Analytical method for stable background reduction for Raman spectra of carbon‐containing meteorite and terrestrial samples suffering from intense fluorescence

Chemical states of carbon in terrestrial (meta) sediments and carbonaceous chondrites gather attention as a geothermometer. As a nondestructive analytical method, Raman spectroscopy has been widely used to study their electronic properties, crystallinity, and structural defects through so‐called D and G bands. For the analysis of Raman spectra, a common problem is coexistence of a fluorescence background, which should be subtracted prior to the peak‐fitting analysis. However, we recently faced a problem that the band shape noticeably changed depending on the background function assumed although the background seemed to be well subtracted at a first glance regardless of the choice of the background function. For the application of the Raman spectroscopy as a geothermometer, a standard background subtraction method must be established to suppress the arbitrariness. In the present study, Raman spectra of seven carbon‐containing natural samples, whose background intensities were significantly different, were measured, and their background shape was evaluated by first‐, second‐, and third‐order polynomials. The results indicated that the third‐order polynomial was necessary and sufficient as a standard background function. Importantly, although lower order polynomials seem to successfully fit the background at a first glance, they falsely caused dispersion of the shoulder band shape.


INTRODUCTION
Carbon is abundantly found both on the Earth and in space, in organic and inorganic forms, and in various bonding state forming with sp, sp 2 , and/or sp 3 hybrid orbitals.The various forms of carbon (diamond, graphite, graphene, carbon black, carbon nanotubes, and fullerenes) allow a variety of bonding states and promote wide variations to electronic (Peres, 2009), thermal, and mechanical (Sykes, 2009) properties in these materials.Extensive investigations regarding the chemical states and the properties of the carbon materials have been performed to understand the nature of carbon and for developing new functional materials (Bonaccorso et al., 2015;Choi et al., 2019;El-Kady et al., 2012;Fang & Wang, 2013;Geim & Novoselov, 2007;Novoselov et al., 2004;Tan et al., 2019;Wei et al., 2018).Furthermore, carbon in the natural samples such as bituminous coals and carbonaceous chondrites has gathered attention as a geothermometer (Busemann et al., 2007;Homma et al., 2015;Kouketsu et al., 2013).
Despite the importance, the evaluation of the bonding states is still a difficult issue in most cases.Difficulties arise because the diamond and graphite structures (sp 3 and sp 2 , respectively) usually coexist in one sample and allow amorphous, not exclusively crystalline morphologies.Instead of usual techniques for structural analysis such as X-ray diffraction, Raman spectroscopy has been employed for a long time.In Raman spectra, carbon materials generally provide so-called D and G bands, which are resonantly enhanced.The intensity ratio of these bands (I D /I G ) and their band widths have been used as "structural indicator" (Bokobza et al., 2015;Dresselhaus et al., 2010;Scardaci & Compagnini, 2021;Wang et al., 2002).While structural ordering and defects in the carbon materials are usually discussed, the overlap of these bands sometimes prevents accurate determination of I D /I G and/or the band widths.Furthermore, the D band is recently considered to possess multiple components (Cancado et al., 2011;Claramunt et al., 2015;Ferrari & Robertson, 2000, 2001;Jawhari et al., 1995;Kudin et al., 2008;Martins Ferreira et al., 2010;Reich & Thomsen, 2004;Vollebregt et al., 2012).Multi-peak fitting is thus inevitable to determine the intensity and band width of each component.One critical problem for the multi-peak fitting is that Raman spectra of carbonaceous samples often suffer from a fluorescence background, which obscures a baseline level.The fluorescence originates in the carbon matters themselves or contamination of fluorescent matters (Buchwald et al., 2021;Kagan & McCreery, 2002;Nakamura et al., 2022).One way to overcome this problem is using near-infrared (NIR) or ultraviolet (UV) laser for Raman excitation.Because the intensity of fluorescence and Raman scattering changes with the excitation wavelength, it can improve the signal and background ratio.However, they are not universally applicable because of the following reasons.First, some of carbon materials are resonant even in NIR region and fluorescence does not vanish.Second, even in the case that fluorescence is efficiently suppressed by NIR excitation, since Raman intensity is inversely proportional to the fourth power of the excitation wavelength, very long exposure time is required for sufficient signal-to-noise ratio.This is troublesome when Raman mapping/imaging is necessary.UV excitation would damage the sample more easily than visible excitation would.
To overcome the problem of the intense fluorescence, mathematical data analysis has been previously discussed (Christ et al., 2022;Gao et al., 2021;Gomez-Mascaraque & Pinho, 2021;Holmi & Lipsanen, 2022;Korepanov, 2020;Villanueva-Luna et al., 2011;Yesiltas et al., 2022).Since the fluorescent spectra are generally asymmetric to wavelength and well described by log-normal function (asymmetric Gaussian function) (Burstein & Emelyanenko, 1996;Siano & Metzler, 1969), a log-normal function is often assumed to estimate the spectral shape of the broad fluorescence spectra (Addison et al., 2013;Bacalum et al., 2013;Caarls et al., 2010;Djikanovic et al., 2007;Humbs et al., 2000;Kimura et al., 2015;Lang et al., 2006;Le et al., 2017;Xiong et al., 2019).The problem to use the log-normal function is that, as the band width of the fluorescent spectra is generally as broad as $4000 cm À1 or more, Raman spectra should also be measured with such the broad region for accurate estimation of the fitting parameters.Because the spectral resolution and measurable region are in the trade-off relation, the lognormal fitting is not always applicable.For example, to determine the crystal structure and/or elemental composition of the materials, the wavenumber resolution higher than 1 cm À1 is sometimes required, and hence, it is unrealistic to measure the spectral region ranging over 4000 cm À1 (Kashima et al., 2022;Urashima et al., 2022).In addition, the fluorescence sometimes originates in two or more different materials in the sample.Thus, the reduction of the background fluorescence with one lognormal function is no longer accurate in such cases, and use of two or more log-normal functions is not realistic because of too many fitting parameters.Therefore, it is in practice difficult to apply a log-normal fitting while it is theoretically reasonable.
Instead of the log-normal fitting, some researchers tried to estimate the fluorescence background shape by a very high seventh-order polynomial functions or by semiautomated principal component analysis (PCA) to the region of interest (Christ et al., 2022;Gao et al., 2021;Gomez-Mascaraque & Pinho, 2021;Holmi & Lipsanen, 2022;Villanueva-Luna et al., 2011;Yesiltas et al., 2022).However, while these methods are advantageous for effective and reproducible removal of the background in wide wavenumber region, the high-order polynomial fitting sometimes overestimate the fluorescence intensity, leading to over-subtracting of the background especially when the Raman peaks are not very sharp.As for PCA, as it contracts the spectral components to reduce the dimension, the automatic PCA analysis would also sometimes lead to the over-subtraction.Because D and G bands of carbon-rich materials can be broader than 200 cm À1 and are composed of multiple peaks, the overestimation of the background is highly problematic to accurately obtain the peak positions and widths for each component.Conversely, a linear assumption has often been used for the background estimation.While the linear background subtraction worked well when the Raman signal is much stronger than the background, it is sample-dependent so that an analytical method that is globally applicable to any carbon-containing samples is required.A further problem is the choice of the background functions is currently entrusted to each researcher.While the researchers may compare the fitting results by changing the functions to choose the best one, such a trial-and-error process is usually not published.It is thus unclear how the multiple peak shape changes if other background functions are employed.
Very recently, through an attempt to track the literature of carbon geothermometer (Kouketsu et al., 2013) using bituminous coal, we found that the shoulder structures in the D and G band region sometimes critically changed depending on the order of the polynomials for background estimation, even though the background seemed to be well subtracted regardless of the polynomial order at a first glance.Because the peak intensity and the band width are the parameters used in geothermometer, the polynomial order dependence is a critical issue.To solve this problem, it is essential to make a standard background subtraction procedure which is globally applicable to any natural carbon-containing matters regardless of their fluorescence intensity.In the present study, we measured Raman spectra of seven carboncontaining natural samples, where various intensities of fluorescence were observed.Using the data set obtained, several background subtraction methods were compared.Because the least-order polynomial function is preferable as long as the background is correctly estimated, their background was subtracted by first-, second-, or thirdorder polynomial functions and compared.To examine how the polynomial order of the background functions affects the shoulder structure, the subtracted spectra were analyzed by multiple-peak fittings.

Experimental
In order to examine the Raman spectroscopy of a variety of carbon-rich samples, six carbonaceous chondrite meteorites and a sample of bituminous coal, collected from Harutori, Kushiro, Hokkaido, Japan, were chosen for analysis.The meteorites used were chips of Ivuna (CI1), Orgueil (CI1), NWA 11732 (CM2), Murchison (CM2), Aguas Zarcas (CM2), and Allende (CV3), which are classified as carbonaceous chondrites (containing $1.6%-5.0%carbon) with their carbon structures known to be similar to that of coals but with a varying degree or history of aqueous alteration (CI1 > CM2 > CV3).The samples were provided from members in International Meteorite Collectors Association (IMCA) and used asreceived, that is, no pretreatment nor cleaning was carried out.
The Raman spectra were measured with Raman-11i (nanophoton) combined with a microscope Eclipse Ti (Nikon).The objective lens, excitation wavelength, and excitation power were Nikon Plan Fluor (40×, NA 0.75, WD 0.66), 532 nm, and 0.8 mW at the sample face.The exposure time was 30 s except Ivuna and Orgueil (it was 60 s for these two because of low signal) and the results of two consecutive measurements were averaged.Under these conditions, the focal size is as small as or less than 1 μm.The diffraction grating provided 300 grooves mm À1 , and the wavenumber was calibrated by the Raman band of a Si wafer (520.6 cm À1 ) (Petriglieri et al., 2015).The Raman spectra were measured from at least 100 different matrix spots for each sample to examine their heterogeneity of the relative abundance of soluble/ insoluble organic matters, partial terrestrial weathering, and so on.
The spectra obtained were analyzed in the following manner.The first step in our analysis was to remove the spectral data showing the signature of coexisting iron (hydr-) oxides.Removal of its strong spectral peak at $1300 cm À1 (Figure S1 in the Supporting Information) allows access and analysis of the D and G bands.The existence of the iron (hydr-) oxides was checked by appearance of the Raman bands at $230 cm À1 (Marshall et al., 2020), $290 cm À1 (Marshall et al., 2020), and $380 cm À1 (Abrashev et al., 2020).Subsequently, because the measured wavenumbers at each pixel were slightly different day by day, the horizontal axis was unified by interpolating the spectra with 0.1 cm À1 step.The first-to third-order polynomial fittings were then applied with using the data points at 800, 950, 1800, and 2000 cm À1 .These wavenumbers were chosen because D and G bands were expected to appear at 1000-1800 cm À1 and other minerals on the carbonaceous chondrites such as olivine (doublet at 820-880 cm À1 ) and enstatite (singlet at 1000 cm À1 ) were often observed together with the carbon-rich compounds (Catalano et al., 2015;Mouri & Enami, 2008;Nascimento-Dias et al., 2021;Reynard et al., 2008;Sharygin, 2020;Zhang et al., 2018).After the background subtraction, the resulting spectra were normalized at the apparent peak of G band ($1600 cm À1 ) for comparison.The peak intensity for the apparent G band was determined by Lorentzian fitting to the region of AE40 cm À1 from the apparent peak top.

Raw Spectra of Each Sample and Fitting Strategy
Figure 1 shows typical Raman spectra of each sample.All spectra measured were shown in Figure S2 in the Supporting Information.As shown in Figure 1, D and G bands at 1000-1800 cm À1 were observed for all samples.The fluorescence background was the largest in Ivuna (the background was approximately 10 times larger than D and G bands), followed by bituminous coal, Orgueil, Murchison, NWA 11732, Aguas Zarcas, and Allende in order.This order sometimes changed, but it is essentially followed.Especially for the first three, the fluorescence was rather strong, and the D and G bands were nearly overwhelmed.The aim of this study is thus to propose a universal background estimation method which is stably applicable to various cases from weak to strong florescence backgrounds coexist.
As described in the Experimental section, we employed only four data points at 800, 950, 1800, and 2000 cm À1 for the background fitting.Although the background is usually estimated using a finite width of spectral region (e.g., 800-950 and 1800-2000 cm À1 ), the fitting only with the four points (not region) is advantageous to stably neglect the contribution of other coexisting minerals.For example, as shown in Figure S1 in the Supporting Information, olivine peaks at 820-880 cm À1 almost always coexisted with D and G bands on Allende.The drawback of this strategy is that the number of the fitting parameters is limited to 4, and hence fourth or higher order polynomial functions cannot be employed.This is problematic if the background shape is complicated and/or wavy.This problem was, however, not critical for the background estimation around the D and G bands.As shown in Figure S3 in the Supporting Information, each of the regions of 800-950 and 1800-2000 cm À1 can be well fitted with a linear function while its gradient slightly differed between 800-950 and 1800-2000 cm À1 regions.Because of the linearity in the narrow region, the use of only the four data points (at 800, 950, 1800, and 2000 cm À1 ) is essentially equivalent to using the regions with a finite width at 800-950 and 1800-2000 cm À1 .In other words, the background only deviates slightly from the linear function through 800-2000 cm À1 .This is consistent to previous reports, where the background was often assumed as a linear function (Kouketsu et al., 2013).

Comparison of the Background Estimated by First-to Third-Order Polynomial Functions
Figure 2 shows the raw spectra shown in Figure 1 together with the estimated background with first, second, or third-order polynomial functions.The backgroundsubtracted (and normalized) spectra are also shown in Figure 2. Note that all spectra analyzed are summarized in Figure S4 in the Supporting Information.For Allende and NWA 11732, which had relatively weak fluorescence, the subtracted spectra were virtually independent to the order of the polynomial.This indicates that the relatively weak background can be well described by a linear function, and the higher order coefficients converged to almost zero.The subtracted spectra for other samples noticeably depended on the polynomial order.Especially with the linear fitting, the spectral intensity did not converge to zero at the edge of the analyzed region (clearly seen in, e.g., the region of 1000-1200 cm À1 of Orgueil and Ivuna), suggesting that the background estimation with the linear function was insufficient.This is consistent to the results that the gradients for 800-950 and 1800-2000 cm À1 were different in the corresponding spectrum (Figure S3 in the Supporting Information).
With the nonzero value of the edge, the spectral shape of D and G band region also depends on the fitting function especially at the valley between D and G bands as well as the shoulders for these bands.Since the multicomponent analysis with four to five Lorentzian functions is sensitive to the shoulder and the edge structures, accurate estimation of the background shape is crucial.Therefore, for the case that fluorescence is as intense as or stronger than D and G bands, second-or third-order polynomial is inevitable.
To quantitatively examine whether the second or third-order polynomials properly estimate the real background shape, the background residue of the subtracted and normalized spectra was evaluated by the root mean square average (RMSA) for the region of 800-950 and 1800-2000 cm À1 for 100 different spots (Figure 3).As expected, for the samples with weak fluorescence (Allende and NWA 11732), the RMSA hardly depends on the fitting order.Note that the RMSA obtained for Allende at 800-950 cm À1 was higher than that at 1800-2000 cm À1 owing to the co-existence of peaks from olivine in the region 800-950.Because the effect of olivine is contained regardless of the background subtraction functions, it does not matter for discussion.As the fluorescence got stronger, the RMSA became more dependent to the fitting order.This again indicated that the linear function failed to express the background when it was strong.For second and third-order polynomials, they provided similar RMSA in most cases.This implies that either a second or third-order polynomial fitting works well for the background subtraction.However, for Ivuna, where the strongest fluorescence background was observed, second-order fitting was not sufficient to effectively suppress the background residue especially at 800-950 cm À1 .This can also be seen in Figure 4, where the background observed in a spectrum of Ivuna was ill-fitted by the second-order function.These results suggest that the third-order polynomial is more globally applicable.
In theoretical point of view, since the spectral shapes of fluorescence are generally asymmetric to the wavenumber, it is better to use third-order functions to express the asymmetricity.However, the use of higher FIGURE 1.Typical Raman spectra of the carbon-containing samples prepared in this study.Some of them were intensitymagnified to make the D and G band intensities of each sample comparable.The magnification coefficient is described in the parenthesis as, for example, ×10 for 10 times magnification.(Color figure can be viewed at wileyonlinelibrary.com) order functions needs special care for overfitting to the fitting points.The fitted functions are no longer trustworthy even in the region 1000-1800 cm À1 if the overfitting does occur to 800, 950, 1800, and 2000 cm À1 .To examine whether overfitting occurred or not, the RMSA of the subtracted spectra at the outside of the fitting region (700-800 and 2000-2050 cm À1 ) was also calculated (Figure S5 in the Supporting Information).Because the overfitted functions are expected to diverge and rapidly go away from the "real" background curve at the outside of the fitted region, the RMSA of the subtracted spectra outside the fitting region should be away from zero if it is overfitted.As shown in Figure S5 in the Supporting Information, the RMSA at these regions was insensitive to whether the polynomials are of second or third order.This result implies that the third-order functions are trustworthy in the region of interest (1000-1800 cm À1 ).The typical spectra for each sample subtracted by the third-order polynomials are summarized in Figure S6 in the Supporting Information.

Peak Fit Analysis for the Background-Subtracted Spectra
The D and G bands of bituminous coals and Ivuna were analyzed to demonstrate the importance of estimating the background with a third-order polynomial.They were chosen because they contained moderate (bituminous coals) and strong (Ivuna) background and the subtracted spectral shape depends on the subtraction functions.Note that although the spectral shape (Figure 2) and the RMSA (Figure 3) of the bituminous coals did not seemingly depend on the background subtraction function at a glance, slight difference can be found especially at the wavenumber region 1000-1200 cm À1 (Figure 2).Furthermore, for bituminous coals, detailed analysis of D and G bands based on linear background subtraction was already reported in literature (Kouketsu et al., 2013).While one can simply assume that the peaks at 1000-1800 cm À1 are composed of two peaks (D and G bands) as described above, the necessity of spectral deconvolution to four to five peaks (by Lorentzian, Gaussian, or (pseudo) Voigt function) has been proposed (Cancado et al., 2011;Claramunt et al., 2015;Ferrari & Robertson, 2000, 2001;Jawhari et al., 1995;Kudin et al., 2008;Martins Ferreira et al., 2010;Reich & Thomsen, 2004;Vollebregt et al., 2012).This is not surprising because the peaks in 1000-1800 cm À1 region clearly had complicated shoulder structures, and hence, it is impossible to fit them with only two peak functions.In the deconvolution analysis, the D band is usually deconvoluted to so-called D1-D4 bands whereas G band is kept a single peak (Kouketsu et al., 2013).G band ($1650 cm À1 ) mainly corresponds to a C-C stretch motion of sp 2 carbons, whereas D bands originate in a stretching motion of sp 3 carbons and defect sites in the material.Depending on the defect structure, a variety of bands (D1: $1350 cm À1 , D2: $1620 cm À1 , D3: $1510 cm À1 , and D4: $1245 cm À1 ) appear in the D band region with slightly changing their band positions and widths.Particularly, it was reported that the width of D2 band sensitively depended on the randomness of the carbon structure.As the G band becomes broad when the sp 2 structure is highly disordered, it is often difficult to deconvolute G and D2 bands in such cases.Because the band around 1600 cm À1 of bituminous coal was broad, Kouketsu et al. deconvoluted the peaks at 1000-1800 cm À1 to four bands (D1, D3, D4, and D2 + G) after the linear background subtraction (Kouketsu et al., 2013).Here, we follow the deconvolution procedures proposed by the literature and demonstrate how the background functions affect to the result.
Figure 5a compares the typical spectra of bituminous coal, whose background was subtracted by the linear or the third-order polynomial.As already described, the spectra whose background was subtracted by the linear function did not converge to zero at the region of 800-1000 cm À1 , and the trend that the signal gradually increased with wavenumber was found.The increasing trend implies that the linear function underestimated the fluorescence background at the lower wavenumber side of the region of interest (1000-1800 cm À1 ).At the first glance, one might think that the difference between the linear-and the third-order polynomial-subtracted spectra is negligible.However, such underestimation would lead to an enhancement of the peak intensity and probably the band width of the peak at the lowest wavenumber (D4; $1250 cm À1 ). Figure 5b,c summarizes the intensities and the band widths of the Lorentzian functions obtained by the multi-peak fitting.The average and standard deviation are also summarized in Table 1.The intensities and the band widths of D4 band were overestimated in the case of linear background subtraction, as expected.Furthermore, the linear background subtraction made broad distribution to the D4 band intensity.This is understandable by considering the background intensities and shapes in each spectrum.Because they differed spotby-spot even in the same sample as shown in Figure S2, the linear functions sometimes noticeably underestimated the background and sometimes did not.Consequently, the D4 band intensity is sometimes overestimated, leading to the broad distribution of the intensity (Figure 5).In contrast, the narrow distribution obtained by the third-order subtraction ensures that the background curve was appropriately and reproducibly estimated by it.These results indicate that the third-order polynomial fitting is essential to the D and G band analysis although the difference between the linear and the thirdorder subtracted spectra appeared tiny.One may think that only D1 band width is important as a parameter of geothermometer and that the fluctuation in the D4 band intensity of D4 band is not a striking matter for discussion.However, D4 band is believed to originate in unordered graphite such as trans-polyacetylene and polyene, which should be relatively abundant in meteorites from highly aqueously-altered parent asteroids.Therefore, in terms of analyzing the aqueous alteration, the proper estimation of D4 band shape and intensity is also essential.Furthermore, as summarized in Table 1, the bandwidth of D1 band is also changed by the background function (161 and 146 cm À1 ($10%) for the case of linear and third-order subtraction, respectively).
Figure 6a shows typical background-subtracted spectra of Ivuna together with its four-band fitting in the same style of Figure 5.Because the fluorescence background was rather strong in Ivuna, the spectral shape more clearly depended on the background function than bituminous coals.The intensity and width of each band are summarized in Figure 6b,c, respectively.Their average and standard deviation are summarized in Table 1 together with those of bituminous coals.As in the case of bituminous coals, the intensity and width of D4 band decreased in the third-order subtraction.Especially for the band width, its scattering was greatly improved by the third-order fitting.Their stability of the D4 band width in the third-order subtraction is also an example to indicate the validity of the third-order subtraction as well as small RMSA shown in Figure 3.In addition to the change in D4 band, it is also crucial that the band width of D1 band noticeably ($10%) decreased in the case of the third-order subtraction.This trend was also seen in bituminous coals.Because the D1 band width is commonly used as a parameter of geothermometer, its 10% decrease only by the background subtraction method is a critical matter to construct a geothermometer for highly aqueously-altered meteorites, which emit strong fluorescence.
At the last of discussion, to more clearly describe the impact of the 10% change of the bandwidth to the geothermometer, let us assign the D1 bandwidth to previously proposed equation.Because geothermometers applicable to highly aqueously-altered CI meteorites (such as Ivuna) has not proposed yet, that for aqueously-altered CM meteorites is tentatively used here.According to Homma et al., peak metamorphic temperatures (PMT) is related to the bandwidth of D1 (Γ D1 ) as  PMT ¼ À6:9 Â Γ D1 þ 1054:4, where PMT and Γ D1 is defined in °C and cm À1 unit in this equation (Homma et al., 2015).By substituting Γ D1 by 166 (linear subtraction) or 149 (third-order subtraction) cm À1 to this equation, PMT of À91 or +26°C is observed, respectively.Note that the exact values obtained here have no physical meaning because the equation is not applicable to CI meteorites.What is important is that the estimated PMT can be affected in about 100°C just by the background subtraction method.While the coefficient À6.9 to Γ D1 should vary for the "real" CI geothermometer, the impact of 10% change in D band width would be more or less similar.The appropriate subtraction of the fluorescence background is thus essential to establish the carbon geothermometer.

CONCLUSION
Raman spectra of carbon-containing natural samples (bituminous coal and meteorites named Ivuna, Orgueil, NWA 11732, Murchison, Aguas Zarcas, and Allende) were measured and the fluorescence background was observed in the region of 800-2000 cm À1 .Analysis was performed with first-to third-order polynomials.While the first (i.e., linear) polynomial had been employed in most of the previous studies (Bonal et al., 2007;Busemann et al., 2007;Chan et al., 2017;Homma et al., 2015;Kiryu et al., 2020;Koøodziej et al., 2021;Kouketsu et al., 2013;Matrajt et al., 2004;Starkey et al., 2013), it was suggested that the linear functions often underestimated the background when the fluorescence is as strong as or stronger than the Raman bands.In contrast, the thirdorder polynomial subtraction effectively suppressed the background even if the fluorescence was strong.While some employed much higher ($7th) order functions for the subtraction, the use of the higher order functions generally needs special care for overfitting to the fitting region.Therefore, it is preferable to employ balanced and the least order function as long as the background can be well subtracted.In the present study, it was confirmed that the third-order fitting function did not diverge even slightly outside the fitting region, indicating that the overfitting did not occur.Conversely, second-order functions sometimes failed to reproduce the background shape, presumably due to multiple origin of fluorescence.When the fluorescence was not very large and linear function was sufficient to reproduce the background, the coefficients for the secondand third-order terms successfully diverged to zero.These results suggested that, as the standard background subtraction procedure, use of third-order polynomial function is necessary and sufficient, at least for carboncontaining geo/cosmochemical samples.
Furthermore, because D and G bands are often analyzed by multiple-peak fittings, we examined how the background functions affected to the peak analysis with four Lorentzian functions.As a result, although the subtracted spectra of moderately fluorescent sample (bituminous coals) looked similar at the first glance regardless of the fitting order, the linear subtraction caused scattering of the band intensities, especially for the D4 band (the lowest wavenumber band in the D band region).The dependence to the background functions was clearer in the case of strongly fluorescent sample (Ivuna), and the band width of even D1 band was noticeably affected.These results also suggest the thirdorder polynomial be employed as a standard procedure for the fluorescent background reduction.Importantly, constructing the geothermometer for primitive meteorites which were highly aqueously-altered and experienced only low temperature is still an ongoing subject inspite of its importance (Chan et al., 2017).Because such meteorites are strongly fluorescent and should possess significant amount of disordered carbon causing D4 band, it is inevitable to establish the background subtraction method which gives the appropriate parameters for D4 band as well as those for D1 band which is commonly used in carbon geothermometers.While the present study does not propose a peak analysis strategy to obtain proper parameters for geothermometer, it should be constructed in near future by preparing various types of meteorites and by examining various conditions of the peak fitting such as peak function type and fitting restrictions.
Since Raman spectroscopy is nondestructive, contactless, and suitable to remote sensing, it is preferable for the analysis of rare samples such as CI carbonaceous chondrites, as well as samples directly corrected from asteroids (e.g., Ryugu by Hayabusa 2 and Bennu by OSIRIS-REx).Although further studies are still required to relate the band intensities and the band width with physicochemical properties of the samples, the present study proposes preferable analytical procedure for carbon abundant meteorites and terrestrial samples with Raman spectroscopy under strong hindrance by fluorescent background.

FIGURE 2 .
FIGURE 2. Comparison of the first-, second-, and third-order polynomial fitting of the fluorescence background.The top panels for each sample show the raw spectra and the fitting function whereas the bottom panels show the subtracted spectra.The dotted vertical lines represent the wavenumbers which were used for the background fitting.The horizontal broken lines in the subtracted spectra indicate the zero level.(Color figure can be viewed at wileyonlinelibrary.com)

FIGURE 3 .
FIGURE 3. The background residue (root mean square error (RMSE)) of the subtracted spectra calculated for the region of 800-950 (top panels) and 1800-2000 cm À1 (bottom panels).The number of appearances was counted for 100 spectra obtained at different spots for each sample.(Color figure can be viewed at wileyonlinelibrary.com)

FIGURE 5 .
FIGURE 5. Results of four band fitting for D and G band region of bituminous coal after the background subtraction.The linear and third-order subtractions were compared.(a) The subtracted spectra together with Lorentzian peak functions.(b, c) Distribution of the band intensity (b) and width (c) obtained by the four band fitting for the spectra obtained at 100 different spots.(Color figure can be viewed at wileyonlinelibrary.com)

FIGURE 6 .
FIGURE 6. Results of four band fitting for D and G band region of Ivuna after the background subtraction.The linear and third-order subtractions were compared.(a) The subtracted spectra together with Lorentzian peak functions.(b, c) Distribution of the band intensity (b) and width (c) obtained by the four band fitting for the spectra obtained at 100 different spots.(Color figure can be viewed at wileyonlinelibrary.com)

TABLE 1 .
Results of four band fitting of bituminous coals and Ivuna, based on first-and third-order background subtraction.