied inside the rover's analytical laboratory. 

"The Raman laser spectrometer will be used to analyze these samples, obtaining information about their mineralogy and chemical composition, and detect possible organic compounds" said Gerald Heidt, CEO of Wasatch Photonics, whose company made the high-performance, volume phase, holographic gratings that are used in this Raman instrument. 

Advancing the Use of Near-Infrared Spectroscopy in Combination with Clinical Magnetic Resonance  Imaging

Engineers from the Thayer School of Engineering at Dartmouth (Hanover, New Hampshire) and radiologists are developing new approaches for an emerging technique in diagnostic imaging for breast cancer that combines magnetic resonance imaging (MRI) with near-infrared (NIR) spectroscopy, as reported in the February issue of the journal 

Combined MRI–NIR spectroscopy may benefit women whose mammograms showed an abnormality and require further testing to rule out cancer. The test would be conducted before an invasive biopsy to look for tumors. For the new method to work successfully in routine patient care, MRI–NIR spectroscopy must adapt to an individual's body size as well as accommodate a range of cup sizes. The equipment must also mobilize and maintain contact with the breast. 

MRI–NIR spectroscopy testing may offer specific advantages to women with dense breasts, who are more likely to develop and die from breast cancer. A dense breast is harder for a radiologist to "see through" when using traditional imaging equipment, which reportedly lacks the sensitivity to penetrate the dense tissue. Standard breast screening is effective 77–97% of the time in a normal breast, but the precision falls to 63–89% when a breast is dense.

Departments

Madrid-based National Institute for Aerospace Technology, a public research organization specializing in aerospace research and technology development, will contribute to the ExoMars mission to Mars in 2018, with an instrument that uses Raman spectroscopy.

News Spectrum

A training set sample selection method based on the simple-to-use interactive self-modeling mixture analysis (SIMPLISMA) algorithm is proposed in this article. We applied this method in near-infrared (NIR) spectral analysis of the content of protein, water, oil, and starch in corn. It is concluded that SIMPLISMA can be used as an alternative path to select training samples for constructing a robust prediction model in NIR spectral analysis.

In the field of quantitative analysis using near-infrared (NIR) spectroscopy, calibration is necessary. Training set sample selection is an important aspect of multivariate calibration, and it has attracted the attention of several researchers. The aim of this technique consists of the following two items: 					

Choosing the smallest set of training samples that can be used without significantly compromising the prediction performance of the model. It is often used to save computational work (1–8). In some situations, the representative samples used in multivariate calibration can benefit both the modeling efficiency and the prediction performance. 

Training set sample selection is also an important part in the context of transfer of multivariate calibration models (9–11), in which a subset of samples must be measured in different spectrometers. The measurements are then used to standardize the instrumental response of one or more spectrometers (slaves) with respect to a single one (master). In this case, a small number of representative samples are chosen so that they will contain sufficient information about the variations of the samples because of different measurement conditions. This benefits the practical application.  

In this article, we mainly discuss the first case, which involves the training set sample selection method and subset selection from full calibration samples. A sufficient number of samples with a wide concentration (or the nature) distribution of the analyte is needed for constructing a calibration model. Especially during the selection of the representative training samples, it is helpful for us to establish a calibration model with higher efficiency and good accuracy.  

Several works have discussed the problem of selecting a representative subset from a large pool of samples (1,2,12–14). In general, there are three types of training set sample selection methods: random sampling; sample selection based on data analysis of instrumental response variables 

 (that is, spectra); and sample selection based on data analysis of instrumental response variables 

 (that is, concentration or the nature of the analyte). 

Random sampling is the most popularly used method because of its simplicity — a group of data randomly extracted from a larger set follows the statistical distribution of the entire set. However, random sampling does not guarantee that representative samples are included in the calibration, and it also does not ensure that the samples on the boundaries of the set are selected in the calibration. 

Therefore, many sample selection methods based on data analysis of instrumental response variables 

 are typically used; an example would be the linear algebra techniques similar to spectral subtraction proposed by Honigs (12), or the Kennard–Stone (KS) algorithm, which is an alternative that is often used. KS is aimed at covering the multidimensional space in a uniform manner by maximizing the Euclidean distances between the instrumental response vectors (

) of the selected samples (13,14). The advantage of the KS algorithm is that it ensures that the selected samples are uniformly distributed in accordance with the spatial distance. Despite the comparative advantages of KS, however, the data conversion and the space distance between samples must be calculated, which is a challenging computation procedure. Another shortcoming of the KS algorithm for multivariate calibration lies in the fact that the statistics of the output vectors (

Recently, some studies of sample selection have focused on the data analysis of instrumental response variables 

(1,2). It could be argued that the inclusion of 

-information in the selection process might result in a more effective distribution of calibration samples in the multidimensional space, thus improving the predictive ability and robustness of the resulting model. In the work of Galvão and colleagues (1), an approach for considering joint 

 statistics in the selection of samples is proposed for the purpose of diesel analysis by NIR spectrometry. The method, termed 

sample set partitioning based on joint x–y distances

 (SPXY), extends the KS algorithm by encompassing both 

-differences in the calculation of inter-sample distances. In other words, in comparison to KS, the 

-information is considered by SPXY. However, the collinearity effect between samples is not included in the algorithm. Especially when hundreds of samples are used in calibration, the collinearity effect exists.  

In this article, we extend the simple-to-use interactive self-modeling mixture analysis (SIMPLISMA) method as a novel, training set, sample selection method for eliminating samples with collinearity. In this method, 

-information are included in the sample selection process. The selected representative samples for calibration are used to improve the modeling efficiency, and good accuracy can be achieved. 

SIMPLISMA was originally developed by Willem Windig and colleagues for pure variable selection (15). A 

 is defined as a variable whose intensity mainly results from one of the components in the mixture under consideration (16). According to the purity spectrum and standard deviation spectrum of variables, the pure variables can be selected straightforwardly. And the determinant-based function is used in SIMPLISMA for determining the independence of variables. The point is to eliminate collinearity of variables. 

				SIMPLISMA has been successfully used for the investigation of peak purity with liquid chromatography (LC) and diode-array detection (DAD) data (17). It also has been applied for the second-derivative NIR spectra to resolve highly overlapping signals with a baseline problem (18). Also, SIMPLISMA has already been applied to the analysis of categorized pyrolysis mass spectra data, Fourier transform infrared (FT-IR) spectroscopy, microscopy data of a polymer laminate, Raman spectra of a reaction followed in time, and so on (19–22).			

This article discusses the use of SIMPLISMA for the selection of samples for a training set for multivariate calibration in NIR spectral analysis. In this study, SIMPLISMA is used to select a subset of calibration samples that are minimally redundant but still representative of the data set. It is not the same as pure variable selection by SIMPLISMA; this approach involves pure sample selection using the SIMPLISMA principle to eliminate the collinearity of samples. Our goal is to reduce computational work and obtain a robust multivariate model with stable prediction performance. The sample selection method takes into account both 

 statistics by combining with wavelength-variable selection, which is helpful in resolving multicomponent chemical or physical information of the mixture from overlapped spectra. The use of SIMPLISMA for sample selection is illustrated for NIR spectra analysis of the protein, water, oil, and starch content in corn. In this application, sample selection by SIMPLISMA is also compared to the KS algorithm and the SPXY method. 

http://www.eigenvector.com/data/Corn/index.html

) used in our study consists of 80 samples of corn measured on three different NIR spectrometers (named m5, mp5, and mp6). In our study, the spectra from instrument m5 are used. The wavelength range is 1100–2498 nm, and the number of wavelength variables is 700. There are four output variables (the content of protein, moisture, oil, and starch).  

				To determine the quality of the corn data used in our work, we first tested the potential sample outliers using principal component analysis (PCA). 			

Then, for each output variable, 20 samples were selected randomly as an independent external prediction set for evaluating the prediction performance of the calibration model, and the remaining 60 samples were used for calibration. As a result, four calibration sets and the corresponding prediction sets are assembled in this study for spectra analysis of the four components in corn, respectively. 

The aim of this experiment is to choose a small quantity of representative samples from the 60 samples (the dimension of original spectra matrix is 60 × 700). Then the selected training samples are used for building partial least squares (PLS) models, which are used for predicting the protein, moisture, oil, and starch content. To make the spectra matrix correlate with each analyte, a wavelength-variable selection method — a successive projections algorithm (SPA) — was used before the training set sample selection. SPA is a forward selection method in that it starts with one wavelength and then incorporates a new one at each iteration. The new wavelength is selected according to a sequence of projection operations, until a specified number 

 of wavelengths is reached. Its purpose is to select wavelengths whose information content is minimally redundant, and to solve collinearity problems (23). In the SPA wavelength-variable selection process, there are four different wavelength-variable sets for quantitative analysis of the content of protein, moisture, oil, and starch, respectively. It is possible to make the new matrices with selected variables and selected samples correlate with the corresponding components' information. Using the variable selection method based on SPA, we can easily extract the most relevant spectral information of a component from the overlapped NIR spectrum. Moreover, the application of wavelength selection benefits SIMPLISMA by selecting training samples that are associated with the analyte in consideration. That means sample selection takes into account both 

 statistics, which is useful for improving prediction performance. 

Thereafter, two training set sample selection methods, KS and SPXY, were introduced in this study for comparison with the proposed method based on SIMPLISMA. PLS models were built by using training samples, which were selected by different training set sample selection methods. Leave-one-out cross-validation (LOO-CV) applied to the training set was used to select the principal components. The prediction performance of the PLS models were evaluated according to the root mean squares error of calibration (RMSEC) set and root mean squares error of prediction (RMSEP) set. Root mean squares error (RMSE) is calculated as follows: 

The algorithms of PCA, SPA, PLS, SIMPLISMA, KS, and SPXY were all performed using Matlab 7.6.0 (The Mathworks, Inc.). 

The classic KS algorithm is targeted at selecting a representative subset from full calibration samples. To ensure a uniform distribution of such a subset along the 

 (instrumental response) data space, the KS algorithm follows a stepwise procedure in which new selections are taken in regions of the space far from the samples already selected (2). The algorithm is described as follows. 

Initialization of the number of the samples proposed to be selected by the analyst. 

) of samples; the calculation equation is as follows: 

 denotes the number of wavelengths in the spectra. 

 is the number of the original full calibration samples.  

According to the results calculated by equation 2, selecting the pair (

Calculate the distances between each remaining sample and the two selected samples. For the remaining samples, these distances are the smallest distance to the selected samples. Then, select the sample for which the distance is the largest as the third sample.  

Repeat step 4 until the number of samples specified in step 1 by the analyst is achieved. 

We can see that, under the KS algorithm, only the 

 information is involved in consideration for sample selection. The SPXY algorithm proposed by Galvão in 2005 (2) is based on KS; the difference is that the information about output variable 

 is involved in the calculation of distance. Such a distance 

) can be calculated for each pair of samples 

To assign equal importance to the distribution of the samples in the 

) are divided by their maximum values in the data set. In this manner, a normalized 

This stepwise selection procedure is similar to the KS algorithm; the difference is that the distance calculation is based on 

Originally, the SPXY method was proposed for calibration and validation subset partitioning. In this article, we introduce this method for training set sample selection and compare the performance of different sample selection methods.  

KS and SPXY algorithms are based on the calculation of Euclidean distances. In this study, based on the SIMPLISMA theory, we used the pure values calculation for elimination of collinearity among samples, and then selected a sample subset with minimal redundant information for calibration. The SIMPLISMA algorithm for training set sample selection is described as follows: 

Initially, the basis of SIMPLISMA is to determine the purity. In this approach, SIMPLISMA is used to calculate the purity of samples for determining the first sample. In this article, the data matrix is represented by X, and the size is 

 is the number of wavelength variables. Because we have selected wavelength variables using SPA before sample selection, 

 is the number of wavelength variables after the wavelength selection step has been executed. The purity value of sample 

 is the mean. The constant α is added to the denominator to avoid the problem from noise-level mean value of samples. Typical values for α range from 1% to 5% of the maximum of 

. The index 1 represents the first sample that will be selected. According to the purity spectrum of the samples, the sample with the highest intensity is selected as the first informative sample, which will be used in calibration later. 

The problem now is how to eliminate collinearity among samples and how to determine the next informative sample for calibration. The 

th sample is the one that is the most independent to the (

- 1)th sample selected. So, it is possible to determine correlation weight by the determinant-based function 

				(15,24,25), which is used for correcting the previous purity value of selected samples. The determinant-based function is calculated as described below. 

The SIMPLISMA algorithm is applied in this method using near-infrared (NIR) spectral analysis of the content of protein, water, oil, and starch in corn.

A Training Set Sample Selection Method Based on SIMPLISMA for Robust Calibration in Near-Infrared Spectral Analysis

An interview with Vassili Karanassios, who is a Professor in the Department of Chemistry and the Waterloo Institute for Nanotechnology at the University of Waterloo, in Waterloo, Ontario, Canada. His research focuses on micro- and nano-analysis and the development of miniaturized instruments for on-site applications. 

You have noted that the sample introduction efficiency of conventional pneumatic nebulizers for inductively coupled plasma (ICP) spectrometry is typically only 1–3% and is a key limitation. Why is it so low?

To generalize, it is not the pneumatic nebulizer but the spray chamber a nebulizer is typically attached to. The nebulizer generates a fine mist (akin to fog) from an analytical sample or from a blank. The droplets of this mist have a wide range of diameters, with many droplets being larger than others. Because the residence time of droplets in an inductively coupled plasma is 2–3 ms, larger droplets may not be completely desolvated as they travel through the plasma. Thus, any analyte contained in larger droplets will likely generate a signal disproportional to the concentration of the analyte in the droplet. Smaller droplets, on the other hand, are more likely to be completely desolvated and thus generate signals proportional to analyte concentration in the droplet. Thus, the analytical signal becomes dependent on droplet size. 

To ensure that a narrow and reproducible range of droplet diameters enters the ICP, nebulizers are connected to a spray chamber. Although there are many spray-chamber designs, a key function of any spray chamber is to ensure that a small, narrow range of droplet diameters is introduced into the plasma. Thus, larger-diameter droplets are excluded and are drained into a waste-collection vessel. It is during this step that large sample-introduction inefficiencies are introduced. 

A field-portable rhenium coiled-filament sampling device for ICP spectrometry that was developed in your laboratory reportedly provides much improved sampling efficiency over traditional nebulizer systems. How did the idea for this device come about? Were other systems tested that met with less success?

Our near-torch vaporization (NTV) system falls in the general category of electrothermal vaporization (ETV) sample introduction for ICP spectrometry, and ETV systems have been around for decades. Although many ETV designs have been described in the literature, to generalize, a typical ETV sample introduction system uses a graphite support (for example, a graphite tube) as the sample holder. There are three main problems with graphite-based ETV sample introduction systems: 					

The use of graphite promotes carbide formation. Because a large number of elements across the periodic table form carbides and because carbides typically have very high vaporization temperature, such elements either do not vaporize at all or they have incomplete vaporization. This incomplete vaporization occurs because a typical graphite-based ETV system can reach a maximum temperature of only about 2800 °C. There are ways of alleviating the adverse effects of carbide formation, but they typically include chemical modification, thus complicating method development and instrumentation. In general, applicability of graphite-based ETV systems is limited to volatile, non-carbide-forming elements (for example, Pd, Cd, and Zn).

Because the graphite support of ETV systems has a relatively large mass (for example, 250 mg), a relatively large power supply must be used (for example, one delivering up to 5 kW). This requirement increases purchasing and operating cost of instrumentation.

Because the size of the vaporization chamber for a typical ETV system is relatively large (roughly the size of one's fist), such systems cannot be brought very close to an ICP torch. They are typically operated 0.5–1 m away from the torch, with a tube connecting the ETV vaporization chamber to the torch. The length of the tube dictates transport losses. As a rule of thumb, the longer the tube, the higher the sample loss. In many cases and depending on vaporization power used, black deposits (from carbon vaporizing from the graphite support) can be seen collecting in the tube after only a few hours of operation. Therefore, frequent tube cleaning or tube replacement is required, thus also necessitating recalibration. For ICP–mass spectrometry (ICP-MS) and in addition to tube replacement, carbon entering the ICP forms "gas phase carbides" that often cause isobaric interferences and spectral interference effects.

This interview has been edited for length and clarity. 

Q&A: SPECTROSCOPY SPOTLIGHT

An interview with Vassili Karanassios, of the University of Waterloo in Waterloo, Ontario, Canada. His research focuses on micro- and nano-analysis and the development of miniaturized instruments for on-site applications.

Field-Portable Sampling for ICP Spectrometry: Bringing a Part of the Lab to the Sample

The focus of this review is the application of infrared (IR) spectroscopy to study human lens and tear lipids with minimal discussion of the role of lipids and the complex etiology of cataracts and dry eye. The power of IR spectroscopy to measure composition, conformation, structure, and environment of biomolecules was applied to diagnose cataracts and dry eye and follow the efficacy of treatment. Principal component analysis and other standard algorithms were used to analyze IR spectra.  

A thin lipid layer on the surface of the tears is believed to contribute to tear stability (1,2). Most of the tear film lipid comes from the meibomian glands located in the eye lids (1–3). The major function of tears is to keep the underlying cornea clear and hydrated. Blinking spreads the tears across the surface of the cornea and the mechanical action of the blink expresses a lipid called meibum from the meibomian glands located in the eye lids on the lid margin (1,2). The meibum finds its way to the tear film surface where it forms a heterogeneous, duplex layer that is about 17 molecules thick (4). It is believed that the lipid layer decreases the surface tension of the tears, which allows them to spread, and lowers the evaporation rate of the underlying aqueous liquid. Shortly after blinking, if one does not blink again, the tear film "breaks up." In all cases of dry eye, the tear film is unstable and tear breakup times are shortened. Dry eye affects more than seven million people in the United States alone (5). The roles of lipids and the etiology of dry eye have been reviewed (1–3). This article reviews the application of IR spectroscopy to study meibum and determine if any relationships exist between tear film stability and meibum lipid composition, environment, and conformation (6–12). 

Meibum and tear lipids can be collected a number of ways, such as by using a spatula, microcapillary pipettes, lipid absorbent tape, or paper strips (3). For most of the studies discussed below, meibum was collected by squeezing the eyelid between two cotton swabs. About 0.5 mg of meibum is expressed on the eyelid surface and collected using a sterile spatula. The meibum is then transferred to a silver chloride window and transmission IR spectra are measured. In the studies reviewed, IR spectra were measured using a Fourier transform IR (FT-IR) spectrometer equipped with a mercury cadmium telluride (MCT) detector (Nicolet 5000 Magna Series, Thermo Fisher Scientific, Inc.). The meibum on the AgCl window was placed in a temperature-controlled IR cell. The cell was jacketed by an insulated water coil connected to a circulating water bath (model R-134A, Neslab Instruments). The sample temperature was measured and controlled by a thermistor touching the sample cell window. The water bath unit was programmed to measure the temperature at the thermistor and to adjust the bath temperature so that the sample temperature could be set to the desired value. The rate of heating or cooling (1 °C/15 min) at the sample was also adjusted by the water bath unit. Temperatures were maintained within ±0.01 °C. IR data analysis was performed using GRAMS/386 software (Galactic Industries). 

The lens is located in the front of the eye behind the cornea and functions to focus light on the retina at the back of the eye. The lipids of the lens do not turn over, and most of the lipids made at birth are present at death (13). Light passing through a human lens traverses through thousands of cellular membranes that serve as impermeable barriers to cations as well as a matrix for proteins. The phospholipid composition of human lens membranes is unusual. The human lens contains dihydrosphingomyelin, found in significant quantities only in the lens. Lens membranes are some of the most saturated membranes in the human body, and contain extremely high levels of cholesterol, particularly near the center of the lens (10:1 mole:mole cholesterol to phospholipid). The composition of the human lens changes dramatically with age and cataract. The roles of lipids and the etiology of cataracts have been reviewed (13). IR spectroscopy was used to study lens membrane lipid conformation in relation to compositional differences between species, and the aging and cataractous human lens (13–34). 

Lipids can be fluid like olive oil, solid like butter, or somewhere in between. Fluid lipids are generally not completely liquid, but interact with one another and are said to be in a gel phase. Solid lipids are not completely solid and contain some mobility so they are said to be in a liquid crystalline phase. Lipids are generally composed of hydrocarbon chains containing methylene (-CH

-) moieties. Conformation is how molecules are arranged in space. The methylene moieties may arrange as gauche rotamers, prevalent in disordered lipids like olive oil, which is fluid at room temperature. The methylene moieties may also arrange as trans rotamers, more abundant in ordered lipids like butter, which is solid at room temperature (Figure 1). Gauche conformations may more properly be termed a 

This article reviews the application of IR spectroscopy to study meibum and determine if any relationships exist between tear film stability and meibum lipid composition, environment, and conformation.

Spectroscopy-02-01-2014

Baseline Correction for Raman Spectra Based on Piecewise Linear Fitting

Units of Measure in Spectroscopy, Part I: It's the Volume, Folks!

News Spectrum

A Training Set Sample Selection Method Based on SIMPLISMA for Robust Calibration in Near-Infrared Spectral Analysis

Field-Portable Sampling for ICP Spectrometry: Bringing a Part of the Lab to the Sample

From the Bench to the Bedside: Infrared Spectroscopy and the Diagnosis and Treatment of Dry Eye and Cataracts

Vol 29 No 2 Spectroscopy February 2014 Regular Issue PDF