Extraction of Pure Spectral Signatures and Corresponding Chemical

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Extraction of pure spectral signatures and corresponding chemical maps from EPR imaging data sets: identifying defects on a CaF2 surface due to a laser beam exposure. Maya Abou Fadel, Xin Zhang, Anna De Juan Capdevila, Romà Tauler, Hervé Vezin, and Ludovic Duponchel Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/ac504733u • Publication Date (Web): 02 Mar 2015 Downloaded from http://pubs.acs.org on March 8, 2015

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Analytical Chemistry

Extraction of pure spectral signatures and corresponding chemical maps from EPR imaging data sets: identifying defects on a CaF2 surface due to a laser beam exposure. Maya Abou Fadel,† Xin Zhang,‡ Anna de Juan,§ Roma Tauler,‡ Hervé Vezin,† and Ludovic Duponchel*,† †

LASIR CNRS UMR 8516, Université Lille1, Sciences et Technologies, 59655 Villeneuve d’Ascq Cedex, France. IDAEA-CSIC, Jordi Girona 18, 08028 Barcelona, Spain. § Chemometrics Group, Department of Analytical Chemistry, Universitat de Barcelona, Diagonal 645, 08028 Barcelona, Spain. ‡

ABSTRACT: A calcium fluoride (CaF2) plate was exposed to pulsed laser irradiations inducing surface morphological and ionization changes on its surface. More precisely surface damages mainly correspond to intrinsic defects. Electron paramagnetic resonance (EPR) hyperspectral imaging is a powerful technique able to characterize the defects formed on the CaF2 surface. Indeed, EPR hyperspectral images provide spatial and spectral information about the sample studied. In fact, these images possess a great potential to obtain accurate and reliable knowledge about the chemical composition and the distribution of the component due to the presence of the spatial aspect. However, the complexity of such hyperspectral data sets imposes the use of advanced chemometric tools to extract valuable information on the considered physico-chemical system. Therefore, Multivariate Curve ResolutionAlternating Least Squares (MCR-ALS) is proposed to identify and locate the different constituents in the images. The originality of this work is that it reports on the application of MCR-ALS, for the first time, on electron paramagnetic resonance (EPR) imaging data sets that will furnish the distribution maps and the spectral signatures of all components present in the sample. The results show the identification of different intrinsic defects on a CaF2 sample from the sole information in the raw image measurements and, therefore, confirm the potential of this methodology and the important role of spatial information contained in the image.

INTRODUCTION Calcium fluoride (CaF2) is a representative alkaline earth fluoride that has been the subject of many experimental and theoretical studies for years. It attracted much attention due to its good transparency from UV to IR range, being used as optical window for UV sensors, filters, and stepper lenses1. In addition to that, it is the only candidate material for microlithography optics using excimer lasers in the vacuum ultraviolet (VUV) and the deep ultraviolet (DUV)2. Therefore, CaF2 is a promising material in various application fields such as dielectric medium for semiconductors as well as optical components35 . CaF2 plate is also an important element used in the generation of the white-light continuum pulses spanning the ultraviolet to the near infrared range that are induced, for instance, by the nonlinear interaction of ultra-intense laser pulse with this condensed transparent media in order to broaden the laser wavelength spectra6. The conversion of specific wavelength to a continuum allows the implementation and the development of coherent control techniques, which are important for the characterization of molecular dissociation pathways in lasermolecule ultrashort pulse interaction in addition to time-resolved broadband absorption, as well as for dynamic characterization of laser-induced structural transitions7. Under high-energy photon flux and laser irradiation, all metal halides have the tendency to form defects due to the damage and degradation of material properties after short exposure time8-10. Therefore, the actual wide use of CaF2 plates imposes the investigation of potential defects in such material. EPR imaging will be considered as the optimum technique in this work because CaF2 material is transparent to many other spectroscopies. Even if undamaged CaF2 compound exhibits no signal in EPR spectroscopy, defects that induce paramagnetic sites will do. Moreover different damages will provide different signals in this technique.

Image analysis is a wide denomination that encloses several kinds of images. For instance, simple classical gray scale images can be noted, in addition to more complex images such as multispectral images that are images collected using a low number of spectral channels and the hyperspectral images that are images exploited in their full extension often with several hundreds or thousands of spectral channels. Hyperspectral images are a kind of instrumental spectroscopic measurements that contain both spatial and spectral information about the sample11. The particularity about hyperspectral images is that they possess a spatial aspect that provides information about the distribution of each component on the sample. Nowadays, these analytical measurements are an active area of research where a drastic growth can be noticed in the last few years. Hyperspectral images can be acquired by several techniques such as mid infrared spectroscopy, near infrared spectroscopy, Raman spectroscopy, fluorescence spectroscopy or electron paramagnetic resonance. Those measurements can be applied in a wide range of fields such as biomedical diagnostic, material science, analytical chemistry, environmental analysis, pharmaceutical and food industry12-19. Electron paramagnetic resonance (EPR) spectroscopy, also called electron spin resonance, is an analytical technique used to detect paramagnetic ions and radicals20. EPR imaging (EPRI) combines the information obtained by EPR spectroscopy with the possibility of imaging21. It is a potent tool for investigating aspects ranging from applications in material science including polymers, ceramics, semiconductors, inorganic materials as well as their defects and impurities to medicine and biological studies22-27. EPRI is an important imaging method in the field of magnetic resonance. There exist two modes for image acquisition in EPRI. In the first mode, image includes only information about the spin concentration in the space (1D, 2D, or 3D

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– purely spatial information). This mode is generally applied when only one type of paramagnetic center is present in the sample. In the case of the second mode, the obtained image contains both spatial and spectral information providing an overall 2D, 3D, and 4D spectralspatial images.28-30 This mode should be applied when more than one paramagnetic center is present in the considered system. However, the great potential of this method is sometimes limited because of the lack of data processing methods able to extract pure contributions from such complex data sets. The image reconstruction mode determines the type of projections that have to be collected, their number, the angular extent around the object, the magnitude of gradient employed and the field span. Then, reconstruction algorithm takes the projections and transforms them into an image. Considering the spectralspatial mode, an EPR spectrum per sample surface unit (pixel) is obtained. Because each acquired spectrum comes potentially from a mixture, data analysis methods are needed in order to extract spectra and distribution maps of all pure components present in the system. Actually, EPR specialists often face problems to identify the total number of pure constituents present in the system as well as to interpret the complex acquired spectra. It is a quite challenging task because of the high degree of signal overlap coming from paramagnetic ions and radicals. In general, the analysis and the interpretation of EPR spectra is difficult due to a rather low signal to noise ratio and also to the lack of a spectral data base in contrast with other spectroscopies, like vibrational ones. An approach EPR specialists use, in the case of weak anisotropy, is to increase the frequency of spectrometer, in order to obtain higher spectral resolution31. Another possibility is the application of principal component analysis (PCA), which is a widespread multivariate method, able to explore EPR data sets and to determine the number of pure contributions needed to reconstruct the original image32,33. Although this algorithm is able to observe relevant sources of variations in the data set, it cannot extract the pure spectra of each constituent since principal component profiles are, by nature, orthogonal, whereas real EPR spectra of different species overlap and present correlation among them. Maximum-likelihood common factor analysis (MLCFA) is another possible approach34,35. It is a multivariate statistical technique that aims to detect the total number of constituents and to decompose a set of multicomponent EPR powder spectra into their spectral components by using minimization procedure or target transformation. However the existing method possesses some limitations. Indeed it retains only the components which express fairly high percentage of the total variance, the remaining ones being considered as non-significant. In addition to the previous limitation, this method has difficulty in identifying real-component spectrum whose line shape are not described by means of analytical functions (i.e Gaussian or Lorentzian character). It also requires sometimes the availability of a reference spectral library. Other EPR specialists use spectral simulation in order to interpret their data sets. For example, Duling’s method consists of rule-based perturbations with trial and error calculations. It is used for fitting EPR data with multiple free radicals as formed in chemical and biochemical spin-trapping systems36,37. The proposed algorithm aims at refining hypothetical simulation parameters to give optimal values that will allow the researcher to test various possible free-radical formation pathways in an unbiased manner. Nevertheless, such calculations are very dependent on initial parameters and on the correctness of the postulated models. Hence, the interpretation of the simulation is complicated in case of absence of any initial information about the studied data. On the basis of the above, a new data analysis method is required to estimate the total number of constituents and to retrieve the spectral signatures of each pure component and their related concentration maps from severely overlapped hyperspectral EPR data sets images without requiring prior knowledge or hypothesis models about the considered system. Multivariate curve resolution-alternating least squares (MCRALS) is an ideal methodology for this purpose. MCR-ALS method, known as a self-modeling algorithm, has been developed to decompose a data set into pure spectral responses and pure concentrations profiles of all constituents present in unknown mixtures. So far, MCR-ALS has been exploited in many kinds of spectroscopy such as Raman spectroscopy38-40, near-infrared spectros-

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copy41-43, FT-IR 44-46, UV-Vis spectroscopy47-49, NMR spectroscopy50, high performance liquid chromatography53-55, gas chromatography 56-58 , and many others… In the end of eighties, a predecessor of MCRALS algorithm (called SPFAC) was already used to explore EPR data sets59,60. Recently, MCR-ALS method has been, successfully, applied on electron paramagnetic resonance spectroscopy61. It was able to decompose a multicomponent system formed by a set of EPR spectra recorded in aqueous solutions from mixtures of paramagnetic compounds in different concentration ratios into the pure spectra of the paramagnetic compounds and their related relative concentrations in all mixtures. On the basis of these satisfactory results, it seemed promising to extend the methodology for the analysis of more complex data sets in EPR imaging. MCR-ALS has been proven to be an adaptable and useful method for such data set analysis due to the ease of introduction of external spectral and spatial information about the image and the facility to work with single or multiset image structures62,63. In MCR-ALS, the experimental mixed raw spectra are described by a concentration-weighted linear combination of their pure spectral components64. The algorithm decomposes the superposed spectral data sets, under adequate constraints, such as nonnegativity on concentration or spectral profile into individual pure contributions i.e. concentration profile (distribution maps in imaging experiments) and pure spectra of the image constituents by the sole use of the raw data. Constraints are used to introduce external spectral and spatial information about the studied data and to drive the algorithm to give meaningful and accurate results. Therefore, the application of this method on such data sets allows recovering the spectral information and the spatial concentration maps of the image analyzed. Hence, MCR proves to be particularly well adaptable to such hyperspectral data sets65. 52

Due to the advantages of this method, the objective of our study is to identify the various unknown defects/impurities present in the CaF2 sample by the powerful multivariate curve resolution-alternating least squares and thus, to extract, simultaneously, the images and the corresponding spectra of each pure product from the spectral-spatial EPR data set.

SAMPLE PREPARATION A CaF2 plate was used in a femtosecond transient absorption setup to convert the laser light into a light with broad spectral bandwidth. The plate was 1-mm-thick, 7 mm wide and 20 mm high. The femtosecond experiments were carried out by using a 1kHz Ti:Sapphire laser system based upon a Coherent (MIRA 900D) oscillator and a BM Industries (ALPHA 1000) regenerative amplifier providing 1mJ, 100 fs pulses at a wavelength of 800 nm. The majority of the energy from the fundamental beam was frequency-doubled to provide pump excitation at a wavelength chosen to be 380 nm. The other small part (a few microjoules) of the fundamental energy was used to generate a white continuum in the CaF2 plate. After several pump-probe spectroscopic experiments, the CaF2 plate was irradiated by pulsed laser. In consequence, bump-like features and cavities were observed on the exposed material. These bumps are related to compressive stresses due to a pressure build-up induced by fast laser heating and their subsequent relaxation. The formation of these nanocavities is attributed to the explosive expansion generated by shock waves due to laserinduced plasma after the nonlinear absorption of the laser energy by the material66. The CaF2 plate was then examined by EPR spectroscopy to explore intrinsic damages.

IMAGE ACQUISITION For data acquisition, the CaF2 plate was analyzed with a continuous wave-electron paramagnetic resonance spectrometer (CW-EPR). EPR images were acquired at room temperature of 20°C using an ELEXSYS E-580 (Bruker) EPR spectrometer operating at the XBand. Images were recorded at modulation field frequency of 100 kHz and a microwave frequency of 9.80 GHz, with an amplitude modulation set at 0.1 mT and a microwave power of 12 mW corresponding to non-saturation conditions. The spatial window (field of view) was 20 mm and the weak pitch from Bruker was used as stand-


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ard reference and contained a known concentration of spin/mass (1.29 × 1013 spins/g). The spin concentration is given by the double integration of the first derivative of the EPR signal. Images were reconstructed from a complete set of projections collected as a function of the magnetic field gradient. EPR spectra were recorded in the interval between 2900 and 3800 Gauss. The full 2D YZ-spectral data set involved 160 000 EPR spectra, each with a different combination of Y and Z gradients. A data cube with a pixel size of 50 µm was acquired given the dimensions 400 × 400 × 400 (x y B, where x and y are the number of pixels in the two directions of the plate surface and B the magnetic field).

DATA TREATMENT Given the 3D structure of the considered EPR data cube, each pixel is a microzone of analysis for which a characteristic spectrum is obtained. From another point of view, the cube possesses a collection of images forming many layers, where each layer represents an image recorded at a certain magnetic field. However, the measurement variation in an image data set is assumed to follow a bilinear model, where the mixed signal measured at every pixel is the concentration weigted sum of the pure signals from the chemical constituents present in the sample. The ultimate goal of the analysis of such images is to provide reliable distribution maps and to characterize each individual pure spectral (signature) component present in the image. For this purpose, MCR is the proposed approach among the various chemometrics methods since this bilinear method is suitable for such images.

Figure 1. Multivariate curve resolution applied on an EPR imaging data set.

Multivariate curve resolution (MCR) methods are a group of chemometric techniques designed to extract simultaneously the spectra of all the pure compounds and their corresponding concentration maps from the experimental data matrix using little prior knowledge (Figure 1)67,68. In order to make the 3D image data set suitable for the MCR analysis, unfolding the data cube into a two-dimensional spectral data matrix D is required. Multivariate curve resolution - alternating least squares (MCR-ALS)69 aims at solving a bilinear factorization of spectral data matrix D (mn) into the product of two simpler matrices, C (kn) and ST(nm), having a physical sense (equation 1). D is the unfolded spectral data matrix that possesses m rows corresponding to m different spectra and n columns corresponding to n different magnetic fields. k is the number of pure compounds present in the system. C is the pure concentration matrix, the profiles of which are individually folded back to recover the distribution maps for each pure compound in the analyzed sample. S is the matrix spectra of pure constituents used for molecular identification. E is the error matrix, which expresses unmodelled variations i.e. noise. D (m×n) = C (m×k) . ST (k×n) E (m×n) (1) As one can see, MCR-ALS algorithm requires only the D matrix, which represents the overall experimental system, to perform the analysis. Nevertheless, the number of pure components and initial estimates of either concentration profile Cini or spectral profile STini are needed to start the optimization process. Therefore, as a first step, singular value decomposition (SVD) is applied on the matrix D in order to determine the mathematical rank used as an estimation of the

total number of pure components present in the system, i.e., k .70 Next, as a second step, a pure variable selection method based on SIMPLeto-use Interactive Self Modeling Analysis (SIMPLISMA) is used to give initial estimates of concentration profiles Cini or spectral profile STini.71 In fact, this method is accessed to select the purest variables (i.e. the more specific ones) from the data set. Because SIMPLISMA implies the use of positive data, integrated EPR data are used only in this part for better variable selection. Given an initial estimate, e.g., of the pure spectral profiles, an iterative alternating least-squares optimization of matrices C and ST is done in each iteration until convergence is achieved. This would imply the operations shown in eq. 2 and 3 C = D S (ST S)-1 (2) (3) ST = (CTC)-1CTD Appropriate constraints are then applied on the estimated concentration profiles and spectra C and ST respectively, in order to reduce the size of the solution space (i.e. rotational ambiguity). Indeed applying constraints is the only way to resolve severely overlapping concentration and spectral profiles72. Constraints are defined as prior chemical information or mathematical properties that help to resolve the profiles. A wide number of different types of constraints can be implemented to help in the improvement of the obtained results such as non-negativity (on concentration or spectral profile), unimodality (unimodal shape), closure (constant total concentration), equality constraint (fixing some known values), in addition to other flexible constraints that can be applied according to the necessity and nature of the data. During the alternating least-squares procedure, the matrices C and ST are iteratively refined to find the more consistent values of C and ST. Along the optimization of MCR-ALS method, the error matrix E and the residual sum of squares RSS are computed according to equations 4 and 5. E = D – C ST

(4)

∑ ∑

(5)

Where eij is the element related to the E matrix. It is obtained from the difference between element of the input data matrix D (pixels i, magnetic field j) and the corresponding elements of the MCR-ALS reproduction. A threshold is set by the user according to the noise level in order to stop the iterative process. The convergence criterion is reached when relative change of standard deviation of RSS error reaches the threshold. Consequently, the extraction of the concentration profile C and the related pure spectral profile ST of each pure constituent are retrieved. Knowing the original position of each spectrum within the image, the concentration profile is refolded to recover the initial spatial image structure (distribution map) for each component. In this work, all calculations were developed with MATLAB environment version R2008b (The MathWorks Inc., Natick, MA, 2000). Multivariate Curve Resolution extractions were obtained with the MCR-ALS toolbox developed by J. Jaumot, A. de Juan and R. Tauler (freely available from the webpage http://www.mcrals.info).73

RESULTS AND DISCUSSION The acquired EPR spectral-spatial data set of the CaF2 plate is in the form of a cube whose dimensions are 400 pixels 400 pixels 400 magnetic fields. Figure 2a shows an overlay of the 160,000 EPR spectra corresponding to all pixels. Different signals are observed but it is very difficult at this stage to establish the number of pure contributions present in the system. In hyperspectral imaging, the global intensity map is often calculated in order to have a first insight about signal over the sample surface. In this case, EPR signal integration is done over the whole spectral domain for each pixel. Figure 2b indicates that the highest EPR contributions (red of the colorbar) are located in the center of the CaF2 plate corresponding to laser beam strike. However, one can notice another zone on the left of the previous one where signal is present but lower. Considering the conventional way of data analysis in EPR imaging, Figure 2c and 2d show images generated from univariate integration at the magnetic field of 3726 Gauss and 3748 Gauss respectively.



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Figure 2. Conventional EPR data set exploration: a) overlay of raw spectra b) global integration 2D image c) single integration 2D image at 3726 Gauss d) single integration 2D image at 3748 Gauss.

At first sight, Figure 2c seems to be consistent with the global intensity image with an intense contribution in C1 zone and a lower one in C2 zone. On the other hand, Figure 2d presents particular features with positive and negative contributions in D1 and D2 zones respectively. From this last observation, we can therefore say that spectral interferences are present at 3748 Gauss. Considering the proximity of the two signals at 3726 Gauss and 3748 Gauss and, therefore, the possible lack of selective EPR channels, doubts could be cast upon considering the plot in Figure 2c as a pure compound image. This simple two magnetic fields example demonstrates the difficulty to generate with a univariate approach real chemical maps from highly overlapping EPR imaging data set without prior knowledge about the system. The idea is thus to apply MCR-ALS on the same data set in order to overcome these limitations. As usual, the spectral data cube is first unfolded into the matrix D (160000 400) where each line represents a spectrum, which is potentially a mixture of various constituents. The first step in MCR-ALS is the application of singular value decomposition (SVD) on the matrix D. As one can see, MCRALS is a real blind signal unmixing procedure because no prior knowledge about the total number of pure compounds is used.

Figure 3. Eigenvalues of the D experimental data matrix obtained by singular value decomposition.

Figure 3 presents the plot of the first ten eigenvalues obtained from the experimental data matrix D. The SVD analysis indicates the presence of four distinct contributions on the hyperspectral CaF2 image. Indeed four significant eigenvalues are clearly distinguished from the rest due to the sudden change in the slopes. In fact, all eigenvalues above the fifth one express variance associated with noise. The next step in MCR-ALS process is the use of SIMPLISMA algorithm to generate the initial estimates. Selecting the purest magnetic fields, an initial guess Cini matrix is generated in order to begin the ALS process. Non-negativity on the concentration profile is the only constraint applied for the considered EPR data set. Figure 4 shows the final results obtained after the application of MCR-ALS on the sole raw EPR spectra i.e. the pure spectral profiles ST and the corresponding concentration profiles C that are folded back to give the distribution map of each pure contributions in the CaF2 plate. Four different pure spectral signatures and corresponding distribution maps are represented. Given the signal to noise ratio in the raw EPR data, a lack of fit of 25 % and explained variance of 94 % is a good figure of merit for the proposed extraction. The absence of signals or structures in the error matrix E is another good sign of the quality of the results. Considering the extracted pure spectra, it is now possible to have a chemical interpretation of the defects generated during laser beam exposure. The fluorite structure possesses the smaller cations Ca2+ that form a face centered cubic lattice with the larger anions F- situated at the corners of the eight cubes of the elementary cell74,75. Therefore, each anion is surrounded by four cations in a tetrahedral manner. The F- sublattice is considered a simple cubic structure. Consequently, only the center of every second cube is occupied by a cation. From this description, we can note that non-damaged CaF2 surface is transparent to EPR spectroscopy due to the lack of any paramagnetic center. When the laser beam strikes the sample, the energy of the photons (h) induces the liberation of electrons from the F- anions. The liberated electron, trapped in an anion vacancy, also called Fcenter (VFx),76-78 possesses an EPR spectrum with one peak according to equation 6. → °


(6)

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The first two spectra extracted by MCR-ALS (red and green lines) correspond to the electrons liberated by the fluoride anion. In fact, the

Figure 4. MCR-ALS extractions: the four pure spectra (in the bottom) and corresponding distribution maps (on the top).

two different spectra are associated with electrons in two different environments. It is worthy to notice that from comparing the positions of the maxima for these two first extracted spectra (i.e. 3726 Gauss and 3746 Gauss) with the ones observed in Figure 2a, it can be concluded that spectral maximum at 3748 Gauss was not related to a pure paramagnetic species. The third extracted spectrum (blue line) corresponds to the fluorine neutral atom that liberated the electrons. In fact, fluorine atom possesses nine electrons therefore has five electrons on their outermost energy level. When the fluoride anion (F-) loses one electron it has the same electronic configuration as the fluorine neutral atom (F°). Therefore it becomes a paramagnetic atom that can be detected by EPR spectroscopy. The fourth extracted spectrum by MCR-ALS (yellow line) corresponds to the coupling between the neutral fluorine atom resulting from the liberation of an electron (F°) and another fluoride anion (F-), which combined form the F2- species, also called the fluorine defect (Vk) according to equation 779. ° → (7) Thus, the defects formed on the alkaline earth fluoride CaF2 are associated with the changes in the valence state of the anion sub-lattice as well as intrinsic damages. Considering now the extracted pure concentrations maps in Figure 4, one can observe that the localization of paramagnetic species was really more complex than the one observed on the global integration image (Figure 2b). Indeed, we can see shifts between consecutive zones with various spatial overlaps. It is

also possible to observe less biased images. Indeed comparing the first MCR extracted chemical map of the electron with the one in Figure 2c, we can conclude that the light blue C2 zone was an overestimation of concentration due to a spectral interference between the two electrons spectra. This problem is even more important considering the second extracted chemical map of the electron and Figure 2d. Indeed D2 zone should have been the most intense contribution and almost no contribution should have been present in D1 zone. All these results demonstrate the importance of applying a multivariate curve resolution method in order first to extract all pure spectra for species identification and second generate unbiased distribution maps.

CONCLUSIONS The novelty of this work is that a series of EPR images acquired at different magnetic fields were analyzed by MCR-ALS to obtain the pure distribution maps and pure spectra of each constituent on the CaF2 surface that was irradiated by a laser. Identification of each defect was achieved from the resolved pure spectra on one hand, and the information at global and local (pixel) levels obtained from the distribution maps, on the other hand. After exposure to laser pulses, it has been proved that CaF2 plate suffered ionization damages. We should emphasize that all extractions were obtained without prior knowledge about the chemical system, which reflects the power of MCR-ALS methodology. We are convinced that the proposed meth-



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odology will provide new trends for data analysis in EPR imaging, particularly when complex and unknown samples are explored.

AUTHOR INFORMATION Corresponding Author * Email: [email protected]. Phone: +33 320434902. Fax: +33 320436755.

Notes The authors declare no competing financial interest.

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Extraction of Pure Spectral Signatures and Corresponding Chemical

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