Univariate Calibration Model Research Articles

Alkali Trace Elements Observed by MarSCoDe LIBS at Zhurong Landing Site on Mars: Quantitative Analysis and Its Geological Implications

AbstractMars Surface Composition Detector (MarSCoDe) is one of the important payloads carried by the Zhurong rover, China's first Mars exploration mission Tianwen‐1. The laser‐induced breakdown spectroscopy (LIBS) instrument of MarSCoDe is mainly used to detect major and trace elements on the surface of Mars. The quantitative analysis of alkali trace elements, namely lithium (Li), strontium (Sr), and rubidium (Rb), holds significance in unraveling the geological evolution of the Zhurong landing site. This study focuses on establishing univariate calibration models using MarSCoDe LIBS spectra from 84 samples tested in the ground laboratory. The accuracy of these models, within a few parts per million (ppm), was subsequently validated through the analysis of 12 onboard MarSCoDe Calibration Targets (MCCTs). With these models, Li, Sr, and Rb concentrations in the surface targets during the initial 300 sols (Martian days) traverse were determined. These concentrations ranged from 6 to 18, 106–628, and 22–87 ppm, respectively. Our results suggest that Li, Sr, and Rb are mainly related to the igneous rock components in the rocks and soils at the Zhurong landing site. The major secondary minerals in MarSCoDe scientific targets are likely small amounts of sulfates, which appear to have formed from the acidic weathering of recent surface brine. Clay minerals are likely either absent or very sparse in the scientific targets. The surface igneous materials at the landing site likely have originated from the most recent lava flow during the Amazonian epoch.

Real-time determination of combustion degree by laser-induced breakdown spectroscopy

The combustion of fuels in industries is one of the sources of greenhouse gases, posing a considerable threat to human health and the natural environment. The monitoring of the combustion process and the measurement of combustion degrees, therefore, are crucial and significant. In this work, an experimental system was developed based on Laser-induced breakdown spectroscopy (LIBS). Charcoals with different combustion degrees were taken as samples, and in the LIBS spectra of charcoals, the characteristic line of C and the molecular bands of CN and CaO were observed. Moreover, a univariate calibration model based on the exponential fitting curve was constructed to predict the combustion degree according to the variation of the C I line intensity under different combustion degrees. Furthermore, different algorithms including support vector machine (SVM), partial least squares (PLS), random forest (RF), and convolutional neural network (CNN) were applied to establish the multivariate calibration model, and the prediction performance was compared according to the 10-fold cross-validation. Particle swarm optimization (PSO) was used to optimize hyperparameters of the selected SVM-based multivariate calibration model. Principal component analysis (PCA) and linear discriminant analysis (LDA) were employed to extract spectral features and reduce dimensions for the improvement of the model's performance, with the final root mean square error of prediction (RMSEP) and mean relative error (MRE) of the LDA-PSO-SVM calibration model of 0.035 and 3.877%, respectively. Finally, c. The results prove feasible to realize the real-time determination of combustion degree to control carbon emissions and monitor carbon concentration through the LIBS-based method with machine learning, which also provides new ideas for the application of LIBS in the atmospheric field.

Releasing fast and slow: Non-destructive prediction of density and drug release from SLS 3D printed tablets using NIR spectroscopy

Selective laser sintering (SLS) 3D printing is a revolutionary 3D printing technology that has been found capable of creating drug products with varied release profiles by changing the laser scanning speed. Here, SLS 3D printed formulations (printlets) loaded with a narrow therapeutic index drug (theophylline) were produced using SLS 3D printing at varying laser scanning speeds (100–180 mm/s). The use of reflectance Fourier Transform – Near Infrared (FT-NIR) spectroscopy was evaluated as a non-destructive approach to predicting 3D printed tablet density and drug release at 2 h and 4 h. The printed drug products formulated with a higher laser speed exhibited an accelerated drug release and reduced density compared with the slower laser scanning speeds. Univariate calibration models were developed based on a baseline shift in the spectra in the third overtone region upon changing physical properties. For density prediction, the developed univariate model had high linearity (R2 value = 0.9335) and accuracy (error < 0.029 mg/mm3). For drug release prediction at 2 h and 4 h, the developed univariate models demonstrated a linear correlation (R2 values of 0.9383 and 0.9167, respectively) and accuracy (error < 4.4%). The predicted vs. actual dissolution profiles were found to be statistically similar (f2 > 50) for all of the test printlets. Overall, this article demonstrates the feasibility of SLS 3D printing to produce drug products containing a narrow therapeutic index drug across a range of drug release profiles, as well as the potential for FT-NIR spectroscopy to predict the physical characteristics of SLS 3D printed drug products (drug release and density) as a non-destructive quality control method at the point-of-care.

Improving quantitative analysis of spark-induced breakdown spectroscopy: Multivariate calibration of metal particles using machine learning

We have recently developed a low-cost spark-induced breakdown spectroscopy (SIBS) instrument for in-situ analysis of toxic metal aerosol particles that we call TARTA (toxic-metal aerosol real time analyzer). In this work, we applied machine learning methods to improve the quantitative analysis of elemental mass concentrations measured by this instrument. Specifically, we applied least absolute shrinkage and selection operator (LASSO), partial least squares (PLS) regression, principal component regression (PCR), and support vector regression (SVR) to develop multivariate calibration models for 13 metals (e.g., Cr, Cu, Mn, Fe, Zn, Co, Al, K, Be, Hg, Cd, Pb, and Ni), some of which are included on the US EPA hazardous air pollutants (HAPS) list. The calibration performance, adjusted coefficient of determination (R2) and normalized root mean square error (RMSE), and limit of detection (LOD) of the proposed models were compared to those of univariate calibration models for each analyte. Our results suggest that machine learning models tend to have better prediction accuracy and lower LODs than conventional univariate calibration, of which the LASSO approach performs the best with R2 > 0.8 and LODs of 40–170 ng m−3 at a sampling time of 30 min and a flow rate of 15 l min−1. We then assessed the applicability of the LASSO model for quantifying elemental concentrations in mixtures of these metals, serving as independent validation datasets. Ultimately, the LASSO model developed in this work is a very promising machine learning approach for quantifying mass concentration of metals in aerosol particles using TARTA.

Detection and analysis of Cd in soil by laser-induced breakdown spectroscopy based on maximum likelihood estimation

Cd is an extremely toxic element and has a great impact on human health. But the detection of Cd in the soil is still a challenge. This study aimed to improve the analytical ability of laser-induced breakdown spectroscopy (LIBS) to measure Cadmium, the trace elements in the soil. Twelve soil samples containing gradient Cd elements were prepared. The sample concentration was quantitatively analyzed and compared by using the conventional univariate calibration model and maximum likelihood estimation algorithm. Calibration analysis revealed that the fitted R2 values are 0.965 and 0.990 by the conventional univariate calibration and maximum likelihood (ML) estimation respectively. The ML estimation has higher stability and predicted concentration is more accurate. Finally, the detection limit of Cd was estimated to be 7.84 μg/g by using the proposed algorithm to correct the intensity.

Multiscale orthogonal matching pursuit algorithm combined with peak model for interpreting ion mobility spectra and achieving quantitative analysis

Ion mobility spectrometry is an important rapid analysis method. However, it is difficult to achieve quantitative analysis when spectral peaks overlap. A new method for analyzing ion mobility spectra is presented here. The method achieves quantitative analysis by combining the advantages of the peak model (in terms of optimal physical and chemical interpretation of the system of interest) and the multiscale orthogonal matching pursuit algorithm (in terms of extracting characteristic peaks). A simulated data set, constructed using the peak model, containing overlapping peaks was analyzed to demonstrate the ability of the multiscale orthogonal matching pursuit algorithm to decompose overlapping peaks. Real data sets for methyl salicylate and a mixture of acetone and methyl salicylate at sixteen concentrations were generated using a vapor generator (using permeation tubes). The characteristic peaks were extracted using the multiscale orthogonal matching pursuit algorithm. Univariate calibrations using the peak area and peak height were prepared to allow quantitative analyses to be performed. Multivariate calibrations using partial-least-squares and poly-partial-least-squares were prepared and the results were compared with the univariate calibration results. Markedly better or similar predictions were made using the univariate calibration models involving physical and chemical interpretations than using the multivariate calibration models.

Determination of leucine and isoleucine/allo-isoleucine by electrospray ionization-tandem mass spectrometry and partial least square regression: Application to saliva samples

Herein we propose, for the first time, a rapid method based on flow injection analysis, electrospray ionization-tandem mass spectrometry (FIA-ESI-MS/MS) and multivariate calibration for the determination of l-leucine, l-isoleucine and L-allo-isoleucine in saliva. As far as we know, multivariate calibration has never been applied to the data from this non-separative approach. The possibilities of its use were explored and the results obtained were compared with the corresponding ones when using univariate calibration.Partial least square regression (PLS1) multivariate calibration models were built for each analyte by analyzing different saliva samples, and were subsequently applied to the analysis of another set of samples which had not been used in any calibration step. For Leu, the model worked satisfactorily with root mean square errors in the prediction step of 17%. This error can be considered acceptable and is common in methodologies that do not include a separation step. Results were compared with those obtained when univariate calibration was used, using the m/z transition 132.1 → 43.0 as the quantitation variable. In this case, the obtained results were not acceptable, with RMSEP of 236%, due to the fact that saliva samples contained another compound, different to the target analytes, which also shared the same transition.Ile and aIle have the same fragmentation patterns, so quantification of the sum of both compounds was performed, with RMSEP of 14% using a PLS1 model. Similar results were obtained when a univariate calibration model using the m/z transition 132.1 → 69.0 was employed. However, the use of this transition should be carefully examined when other compounds present in the matrix contribute to the analytical signal.The method increases sample throughput more than one order of magnitude compared to the corresponding LC-ESI-MS/MS method and is especially suitable as screening. When abnormally high or low concentrations of the analytes studied are obtained, the use of the method that includes separation is recommended to confirm the results.

Copper enrichments in the Kimberley formation in Gale crater, Mars: Evidence for a Cu deposit at the source

Copper quantification with laser induced breakdown spectroscopy (LIBS) using a univariate calibration model enables the ChemCam instrument onboard the Curiosity rover to measure unusually elevated Cu concentrations in potassic sandstones and Mn-oxide-bearing fracture fills in the Kimberley region of Gale crater, Mars. Mostly, the copper phases occurring in sedimentary bedrock are associated with detrital silicates, including feldspars, pyroxenes and K-phyllosilicates, likely coming from a potassic igneous source near the northern crater rim, while those present in the fractures are likely adsorbed on the surface of manganese oxides. These two different mineralogical associations imply at least two distinct processes: Cu enrichment in bedrock at the source, likely during crystallization of the igneous silicates, and adsorption of Cu on Mn-oxides precipitated from groundwater that encountered oxidizing conditions within fractures in the bedrock. The potassic sediments enriched in copper may be evidence of a porphyry copper deposit or an impact-induced hydrothermal deposit in the source region.

Accuracy enhancement of a multivariate calibration for lead determination in soils by laser induced breakdown spectroscopy

We have investigated matrix effects and spectral interferences on example of lead determination in different types of soils by laser induced breakdown spectroscopy (LIBS). Comparison between analytical performances of univariate and multivariate calibrations with the use of different laser wavelength for ablation (532, 355 and 266nm) have been reported. A set of 17 soil samples (Ca-rich, Fe-rich, lean soils etc., 8.5–280ppm of Pb) was involved into construction of the calibration models. Spectral interferences from main components (Ca, Fe, Ti, Mg) and trace components (Mn, Nb, Zr) were estimated by spectra modeling, and they were a reason for significant differences between the univariate calibration models obtained for a three different soil types (black, red, gray) separately. Implementation of 3rd harmonic of Nd:YAG laser in combination with multivariate calibration model based on PCR with 3 principal components provided the best analytical results: the RMSEC has been lowered down to 8ppm. The sufficient improvement of the relative uncertainty (up to 5–10%) in comparison with univariate calibration was observed at the Pb concentration level>50ppm, while the problem of accuracy still remains for some samples with Pb concentration at the ~20ppm level. We have also discussed a few possible ways to estimate LOD without a blank sample. The most rigorous criterion has resulted in LOD of Pb in soils being ~13ppm. Finally, a good agreement between the values of lead content predicted by LIBS (46±5ppm) and XRF (42.1±3.3ppm) in the unknown soil sample from Lomonosov Moscow State University area was demonstrated.

Enzymatic determination of urinary citrate based on flow injection system using NUV spectroscopy and PLS regression

In this study, a flow injection analysis (FIA) system with enzymatic detection was proposed for determination of citrate in urine using a lab-made microfluidic chip. A microfluidic device based on polydimethylsiloxane (PDMS) channels was designed and fabricated. And the analytical variables of this method, such as accuracy, precision and interference factors, have been discussed. Furthermore, in order to determinate the citrate concentration in real samples, three univariate calibration models with different standard solutions of citrate and one partial least squares regression (PLSR) model using near ultraviolet (NUV) spectroscopy were established, and the predictive performance of the proposed models was evaluated externally by making the correlation analysis between prediction values and reference values from capillary electrophoresis (CE) of citrate level in real urine samples. The correlation coefficients of three univariate models were 0.9989, 0.9955 and 0.9976 within the range from 0.1mM to 6mM and the root-mean-square error of prediction (RMSEP) for univariate models and PLSR model were 0.65mM and 0.40mM, respectively. The models were validated and the values of correlation coefficients of prediction found for univariate and multivariate models were 0.85 and 0.88, respectively. Results indicate that multivariate calibration based on NUV/PLS method has improved the practicability greatly comparing with the univariate regression in urinary citrate analysis because of its high sensitivity and validity of prediction. What’s more, combining with the advantages of enzymatic detection and microfluidic chip, this method looks more promising in the complex biomedical analysis without tedious pretreatments.

Voltammetric Determination of Ternary Phenolic Antioxidants Mixtures with Peaks Separation by ICA

The paper refers to the problem of separation of the overlapping signals in voltammetry, which was resolved by the assumption that the univariate calibration models for the individual analytes are requested. It was demonstrated that Independent Components Analysis (ICA) is an effective tool for reconstruction of the successive signals shape, peak positions and also the basic validation parameters meet the typical criteria. Simulation approach enabled selection of the optimal set of mixtures, necessary for the effective operation of the ICA and high predictive ability of the calibration models. It was proved that the triples of analytes chosen from the list of four phenolic acids, ie. caffeic of 9.9 – 87.6 μM, ferulic of 5.9 – 52.6 μM, syringic of 9.9 – 87.3 μM, and vanillic acid of 13.9 – 122.7 μM may be successfully simultaneously determined by differential pulse voltammetry on boron doped diamond electrode, excluding samples at concentrations close to the lower limit of linearity.

Evaluation of a Raman spectroscopic method for the determination of alcohol content in Greek spirit Tsipouro

A Raman spectroscopic method and the conventional distillation method for the determination of alcohol content % (v/v) in Greek spirit Tsipouro used. A univariate calibration model was constructed employing the band area at 880 cm-1 of standard ethanol solutions. The concentrations of 46 samples were then measured using the calibration model and the results were compared with those obtained using the conventional analysis employing a distillation step. Alcohol content in Greek spirit Tsipouro measured with the conventional method ranged from 35.1 to 71.2 % (v/v). The determination coefficient (R2) value was 0.9997 while the corresponding values of the relative errors ranged between – 13.1 -1.0 %. According to the proposed method the alcohol concentration in Greek spirit Tsipouro ranged from 27.7 to 68.2 % (v/v). The proposed method is simple, rapid, economical and does not require any sample pre-treatment steps. It could be a starting point for the design of more specific models according to the requirements of the spirit industry.

Analysis of intensity and spatial patterns of public use in natural treatment systems using geotagged photos from social media

Patterns of public use in 273 natural treatment systems worldwide are investigated by means of geotagged data from two popular photo-sharing websites, using spatial analysis and regression techniques. Standardized Major Axis (SMA) regression is found to perform better than other univariate calibration models in terms of goodness of fit with reported visitation frequencies and predictive accuracy, and is used to predict visitation rates in 139 systems that are associated with at least one geotagged photograph. High visitation rates are found in free-water surface (FWS) constructed wetlands and mixed pond-constructed wetlands systems, as well as systems treating surface water or stormwater runoff. Geographic Information System (GIS) techniques are used to map hot and cold spots of public use in two highly visited systems. Binomial logit regression reveals that the probability to be associated with at least one geotagged photograph is a function of system size, system type, and influent water quality. The findings are discussed in terms of their implications for the evaluation of public use in multifunctional ecologically engineered systems as well as the applicability of the proposed methodology to other natural and man-made ecosystems.

Nondestructive and rapid concurrent estimation of paracetamol and nimesulide in their combined dosage form using Raman spectroscopic technique.

A rapid, nondestructive Raman spectroscopic method was developed for quantitative estimation of paracetamol and nimesulide in their combined dosage form. A Raman univariate calibration model was developed by measuring the peak intensities of paracetamol and nimesulide at 853 cm(-1) and 1336 cm(-1), respectively. The developed method was successfully applied for in situ, concurrent estimation of paracetamol and nimesulide in their combined dosage and method was also validated according to International Conference on Harmonisation guidelines. Thus, the developed Raman spectroscopic method can be applied for simultaneous estimation of paracetamol and nimesulide in their combined dosage form as a process analytical technology tool by pharmaceutical industries for routine quality control.

Generalized multiple internal standard method for quantitative liquid chromatography mass spectrometry

In this contribution, a multiplicative effects model for generalized multiple-internal-standard method (MEMGMIS) was proposed to solve the signal instability problem of LC–MS over time. MEMGMIS model seamlessly integrates the multiple-internal-standard strategy with multivariate calibration method, and takes full use of all the information carried by multiple internal standards during the quantification of target analytes. Unlike the existing methods based on multiple internal standards, MEMGMIS does not require selecting an optimal internal standard for the quantification of a specific analyte from multiple internal standards used. MEMGMIS was applied to a proof-of-concept model system: the simultaneous quantitative analysis of five edible artificial colorants in two kinds of cocktail drinks. Experimental results demonstrated that MEMGMIS models established on LC–MS data of calibration samples prepared with ultrapure water could provide quite satisfactory concentration predictions for colorants in cocktail samples from their LC–MS data measured 10days after the LC–MS analysis of the calibration samples. The average relative prediction errors of MEMGMIS models did not exceed 6.0%, considerably better than the corresponding values of commonly used univariate calibration models combined with multiple internal standards. The advantages of good performance and simple implementation render MEMGMIS model a promising alternative tool in quantitative LC–MS assays.

Rapid Analysis of Inorganic Species in Herbaceous Materials Using Laser-Induced Breakdown Spectroscopy.

Inorganic compounds in biomass, often referred to as ash, are known to be problematic in the thermochemical conversion of biomass to bio-oil or syngas and, ultimately, hydrocarbon fuels because they negatively influence reaction pathways, contribute to fouling and corrosion, poison catalysts, and impact waste streams. The most common ash-analysis methods, such as inductively coupled plasma-optical emission spectrometry/mass spectrometry (ICP-OES/MS), require considerable time and expensive reagents. Laser-induced breakdown spectroscopy (LIBS) is emerging as a technique for rapid analysis of the inorganic constituents in a wide range of biomass materials. This study compares analytical results using LIBS data to results obtained from three separate ICP-OES/MS methods for 12 samples, including six standard reference materials. Analyzed elements include aluminum, calcium, iron, magnesium, manganese, phosphorus, potassium, sodium, and silicon, and results show that concentrations can be measured with an uncertainty of approximately 100 parts per million using univariate calibration models and relatively few calibration samples. These results indicate that the accuracy of LIBS is comparable to that of ICP-OES methods and indicate that some acid-digestion methods for ICP-OES may not be reliable for Na and Al. These results also demonstrate that germanium can be used as an internal standard to improve the reliability and accuracy of measuring many elements of interest, and that LIBS can be used for rapid determination of total ash in biomass samples. Key benefits of LIBS include little sample preparation, no reagent consumption, and the generation of meaningful analytical data instantaneously.

In situ analysis of steel melt by double-pulse laser-induced breakdown spectroscopy with a Cassegrain telescope

A laser-induced breakdown spectroscopy (LIBS) system combining a Cassegrain telescope and a double-pulse laser mode was developed for the in situ analysis of steel melt. Optical- and electrical-related devices were sealed in an enclosed box away from the high-temperature steel melt surface. Connected to the box by a flange, a long hollow steel tube was used for the laser and plasma emission transmission path. At the tip of the steel tube, a refractory lance that can withstand high temperatures was immersed into the molten steel surface to pass through the surface slag layer. The designed optical structure successfully keeps the photoelectric-associated system components away from the high-temperature environment, thus reducing the complexity of system protection and maintenance. The signals obtained from single-pulse and double-pulse LIBS were comprehensively compared; the effect of argon blowing on spectral stability was analyzed; and the quantitative analysis of Si, Mn, Cr, Ni and V in molten steel samples was evaluated using both a univariate model and a partial least squares (PLS) model. The relative root mean square error of prediction (RMSEP) values and average relative standard deviations (RSDs) of the PLS model were approximately 5% and 2%–3%, respectively, both of which are less than those of the univariate calibration model. The sealed LIBS setup was also transferred to a steel plant for application testing, and the obtained accuracy approached the plant's accuracy requirements. Furthermore, quantitative analysis of carbon was also achieved on the basis of the PLS models. These results demonstrate that the developed system is promising for the in situ analysis of melt steel in the steelmaking industry.

Real‐time monitoring of high‐gravity corn mash fermentation using in situ raman spectroscopy

In situ Raman spectroscopy was employed for real-time monitoring of simultaneous saccharification and fermentation (SSF) of corn mash by an industrial strain of Saccharomyces cerevisiae. An accurate univariate calibration model for ethanol was developed based on the very strong 883 cm(-1) C-C stretching band. Multivariate partial least squares (PLS) calibration models for total starch, dextrins, maltotriose, maltose, glucose, and ethanol were developed using data from eight batch fermentations and validated using predictions for a separate batch. The starch, ethanol, and dextrins models showed significant prediction improvement when the calibration data were divided into separate high- and low-concentration sets. Collinearity between the ethanol and starch models was avoided by excluding regions containing strong ethanol peaks from the starch model and, conversely, excluding regions containing strong saccharide peaks from the ethanol model. The two-set calibration models for starch (R(2) = 0.998, percent error = 2.5%) and ethanol (R(2) = 0.999, percent error = 2.1%) provide more accurate predictions than any previously published spectroscopic models. Glucose, maltose, and maltotriose are modeled to accuracy comparable to previous work on less complex fermentation processes. Our results demonstrate that Raman spectroscopy is capable of real time in situ monitoring of a complex industrial biomass fermentation. To our knowledge, this is the first PLS-based chemometric modeling of corn mash fermentation under typical industrial conditions, and the first Raman-based monitoring of a fermentation process with glucose, oligosaccharides and polysaccharides present.

Determination of Cr in water solution by laser-induced breakdown spectroscopy with different univariate calibration models

In order to prove the feasibility of laser-induced breakdown spectroscopy (LIBS) in measuring toxic metals Cr in water solution, a series of potassium bichromate standard solutions were prepared in the lab. The characteristic line intensity of Cromium (Cr) element at 357.87, 359.35, 360.53, 425.43, 427.48, and 428.97 nm was taken to build up the correlation with concentration. The indexes of relative standard deviation, intercept, slope, R2 (coefficient of determination), and root mean square error of calibration were selected to verify the precision and accuracy of models. The comprehensive results showed that the 425.43 nm line had better superiority than other lines. And the detection limit of 6 ug/ml and repeatability of 3 % are reported. To improve the model accuracy further, the intensity ratio of single 425.43 nm line to the whole spectrum was extracted. And a linear relationship between the intensity ratio and the element Cr concentration was constructed. The results demonstrated the intensity ratio calibration had better accuracy than single line calibration, especially after smoothing. To verify the accuracy of prediction, the 100 ug/ml concentration sample was used as prediction sample. The relative error values are 13.2, 11.7, and 10.8 % for single line calibration, intensity ratio calibration with raw data, and by use of smooth processing data, respectively. The results further indicated that the intensity ratio calibration improved the accuracy of measurement than single line calibration. It is worth mentioning that the application of LIBS aiming the direct analysis of heavy metals in water is a great challenge that still needs efforts for its development and validation.

Confocal Raman Microscopy as a Tool to Investigate Concentration Profiles of Melt Crystallized Ibuprofen/Carnauba Wax

AbstractCoatings are of great significance for pharmaceutical solid dosage forms. They fulfil a number of functions and are often necessary to control drug delivery, to mask bitter taste, or to protect the active pharmaceutical ingredient from detrimental environmental factors. The process of self‐coating by melt crystallization of a suitable binary mixture eliminates the need for an additional process step in the manufacture of a solid drug. Self‐coating relies upon the physical and spatial separation of individual components in a melt during solidification. This paper focuses on the use of confocal Raman microscopy as a nondestructive technique for quantifying the spatial distribution of the components in self‐coated pastilles manufactured from the binary system ibuprofen/carnauba wax. Pastilles are produced from the melt. Raman spectroscopy allows the direct analysis of concentration profiles across the surface of the pastille. Here, the samples are cleaved and the cleaved surface is investigated in order to establish the distribution of the components in the interior of the solid. A univariate calibration model was developed and statistically validated with standard mixtures of ibuprofen and carnauba wax. Different regression models (linear or polynomial, using different significant peaks for the respective compounds) were assessed and a linear model was found to be adequate to determine the concentration gradient in the pastilles.