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Oct 6, 2017 - scattering layers such as stratified paint samples, enabling their nondestructive chemical characterization. The technique has a...
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Investigation of Heterogeneous Painted Systems by Micro-Spatially Offset Raman Spectroscopy Claudia Conti,*,† Alessandra Botteon,† Chiara Colombo,† Marco Realini,† and Pavel Matousek‡ †

Consiglio Nazionale delle Ricerche, Istituto per la Conservazione e la Valorizzazione dei Beni Culturali (ICVBC), Via Cozzi 53, 20125, Milano, Italy ‡ Central Laser Facility, Research Complex at Harwell, STFC Rutherford Appleton Laboratory, Harwell Oxford, OX11 0QX, United Kingdom S Supporting Information *

ABSTRACT: A recently developed technique of Micro-Spatially Offset Raman Spectroscopy (micro-SORS) extends the applicability of Raman spectroscopy to probing thin, highly diffusely scattering layers such as stratified paint samples, enabling their nondestructive chemical characterization. The technique has a wide applicability across areas such as cultural heritage, polymer research, forensics, and biological fields; however, currently, it suffers from a major unaddressed issue related to its ineffectiveness with highly heterogeneous samples. In this paper, we address this unmet need while demonstrating an effective strategy to probe such samples, involving a mapping on scales substantially larger than the scale of heterogeneity. This approach provides an effective means of obtaining robust and representative micro-SORS datasets from which sample composition can be effectively deduced, even in these extreme scenarios. The approach is compared with a basic point collection approach on two-layer paint systems where different layerstop, bottom, or bothare heterogeneous. The study has particular relevance to cultural heritage, where heterogeneous layers are often encountered with painted stratigraphies.

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To determine the chemical composition of a sublayer, for a two-layer sample, a very simple mathematical manipulation of the zero spatial offset and nonzero spatially offset Raman spectra is performed. This process consists of a scaled subtraction of the zero-spatially offset spectrum from the nonzero one, canceling the residual contribution of the top layer. More offset spectra must be acquired and processed linearly for the separation of layers in a stratified system consisting of more than two layers.5 The most basic variant of micro-SORS is defocusing micro-SORS, which can be practiced without any modifications on conventional Raman microscopes;9,10 for this reason, it is currently a topic of widespread potential interest to the community. A related concept is full micro-SORS, which includes fully separated illumination and collection zones and, consequentially, can achieve a higher penetration depth and higher discrimination power between layers.11,12 However, this approach is less widely applicable, because it requires instrumental modifications that involve hardware and/or software changes. MicroSORS has also been demonstrated in determining overlayer depth,13 rejecting overlayer fluorescence,14 and in two-dimensional (2D) mapping of hidden images or writings.15

aman microscopy is often a technique of choice for the characterization of surface layers of paints in art for its high chemical specificity.1,2 However, subsurface stratigraphy (typically a few tens of micrometers thick), which can often be present, is beyond the reach of this technique, because of high turbidity (due to diffuse scattering) of such layers. This precludes the measurement of detailed chemical information on sublayer makeup, which is important, for example, in conservation of art or when studying an artist’s technique. In these situations, one often must resort to cross-sectional analysis using Raman microscopy.3,4 However, this approach is highly undesirable or not even permissible with some objects of art, because of their high cultural value. A similar requirement for noninvasive and nondestructive analysis can arise in other disciplines too, for example, in polymer, catalytic, biological, biomedical, and forensics investigations, where highly turbid stratified layers can also be present and where invasive analysis may be undesirable or impossible. Recently, a new Raman concept with considerably higher penetration depth than that available from conventional Raman microscopy has emerged: Micro-Spatially Offset Raman Spectroscopy (micro-SORS).5,6 The method is conceptually derived from its parent technique, (macro-scale) SORS,7,8 by combining SORS with microscopy. This enables resolving thin, micrometerscale stratified layers such as painted layers. © XXXX American Chemical Society

Received: July 11, 2017 Accepted: October 6, 2017

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DOI: 10.1021/acs.analchem.7b02700 Anal. Chem. XXXX, XXX, XXX−XXX

Analytical Chemistry



MATERIALS Three mock-up samples were prepared by superimposing two painted layers. The first sample (S1) consisted of a heterogeneous layer (80 μm) of azurite particles embedded in a lime binder (calcite) located on top of a homogeneous (1.5 mm) lime layer (calcite). Both layers were spread on a microscope slide with a brush. The second sample S2 was assembled by placing a thin (60 μm) removable homogeneous film made of Cobalt Violet in an acrylic medium on top of a heterogeneous layer (1.5 mm) made of Ultramarine Blue particles in a lime binder. The Cobalt Violet layer consists of a 2.5-cm-diameter disk prepared by mixing the pigment powder with epoxy resin and then abrading it until a suitable thickness was obtained. The bottom layer of sample S2 was spread on a microscope slide with a brush. In sample S3, both top and bottom layers were heterogeneous: the top layer (50 μm) was composed of azurite particles and a red acrylic spray (a mixture of PR 170 and PY 139), the bottom layer (300 μm) consisted of a mixture of vermillion particles in a Phthalocyanine Blue and acrylic medium matrix. In the heterogeneous layers, the compounds were mixed together in a way that particles and matrixes were very distinct on a micrometer scale. The selection of compounds has been carried out, considering their different Raman scattering cross section, from weak (i.e., azurite) to strong (i.e., vermillion).

Table 1. Integrated Bands for Each Pigment −1

pigment

integrated band range (cm )

azuritea calcite Cobalt Violet Ultramarine Blue red spray Phthalocyanine Blue vermillion

385−420 (S1), 385−405 (S3) 1075−1095 960−920 557−538 1373−1351 1538−1522 251−258

Article

a For azurite, two different integration ranges were selected for samples S1 and S3, because of partial overlapping between the azurite peak at 400 cm−1 and one of the band of red spray in sample S3.

Generally, to date, the most significant outstanding challenge for applying micro-SORS to real objects of art is related to handling of heterogeneous samples. High sample heterogeneity is rather a common occurrence in cultural heritage, and, in micro-SORS measurements, its presence can lead to confusing data, which are difficult or impossible to interpret correctly. This challenge has been identified in our earlier work, and a solution in a form of mapping across a large number of points to average such signals was proposed.6 To date, however, no experimental demonstration and evaluation of the effectiveness of this methodology has been carried out. To address this issue, we have proposed a mapping strategy to mitigate the detrimental effects of heterogeneity and compared it with a basic single-point data acquisition approach. The study is carried out on a set of artificially prepared two-layer samples with controlled heterogeneity outlining the benefits of this approach as well as its limitations.



METHODS Measurements were carried out using a Senterra dispersive Raman microscope (Bruker Optik GmbH) that was equipped with a Peltier cooled CCD detector (1024 × 256 pixels). The laser

Figure 1. (a) Schematic of sample S1, (b) six averaged linear maps spectra, (c) six random points spectra, and (d) three selected points (over the azurite particle (spectrum 1), next to the azurite particle (spectrum 2), and over the calcite particle (spectrum 3)) at the imaged position and at a defocusing distance of 50 μm. B

DOI: 10.1021/acs.analchem.7b02700 Anal. Chem. XXXX, XXX, XXX−XXX

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Analytical Chemistry

Figure 2. (a) Azurite over calcite intensity ratio versus defocusing distance for sample S1, showing a comparison between averaged linear maps spectra (red squares, M1) and random points spectra (blue circles, M2). (b) Enlargement of the section corresponding to the gray area in panel (a), highlighting the lowest-value data points in the graphs. (c) Azurite over calcite intensity ratio versus defocusing distance for sample S1, showing a comparison between random points spectra (blue circles, M2) and selected points spectra (colored triangles, M3). (d) Enlargement of the section corresponding to the gray area in panel (c), highlighting the lowest-value data points in the graphs.

100 s per point). In sample S1, the first spectrum was collected when directly centered on an azurite particle; the second spectrum was acquired on calcite alone with no azurite particle present in the immediate neighborhood; and the third spectrum was collected just next to an azurite particle. In sample S2, one spectrum was collected on an Ultramarine Blue particle, the second on calcite alone, and the third one next to an Ultramarine Blue particle. These positions were selected by temporarily removing the top Cobalt Violet layer and placing it back again after the selection. In sample S3, one spectrum was collected on an azurite particle, the second on red spray, and the third next to an azurite particle.

excitation wavelength was 785 nm. On each sample three different typologies of measurements were performed: • M1: Linear Maps. Six linear maps with an overall length of >1 mm, consisting of 100 measured points each (Δx = 10 μm, 1 s per point for a total acquisition time of 100 s). The spectra of each linear map were averaged to obtain representative spectra of the mapped lines. • M2: Random Points. Six spectra were collected on six individual random points (acquisition time of 100s per point) within the same area as that for the linear maps. • M3: Selected Points. Three spectra were collected at specially selected individual points (using an acquisition time of C

DOI: 10.1021/acs.analchem.7b02700 Anal. Chem. XXXX, XXX, XXX−XXX

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Analytical Chemistry

Figure 3. (a) Schematic of sample S2, (b) six averaged linear maps spectra, (c) six random points spectra, and (d) three selected points spectra (over the ultramarine particle (spectrum 1), next to the Ultramarine Blue particle (spectrum 2), and over the calcite particle (spectrum 3)) at the imaged position and at a defocusing distance of 150 μm.



RESULTS AND DISCUSSION Sample 1. In the first sample (S1), the top layer is heterogeneous and the sublayer is homogeneous. The repeat averaged linear maps spectra (M1) acquired both at imaged positions and defocused positions produced very consistent, reproducible results (Figure 1b); at the imaged positions, azurite and calcite of the lime binder are always detected and calcite is always the most intense band. As shown in the conventional high-resolution map (Figure S1 in the Supporting Information), the areas occupied by calcite and azurite are approximately equal. The preponderance of calcite in these spectra can be explained by two main factors: first, calcite is a better Raman scatterer, compared with azurite; second, in the imaged position, a contribution of the bottom layer signal (also calcite) is detectable. Azurite decreases with defocusing up to 300 μm, where no azurite signal is detectable, while calcite is always detected and quite visible at all defocusing distances (Figure S2 in the Supporting Information). The bands and shoulders emerging around the azurite peak are probably due to impurities or silicates from the products used for the specimen preparation. In contrast, the random point spectra (M2) acquired at the imaged position (Figure 1c) show an extremely high level of fluctuation: three of them do not exhibit the azurite signal at all; in two of them, the azurite signal has a very high level, relative to the calcite signal; and in one point, it shows a very low signal. Calcite is clearly present in four of six spectra. Defocusing sequences carried out starting from the points with the azurite particle show a progressive decrease of the pigment (azurite) signal; when the azurite signal is intense at the imaged position, its signal is detectable up to a defocusing distance of

The maps, random points, and selected points were acquired at imaged positions (where the sample surface is sharply imaged by the Raman microscope) using a confocal pinhole and at selected defocusing distances, namely, 50, 150, and 300 μm, without the confocal pinhole. All the spectra were collected using a 20× objective, a laser power of 10 mW at the sample, and a 400 grooves/mm grating. The spectra were baseline-corrected and normalized to the most intense Raman band. To evaluate the relative changes of the sublayer signal, the top/bottom ratios of selected Raman band intensities were calculated. The integrated bands for each pigment are given in Table 1. If the signal of a certain sublayer compound was not present in the spectrum, the ratio was not evaluated; if the signal of a certain top layer compound was not present in the spectrum, the ratio value was set to zero. The intensities were obtained by integrating the bands with the K method (summing the band intensity above a local baseline). The ratios were then plotted over the defocusing distances to visualize both the relative change of the sublayer signal with distances Δz and to compare the signals fluctuation of linear maps, random points, and selected points. From all samples, a conventional Raman map also was acquired on the heterogeneous layers alone to evaluate the actual distribution of the compounds. Areas of 350 μm × 350 μm were mapped (35 × 35 points, 5 s per spectra for a total acquisition time of ∼2 h), using a 20× objective, a power of 10 mW on the sample, and a 400 grooves/mm grating. In sample S2, the map was acquired with the top Cobalt Violet disk removed. In sample S3, only the top heterogeneous layer was mapped. D

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Figure 4. (a) Cobalt Violet over calcite intensity ratio versus defocusing distance in sample S2, showing a comparison between averaged linear maps spectra (red squares, M1) and random points spectra (blue circles, M2). (b) Enlargement of the section corresponding to the gray area in panel (a), highlighting the lowest-value data points in the graphs. (c) Cobalt Violet over Ultramarine Blue intensity ratio plotted versus defocusing distance in sample S2, showing a comparison between averaged linear maps spectra (red squares, M1) and random points spectra (blue circles, M2). (d) Enlargement of the section corresponding to the gray area in panel (c), highlighting the lowest-value data points in the graphs.

150 or 300 μm (see Figure S2); starting in the single point, where azurite is low or absent at the imaged position, its signal disappears or is also absent at and above 50 μm. As expected, the selected spectra (M3) also show high spectral fluctuations (see Figure 1d); at the imaged position, the azurite signal is detectable just in the position over the crystal particle (Figure 1d, spectrum 1). Next to the particle, no azurite signal can be observed (Figure 1d, spectrum 2). Starting from azurite particles, the defocusing measurements show the presence of the azurite band up to a distance of 150 μm (Figure S2). Interestingly, a defocusing distance of 150 μm, relative to the point next to azurite, exhibits a (rather weak) azurite signal, although it does not appear at the imaged position. This can be

explained by the fact that the enlargement of laser illumination and Raman collection areas allowed the inclusion of the pigment particle in the detection zone. At distances of >300 μm, the signal is no longer visible. Furthermore, the ratio between the top and bottom layers shows large fluctuations for imaged random (M2) and selected points (M3); some of the data points completely lack the presence of one of the two surface layer compounds (see Figure 2). Although for measurements starting at the azurite particle (M3), the profile appears to decay as expected, the overall ratio values remain elevated throughout. In contrast, the averaged linear maps spectra (M1) do not exhibit such high levels of spectral fluctuation and, as such, are more representative of the E

DOI: 10.1021/acs.analchem.7b02700 Anal. Chem. XXXX, XXX, XXX−XXX

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Analytical Chemistry

Figure 5. (a) Schematic of sample S3, (b) six averaged linear maps spectra, (c) six random points spectra, and (d) three selected points spectra at the imaged position and at a defocusing distance of 300 μm.

sample overall constitution, indicating that, of the strategies studied to analyze such heterogeneous samples, this one is the most effective. Sample 2. In this sample (S2), the top layer is homogeneous and the sublayer heterogeneous. Here, the averaged linear maps spectra (M1) at the imaged position show a certain degree of fluctuation (see Figure 3b). Cobalt Violet (top layer) dominates each spectrum, but the contribution of the bottom layer is very weak and fluctuates, to some degree: two spectra show both calcite and Ultramarine Blue; three spectra exhibit just one of the two pigments (calcite or Ultramarine Blue); and, in one case, no signal of the bottom layer is visible at all. On the other hand, micro-SORS defocusing spectra carried out at 150 μm exhibit very good stability, indicating that defocusing also leads to averaging as expected, since there is interaction with a much larger sample area. A notable feature is a strong decrease in relative intensity between the top and bottom layers with defocusing, as expected for micro-SORS; at a defocusing distance of 150 μm, the bottom pigments begin to dominate the spectra. The trends then continue as the defocusing distance increases, and at a defocusing distance of 300 μm, the Cobalt Violet signal becomes very low, with all the six repeated linear maps showing consistently similar trends (see Figure S3 in the Supporting Information). In contrast, the random measurements (M2) are again less representative than average linear maps (Figure 3c). At the imaged position, three out of six random measurements (M2) exhibit just a Cobalt Violet signal (top layer) and only one spectrum exhibits a weak signal of both pigments from the bottom layer, probably because, in these areas, the thickness of the top layer was smaller. Defocusing again leads to a very good relative

enhancement of the sublayer signal (see Figure 3c, as well as Figure S3), and random points spectra compare very well with each other, as well as with average linear maps defocused spectra, confirming that defocusing, in itself, also averages the signal to some degree. At the point selected over or next to the Ultramarine Blue particle (M3), both the pigment and calcite Raman signals are visible at the imaged position (Figure 3d, spectra 1 and 2); the detection of Ultramarine Blue even next to the particles is ascribed to photon diffusion within the top layer with the consequential irradiation and interrogation of wider area in the sublayer. Consistent with expectations, calcite and Ultramarine Blue signals (M3) increase in relative terms with defocusing (see Figure 3d, as well as Figure S3). In contrast, in the point selected over the calcite particle (Figure 3d, spectrum 3), there is no Ultramarine Blue signal, neither at the imaged positions nor the defocusing positions. To further elucidate the behavior of micro-SORS signals under different scenarios, the ratio of the top layer signal over the sublayer signal was plotted as a function of defocusing distance for the two subsurface compounds separately; as a consequence, two different ratios have been produced (Figure 4). Note that, in both ratios, the values at the imaged positions are not very significant, because the bottom signal is often not detectable and, thus, the graphs have many absent data points. More significant are the ratios of average linear maps (M1) calculated at defocusing positions, where the subsurface signal becomes more prominent and emerges above the noise level. Here, the Cobalt Violet/calcite signal ratio only shows a very small degree of fluctuation, similar to or slightly smaller than that for sample S1 (see Figures 4a and 4b); this is consistent F

DOI: 10.1021/acs.analchem.7b02700 Anal. Chem. XXXX, XXX, XXX−XXX

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Figure 6. (a) Red spray over Phthalocyanine Blue intensity ratio versus defocusing distance for sample S3, showing a comparison between averaged linear maps spectra (red squares, M1) and random points spectra (blue circles, M2). (b) Enlargement of the section corresponding to the gray area in panel (a), highlighting the lowest-value data points in the graphs. (c) Red spray over Phthalocyanine Blue intensity ratio versus defocusing distance for sample S3, showing a comparison between random points spectra (blue circles, M2) and selected points spectra (colored triangles, M3). (d) Enlargement of the section corresponding to the gray area in panel (c), highlighting the lowest-value data points in the graphs.

with expectations, in that, as in sample S2, the heterogeneous bottom layer is hidden behind the surface homogeneous layer and, when light diffuses on its way to the second layer, it is already “defocused” to some degree and is more averaged to the local neighborhood area. In contrast, the Cobalt Violet/ Ultramarine Blue signal ratio (Figures 4c and 4d) exhibits a completely different behavior: more fluctuations are present than for sample S1. This result can be explained by a higher degree of heterogeneity for Ultramarine Blue in this layer, if compared with the top layer of sample S1, as demonstrated by the conventional Raman map (see Figure S1). The Cobalt Violet over Ultramarine Blue ratio is particularly significant for the comparison of the degree of fluctuation

between average maps (M1) and random points spectra (M2). At defocusing positions, the random points spectra (M2) are fluctuating more, to some degree, than average maps (M1), which is consistent with expectations (see Figures 4c and 4d). Sample 3. In the third sample (S3), both layers are heterogeneous. Consistent with the other samples, the random points spectra (M2) and selected points spectra (M3) exhibit a higher degree of fluctuations than the average map spectra (M1), especially for the imaged position (Figure 5b). In defocusing positions, the degree of fluctuation again strongly decreases, despite heterogeneity involving both layers. The average maps spectra (M1) at the imaged position are dominated by red spray Raman signal (top layer); azurite, G

DOI: 10.1021/acs.analchem.7b02700 Anal. Chem. XXXX, XXX, XXX−XXX

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Analytical Chemistry which is the second compound signal of the top layer, is observable in four out of six spectra and its signal is very low. Although Phthalocyanine Blue is present at the bottom position, it is also quite visible at the imaged position; this is explained by the very high Raman scattering cross section of this compound. On the other hand, a vermillion Raman band of the bottom layer is barely visible in four out of six spectra, due to the partial overlapping with a band of the red spray (top layer). In defocused positions, the relative intensity ratios among the pigments change as expected: the azurite signal (top layer) completely disappears, while Phthalocyanine Blue and vermillion (sublayer pigments) signals become very clearly visible (see Figure 5b, as well as Figure S4 in the Supporting Information). The random point spectra (M2) reflect the high heterogeneity of this sample (see Figure 5c). At the imaged position, red spray and Phthalocyanine Blue are always present (except for one spectrum, in which Phthalocyanine Blue is not visible), azurite (top layer) and vermillion (bottom layer) appear in just three out of six spectra. With increased defocusing, the azurite signal (top layer) rapidly disappears and the signals from the bottom compounds progressively increase (see Figures 5c, as well as Figure S4). Of all possible ratios between the pigments of the top and bottom layers, the most informative is the ratio of the red spray over Phthalocyanine Blue (Figure 6). This is because these pigments are always clearly detectable in the spectra, even at the imaged position. The results are consistent with the conclusions for samples S1 and S2: the average maps spectra (M1) exhibit significantly lower degree of fluctuations, compared with random points spectra (M2) and selected points spectra (M3), especially at the imaged position. Increased defocusing leads to a progressively higher degree of averaging, as also observed for the other samples. The results obtained with the three examples suggest that the linear mapping (M1) with a large number of points with short acquisition times have proved to be superior to both the random points or selected points sampling strategies carried out under equivalent overall acquisition times, in terms of both averaging sample heterogeneity and providing representative information on sample constitution. The mapping can be performed in linear fashion, as presented in this study, or across two dimensions. Importantly, for the approach to be effective, the dimensions of the mapping zone should be much larger than the spatial scale of the heterogeneity.

generally recommended for dealing with heterogeneous samples such as objects of art.



ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.analchem.7b02700. Conventional Raman maps of the investigated samples (Figure S1); and averaged linear maps spectra, random points and selected points spectra at different defocusing distances for samples S1 (Figure S2), S2 (Figure S3), and S3 (Figure S4) (PDF)



AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Claudia Conti: 0000-0002-5379-7995 Notes

The authors declare no competing financial interest.



REFERENCES

(1) Casadio, F.; Daher, C.; Bellot-Gurlet, L. Top Curr. Chem. (Z) 2016, 374, 62. (2) Bersani, D.; Conti, C.; Matousek, P.; Pozzi, F.; Vandenabeele, P. Anal. Methods 2016, 8, 8395−8409. (3) Valadas, S.; Freire, R.; Cardoso, A.; Mirão, J.; Vandenabeele, P.; Caetano, J. O.; Candeias, A. Micron 2016, 85, 15−25. (4) Pozzi, F.; Arslanoglu, J.; Carò, F.; Stringari, C. Appl. Phys. A: Mater. Sci. Process. 2016, 122, 1−15. (5) Conti, C.; Colombo, C.; Realini, M.; Zerbi, G.; Matousek, P. Appl. Spectrosc. 2014, 68, 686−691. (6) Conti, C.; Realini, M.; Colombo, C.; Matousek, P. J. Raman Spectrosc. 2015, 46, 476−482. (7) Matousek, P.; Clark, I. P.; Draper, E. R. C.; Morris, M. D.; Goodship, A. E.; Everall, N.; Towrie, M.; Finney, W. F.; Parker, A. W. Appl. Spectrosc. 2005, 59, 393−400. (8) Buckley, K.; Matousek, P. Analyst 2011, 136, 3039−3050. (9) Conti, C.; Colombo, C.; Realini, M.; Matousek, P. Analyst 2015, 140, 8127−8133. (10) Realini, M.; Botteon, A.; Conti, C.; Colombo, C.; Matousek, P. Analyst 2016, 141, 3012−3019. (11) Matousek, P.; Conti, C.; Realini, M.; Colombo, C. Analyst 2016, 141, 731−739. (12) Realini, M.; Conti, C.; Botteon, A.; Colombo, C.; Matousek, P. Analyst 2017, 142, 351−355. (13) Conti, C.; Realini, M.; Colombo, C.; Botteon, A.; Bertasa, M.; Striova, J.; Barucci, M.; Matousek, P. Philos. Trans. R. Soc., A 2016, 374, 20160049. (14) Conti, C.; Botteon, A.; Colombo, C.; Realini, M.; Matousek, P. Analyst 2016, 141, 5374−5381. (15) Botteon, A.; Conti, C.; Realini, M.; Colombo, C.; Matousek, P. Anal. Chem. 2017, 89, 792−798.



CONCLUSIONS We have compared three different strategies for performing micro-SORS measurements on heterogeneous samples: linear mapping, measurements at random points, and measurements at preselected points. The measurements were performed for three different two-layer samples with only top or bottom layer being heterogeneous and where both layers were heterogeneous. The overall data acquisition times were kept identical to enable direct comparisons. In all cases, the strategy of performing a larger number of short measurements through sample mapping proved to be the most robust, yielding the lowest degree of sample fluctuations and providing the most informative data on the overall chemical makeup of the sample. In order to achieve effective averaging, it is important that the mapping is performed across a zone that is much larger than the spatial scale of the present heterogeneity. This strategy is H

DOI: 10.1021/acs.analchem.7b02700 Anal. Chem. XXXX, XXX, XXX−XXX