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Advanced absorption correction for 3D elemental images applied to the analysis of pearl millet seeds obtained with a laboratory confocal micro X-ray fluorescence spectrometer Ioanna Mantouvalou, Tim Lachmann, Sudhir P Singh, Katarina Vogel-Mikus, and Birgit Kanngiesser Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.7b00373 • Publication Date (Web): 13 Apr 2017 Downloaded from http://pubs.acs.org on April 18, 2017
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Analytical Chemistry
Advanced Absorption Correction for 3D Elemental Images Applied to the Analysis of Pearl Millet Seeds Obtained with a Laboratory Confocal Micro X-ray Fluorescence Spectrometer Ioanna Mantouvalou*§, Tim Lachmann*†, Sudhir P. Singh‡, Katarina Vogel-Mikuš+#, and Birgit Kanngießer* * Institute for Optics and Atomic Physics, Technical University of Berlin, 10623 Berlin, Germany ‡Center of Innovative and Applied Bioprocessing India, Mohali, Punjab, India - 160071 + Biotechnical faculty, University of Ljubljana, 1000 Ljubljana, Slovenia #Jozef Stefan Institute, 1000 Ljubljana, Slovenia
ABSTRACT: We present a novel absorption correction approach for elemental distribution images obtained with a laboratory confocal micro X-ray fluorescence spectrometer. The procedure is suited especially for biological samples, as a constant dark matrix with a varying minor or trace element distribution is assumed. The constant absorption in the sample is extracted from depth dependent measurements. By using the concept of an effective excitation energy, depth-dependent and element-specific excitation energy values are calculated. For each voxel of a full 3D measurement, a correction is performed taking into account the actual number of voxels in the excitation and detection path. As proof of concept, the embryonic region of pearl millet seeds is investigated. Data are measured from the top and bottom side, resulting in a good agreement after the application of the absorption correction procedure. The distribution of elemental micronutrients is compared in seeds of two pearl millet genotypes. The corrected images illustrate different localization patterns of the micronutrient elements in pearl millet seed tissues.
Confocal micro X-ray fluorescence (XRF) spectroscopy is a method for the three-dimensionally resolved analysis of elemental distributions. Through the use of two X-ray optics in a confocal arrangement, a probing volume is defined from which information is in first approximation exclusively derived. By moving a sample through this probing volume on a tens of micrometer scale, 3D imaging is rendered feasible. The interpretation of measured data, though, must be handled with care due to absorption and resolution effects. Both the size of the probing volume as well as the information depth for a specific element are energy-dependent1 and can, thus, distort the obtained images. The method was first developed in the beginning of the century2,3 with setups utilizing both X-ray tube and synchrotron radiation. Early applications included the analysis of specimen related to cultural heritage4, biology5 and mineralogy6. For the quantitative interpretation of the measured data, collection times of single spectra are in the range of minutes, yielding measurement times for a full 3D map of hours to days. New laboratory equipment7,8 can enable such measurements. In the past years, much work has been performed for the reconstruction of depth profiles. In this mode, the measurement time is reduced substantially compared to full 3D mapping, while at the same time only stratified samples with homogeneous layers can be investigated9–12. When dealing with 3D imaging, Szaloki et al.13 recently presented the quantification
of the elemental concentrations in 2D maps of a homogeneous specimen. While the algorithm is suitable for 3D reconstructions, a quantitative evaluation of the elemental distributions of a heterogeneous sample is still missing. This fact is presumably caused by the complexity of the task. In order to reconstruct the elemental distributions of a heterogeneous specimen, a full model of the object must be simulated because the absorption of excitation and fluorescence radiation is dependent on the material on top. So, for each measured spectrum collected in a specific position in the threedimensional space (voxel), a full quantification must be performed, which includes the assumption of density and dark matrix, i.e. the elements not accessible with XRF. Additionally, as the absorption follows the Lambert-Beer law, the uncertainties for deeper voxel increase exponentially. Simple absorption correction procedures have already been applied for 2D and 3D data. Faubel et al.14 used a constant absorption coefficient for the visualization of parts of a painting. Mazel et al.15 investigated pharmaceutical tablets and developed an absorption correction for one fluorescence line based on the measured scattered radiation using one excitation energy as an approximation for the excitation spectrum. We present an advanced absorption correction procedure based on measured absorption coefficients and element specific mean excitation energies, which is applicable to heterogeneous specimen with a homogeneous absorption. In other words, this procedure can be utilized for samples where the
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Analytical Chemistry main matrix composition and density are constant and the distribution of minor or trace elements is heterogeneous as is the case for many biological samples. The procedure is demonstrated with measurements on grains of two different genotypes of pearl millet (Pennisetum glaucum (L.) R. Br.), which differ in their Fe and Zn contents.
the endosperm, the pericarp and the germ (embryo). For the visualization of the distribution of metals, the germ was chosen (marked with the red square in Figure 1), as it contains the highest concentration of elements in the seed and represents highly heterogeneous region including the pericarp with pigment strand, the coleoptile and the plumule.
Pearl millet (PM) is common in West-Africa and India, and is well adapted to growing areas characterized by drought, lowsoil fertility, and high temperature. Because of its tolerance to difficult growing conditions, it can be grown in areas where other cereal crops, such as maize, would not survive. It accounts for approximately 50% of the total world-production of millet. Biofortified PM was reported to deliver more absorbable-Fe as evidenced by the increased Hb and Hb-Fe status16. Fe is mainly localized in the aleurone layer and the scutellum as shown by 2D micro-proton induced X-ray emission imaging, while Zn is localized more in the embryonic tissues17. The disadvantage of the 2D imaging of element distribution in seeds/grains is that such information is only provided from one single layer; usually the cross-section through the middle of the grain is taken, while nothing is known about the gradients of element distribution in tissues. Moreover, no particular sample preparation is needed for 3D imaging which ensures against the introduction of any artifacts in sample morphology and element distribution patterns.
Absorption correction procedure The absorption correction procedure consists of three individual parts described in the following.
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By performing 3D measurements from the top and bottom side of the two kinds of seeds, the validity of the absorption correction procedure is assessed. As the uncertainties of the reconstructed counts increase exponentially with depth, the maps are compared and combined for a more reliable evaluation. Last but not least, the differences between the two pearl millet genotypes with contrasting levels of Fe and Zn contents are investigated. Samples
Figure 1: A) A cross-section of pearl millet seed. Endosperm: C-EN - corneous endosperm, F-EN - floury endosperm; Embryo: Sc- scutellum. R- radicule, Pl- plumule, Co - coleoptile, Cr- coleorhiza. H-hillum, PS- pigment strand, A-aleurone, Pepericarp. B) top view of the pigment strand in an intact seed. The seeds were supplied by ICRISAT, Hyderabad, India. Two genotypes MRCHS, and ICMB92111 were investigated, with MRCHS being superior in accumulation of Fe and Zn (see Figure S1 in the supporting information). In the following they are referred to as seeds with low Fe (lFe) and high Fe (hFe) content. The seed (see Figure 1) consists of three main parts,
Figure 2: Spectra obtained at different depths for a measurement on the endosperm of the lFe seed: The center of gravity of the spectrum shifts to higher energies with increasing depth.
a) Derivation of linear absorption coefficient The depth dependent absorption coefficient was derived by using the data from confocal depth scans on the floury endosperm of both genotypes. While the germ has a higher level of lipids (30%) and proteins (25%) (www.fao.org) resulting in a slightly reduced density, the main constituents are the same (carbohydrates – cellulose and starch). Thus, the assumption was made, that the variation of the overall composition and density of the seed is negligible for the interaction with Xrays. In a scatter measurement, the Bremsstrahlung spectrum I0 from the tube is modified by the transmission T1 of the first polycapillary lens, scattered by the sample and then again modified by the transmission T2 of the second polycapillary lens. When only taking into account elastic scattering, the measured intensity I is directly linked to the total linear mass absorption coefficient µlin via the Lambert-Beer law. The total linear mass absorption coefficient µlin can, thus, be derived, assuming a negligible contribution from minor and trace elements: I(z,E)=I0 E
exp
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µlin (E)
(1)
with z the depth of the probing volume in the sample and Φ the angle between excitation/detection axis and sample surface. One depth scan per seed is collected with 300 s live time, 20 µm step width, 91 (lFe) and 101 (hFe) spectra as a function of
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depth in 8 to 9 hours. Figure 2 displays selected spectra collected on the lFe seed. The spectra are divided into 100 eV wide regions of interest (ROI) and the summed counts displayed as a function of depth. These curves are fitted with equation 1, yielding the linear mass absorption coefficient µlin.
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For each considered fluorescence line this procedure has to be repeated because the fluorescence production cross section is fluorescence line specific.
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dependent spectra Id(E) displayed in Figure 2 are used and multiplied with the fluorescence production cross section σF(E) in order to take the fact into account that the probability of the production of a fluorescence photon is highest at the absorption edge and decreases with increasing energy. This product is then numerically integrated in order to find the median energy value. This value represents the effective excitation energy Eeff when following equation is true:
lFe hFe CXRO used fit
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Figure 4 shows the effective energy values for five fluorescence lines (Ti, Mn, Fe, Cu and Zn Kα) as a function of depth. The symbol values were derived with the proposed procedure and the solid lines are linear fits of these data. For comparison, the respective absorption edge energy values are displayed as dashed lines.
Figure 3: linear mass absorption coefficient derived through depth scans on the endosperm. Shown are the fitted data points for two measurements on the two different kinds of seeds with exponential fits and a calculation with tabulated fundamental parameters.
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Figure 3 displays the linear mass absorption coefficient as a function of energy. Both measurements are displayed as well as a calculation based on a cellulose matrix with a mean density of 1.5 g/cm³ with fundamental parameter values taken from 18 . All three graphs show a good agreement with deviations in the range of 1 – 4 %. The deviations in the regions of the Fe and Zn fluorescence lines can be explained by the presence of these elements in the Pericarp, leading to a distorted curve. While in this case, the tabulated values could also be used, measured data are preferable, especially when an assumption about the density and composition of a specimen is not readily made. For the following procedure, the µlin values derived by an exponential fit of the experimental data also displayed in Figure 3 are used. b) Determination of the effective excitation energy In order to correct for absorption effects both the absorption in the excitation and the detection path must be taken into account. With the derived linear mass absorption coefficient, the correction for the detection path is trivial, because the energy of the fluorescence line remains unchanged. The shape of the excitation spectrum, though, is depthdependent. With the assumption, that the scattered spectrum resembles in first approximation the excitation spectrum, this effect can be seen clearly in the curves of Figure 2. The center of gravity of the spectrum shifts to higher energies with increasing depth. The concept of utilizing an effective or equivalent excitation energy is known in XRF analysis for the calculation of influence coefficients19 or calibration purposes20. Similarly, we propose the use of a depth and fluorescence line dependent effective excitation energy in order to take the change of excitation spectrum with depth into account. The energy and depth
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Analytical Chemistry
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Figure 4: Effective excitation energy for the Ti, Mn, Fe, Cu and Zn Kα lines as a function of depth. The symbols are the data derived with the proposed method, the solid lines are linear fits and the dashed lines the respective absorption edge energies.
As expected, the effective energy increases with increasing depth and the slope is steeper for lower energies. The fluctuations in the first five data points are due to the incomplete overlap of the probing volume with the sample. If only the first 1.5 mm of a sample are of interest (orange rectangle) a linear fit is a good approximation and the derived fitting values are used in the following. c) 3D correction procedure With the values derived in a) and b) an absorption correction is possible. In order to correct geometrically heterogeneous sample, for each voxel the number of voxel with material in both the excitation and detection path must be determined. As the criterion if the probing volume is situated in material or not, the overall detected radiation is used with a specific threshold value. For the presented measurements, the threshold was set to 3 counts per spectrum as the statistics for the single spectra in deeper layers was very low. With this
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Analytical Chemistry knowledge, a 3D model of the seed can be constructed. In the actual absorption procedure, the setup geometry (50°/50°) is included. At the edges of the 3D map this is not possible and there, the voxels directly on top of the considered voxel are utilized.
absorption correction procedure will be discussed using as example the Fe Kα intensity distribution of this measurement.
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The corrected intensity Icor can, thus, be written as = exp
! & ( + & (')* , "#$Φ ' ')* '
with Im the measured intensity in a specific voxel, dv the voxel size in the depth direction, Φ the excitation/detection angle, NFl/NE the number of voxels in the path of the fluorescenc/excitation radiation and EFl/EE the fluorescence/excitation energy with -.. = . Thus, for each fluorescence line, first the µlin value is derived from Figure 3, then the Eeff value is calculated (Figure 4), In a final step the absorption correction is performed, yielding a corrected full 3D map for this specific line. For other fluorescence lines, the procedure is repeated and in the end the 3D maps can be combined. Experimental The work was conducted with a modified Bruker M4 tornado with a Rh microfocus X-ray tube, two polycapillary lenses (XOS) and two SDD detectors21. The instrument allows for micro-XRF and confocal micro-XRF sequentially. For the 3D imaging the germ part of the seeds was selected because of the rich morphological and elemental structure. Additionally, in this part differences in the metal distribution and intensity are expected. The seeds were mounted in a way that measurements from the top and the bottom side were feasible with defined depth positions. Both genotypes were measured, resulting in four full 3D measurements of embryonic region. The measurements were performed in a step-by-step collection mode, with 15 s live time per voxel, 30 µm step width and approximately 30 steps in all three directions. For each voxel the X-ray spectrum was saved, resulting in 27000 spectra per map and approximately two weeks collection time. The size of the probing volume is energy dependent, ranging from about 47 µm full width at half maximum (FWHM) for Ti Kα to 28 µm for 9 keV radiation21, thus, the 30 µm step width constitutes a compromise with slight overlap for most analyzed energies. Results absorption correction Figure 5 shows the sum spectrum of the 3D measurement on the pearl-millet seed with low Fe content measured from the top. Besides elements with fluorescence peaks with low energy such as Si, P, S, Ca and K, where an absorption correction is not useful due to the small information depth, the K lines of five metals (Ti, Mn, Fe, Cu and Zn) can be discerned. Due to the low count rate statistics, no spectral deconvolution was performed, but the sum of the intensity of ROIs for each element as marked in Figure 5 are presented. In the following the
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Figure 5: Sum spectrum of the 3D measurement of the pearlmillet seed with low Fe content
Figure 6 displays the montage of the measured (left) and absorption corrected (right) Fe Kα intensity in counts for the virtual slices through the germ region of the lFe seed measured from the top. The top virtual slice is in the top left corner, the bottom slice in the bottom, right.
Figure 6: Montage of the Fe Kα intensity of the virtual slices through the germ region of the lFe seed measured from the top. left: measured data, right: corrected data; the top virtual slice is
in the top left corner, the bottom slice in the bottom, right. As can be seen, the rich geometrical structure of the germ is visualized with better contrast in the corrected pictures. Due to the exponential form of the Lambert-Beer absorption law, the uncertainties increase with increasing depth, resulting in more ‘noise’ in the 2D distributions of the bottom slices. In order to verify the absorption correction procedure, the corrected measurements from the top and the bottom were compared. Figure 7 shows XZ and YZ slices through the Fe Kα intensity representation of the measurements from the top and bottom on the lFe seed. In the original data (top row) the distinct structures in the germ region can be discerned, while an intensity gradient is predominant due to the absorption. In the corrected images (middle row), this absorption is corrected. An increase in noise in the corrected part of the maps can be explained by the low count rate statistics. The red lines mark a region of nearly homogeneous XY-structures. This 5 by 5 voxel region was used in order to create a mean depth profile for enhanced statistics, see Figure 8.
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Figure 7: XZ (left) and YZ (right) cuts through the 3D representation of the measured Fe Kα intensity on the lFe seed from top (t) and bottom (b). top row: original data (o), middle row: corrected data (c), bottom row: combined data (cmb) The yellow lines mark the area of similar structure of both measurements, which is represented as depth profiles in Figure 8. The green arrows mark the Z position, where the top and bottom maps were combined. The measured data exhibit large deviations when the depth profiles from the top (blue squares) and bottom (red triangles) are compared. After absorption correction, the profiles from top (cyan circles) and bottom (orange triangles) show a good agreement, which shows the validity of the absorption procedure. from top original from bottom original 400
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Analytical Chemistry
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generated (black diamonds) by combining the top half of the profile of the measurement from the top with the bottom half from the measurement from the bottom. Such a combination is also feasible for the 3D data sets, as presented in the bottom row of Figure 7. The good agreement for the 3D data is clearly visible as there is no sudden change in intensity at the transition marked with the green arrows.
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The combination relies on the presumption, that the Zpositions of the 3D map are comparable for the measurements from the top and the bottom. In our measurements, this fact was assured through a specially developed sample holder, in which the seeds were fixed and could be turned precisely. Thus, for the combination, the bottom map data was only translated in the X- and Y-direction for a match of structures. Then, the maps were divided in the middle depth position and the top half of the map from the top and the bottom half of the map from the bottom were combined.
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Figure 8: Depth profiles of the areas marked of Figure 7. In contrast to the measured data (blue squares and red triangles), the corrected data (cyan circles and orange triangles) show a good agreement. The uncertainties for the corrected data increase due to the count statistics with depth, as already explained. The uncertainties can be kept below 30% if a composite depth profile is
The absorption procedure was performed for the Ti, Mn, Fe, Cu and Zn Kα intensity distributions. Additionally, as no deconvolution was applied, the counts in an energy ROI without fluorescence lines (9 – 9.4 keV, see scatter in Figure 5) was treated the same way as a measure for the scattered, i.e. density information. Typically, the Rayleigh or Compton scattered peaks of the characteristic lines are used for such a comparison. This is in not practical here, as the sensitivity of the spectrometer decreases due to the second lens with increasing energy, resulting in very low count rates for these peaks.
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Analytical Chemistry
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Figure 9: XZ and YZ slices through the high Fe and low Fe seed for comparison of the Ti, Mn, Fe, Cu, Zn Kα fluorescence and the scattered intensity. The images are scaled according to the threshold values of Table S1 in the supporting information. For all distributions, the absorption correction was checked with depth profiles. For the lFe map the agreement was for all distributions good, while for the hFe map a slight mismatch (
