Talanta 113 (2013) 62–67

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Talanta

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Direct deconvolution approach for depth profiling of elementconcentrations in multi-layered materials by confocal micro-beamX-ray fluorescence spectrometry

Pawel Wrobel n, Mateusz CzyzyckiFaculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakow, Poland

a r t i c l e i n f o

Article history:Received 7 February 2013Received in revised form27 March 2013Accepted 29 March 2013Available online 6 April 2013

Keywords:Confocal X-ray fluorescence spectroscopyChemical imagingQuantitative analysisMulti-layered materialsDeconvolution

40/$ - see front matter & 2013 Elsevier B.V. Ax.doi.org/10.1016/j.talanta.2013.03.087

esponding author. Tel.: +48 12 6172956; fax:ail address: Pawel.Wrobel@fis.agh.edu.pl (P. W

a b s t r a c t

A new approach for the determination of element concentration profiles in stratified materials byconfocal X-ray fluorescence spectrometry was elaborated. The method was based on a direct deconvolu-tion of the measured depth-dependent X-ray fluorescence intensity signal with the established responsefunction of the spectrometer. Since the approach neglects the absorption of primary and secondaryradiation within the probing volume, it is applicable only to low absorbing samples and small probingvolumes. In the proposed approach the deconvolution is performed separately for all detectable elementsand it is followed by the correction of absorption effects. The proposed approach was validated by usingstratified standard samples. The determined elemental profiles were compared with the results obtainedby using existing analytical approaches.

& 2013 Elsevier B.V. All rights reserved.

1. Introduction

The confocal micro-beam X-ray fluorescence (confocal μ-XRF)technique is an analytical tool that enables examination of spatialdistributions of elements within a sample with a resolutionranging from several up to tens of micrometers. The method wasproposed in 1993 by Gibson and Kumakov [1] and since then manyauthors proved its capability for analyzing samples of differentorigin, such as pigment layers in art objects or elemental distribu-tions in biological and environmental samples [2–5]. The techni-que has been used with spectrometers operated either withsynchrotron radiation or the radiation generated by X-ray tubes[6–8]. The main advantage of the technique is its capability forcollecting depth resolved elemental information with extremelyhigh signal to background ratio arising due to the inherentlylimited probing volume. The disadvantages include limited sensitiv-ity for high-Z elements and element-dependent spatial resolution,both effects linked to the way in which X-rays are transmitted andreflected in the focusing/collimating optics of the spectrometer.Nevertheless, for certain applications, the technique was foundvery useful as the only one the technique capable of non-invasiveprobing the sequence and chemical composition of sample layers.The comparison of the detection limits and elemental sensitivities

ll rights reserved.

+48 12 6340010.robel).

of conventional μ-XRF versus confocal μ-XRF techniques can befound in [9].

The elaboration of any quantification procedure for confocalμ-XRF technique is a demanding task since the spatial descriptionof the matrix effects inside heterogeneous sample is much moredifficult than in the case of conventional XRF. So far a few methodwere developed. The first quantification procedure for confocalμ-XRF was presented in 2004 by Smit et al. [10]. In this work thefundamental parameter approach assuming a spherical probingvolume was proposed for the investigation of paint layers. A moredetailed model of confocal volume was proposed by Malzer andKanngieβer in 2005 [11]. The authors also derived a generalequation for the depth-dependent intensity of X-ray fluorescenceradiation in confocal geometry as well as a calibration procedure.Mantouvalou et al. [12] used this approach to derive the equa-tions describing the intensity of X-ray fluorescence radiationversus the probing depth in multi-layered samples. A MonteCarlo (MC) based quantification approach was presented andcompared with the existing analytical methodologies by Czyzyckiet al. in two articles [13–14]. Perez et al. [2] applied the model ofMalzer and Kanngieβer [11], neglecting the self-absorptioneffects, for the analysis of metals in thin biological samples. Boththe analytical and MC approaches used the parallel beamapproximation [15]. Schoonjans et al. [16] elaborated a funda-mental parameter method for nano-X-ray fluorescence analysisof cometary dust particles trapped in silica-based aerogelreturned by NASA's Stardust mission. The analytical approach

P. Wrobel, M. Czyzycki / Talanta 113 (2013) 62–67 63

used in our work was based on the initial equation proposedoriginally by Malzer and Kanngieβer in [11].

2. Theory

In the model derived by Malzer and Kanngieβer [11] thespectrometer sensitivity function ηj xð Þ was introduced. In thismodel, depth-dependent intensity of X-ray fluorescence radiationof given element j recorded in confocal geometry, assumingmonochromatic excitation, paraxial X-ray optics, and neglectingenhancement effects, is given by:

ΦjðxÞ ¼Z D

0η′jðζ−xÞρjðζÞexp −

Z ζ

0μlin;jðξÞdξ

� �dζ; ð1Þ

η′jðxÞ ¼Φ0τF ;jηjðxÞ ¼Φ0τF;j~η jffiffiffiffiffiffi

2πp

sx;jexp

−x2

2s2x;j

!; ð2Þ

μlin;jðxÞ ¼∑iρiðxÞ

μ0;icos φ

þ μj;icos ψ

� �; ð3Þ

where ~η j takes into account the geometry of the confocal volumeand the transmission factors of the excitation/detection X-rayoptics and the detection efficiency, sx;j is the width of thesensitivity profile, Φ0 is the flux of the impinging beam, τF ;j isthe X-ray peak production cross section, φ and ψ are the incidenceand take off angles measured to the sample normal, μ0;i andμj;i arethe mass absorption coefficients for the primary and secondaryradiation. The function ρjðxÞ describes the local density profile ofthe analyzed element. For thin samples, when the absorptioneffects can be omitted

ΦjðxÞ ¼ η′jðxÞQj; ð4Þ

where Qj is the mass deposit per unit area of the analyzed element.In the approach proposed in this work the absorption term in Eq.(1) is split in two separate terms:

exp −Z ζ

0μlin;jðξÞdξ

� �¼ exp

Z x

ζμlin;jðξÞdξ

� �exp −

Z x

0μlin;jðξÞdξ

� �:

ð5Þ

The first term in the right side of Eq. (5) corrects for theabsorption effects within the confocal volume. The second termcorrects for the attenuation of the primary and secondary radia-tion on the path from the sample surface to the probing position x.This term does not depend on ζ and therefore it can be excludedfrom the main integral

ΦjðxÞ ¼ exp −Z x

0μlin;jðξÞdξ

� �Z D

0Gjðζ; xÞρjðζÞdζ; ð6Þ

Gjðζ; xÞ ¼ η′jðζ−xÞexpZ x

ζμlin;jðξÞdξ

� �: ð7Þ

Function Gj ζ; xð Þ takes into account the absorption effectswithin the probing volume. It can be considered as an expandedversion of the original sensitivity function η′jðxÞ. As shown in Eq. (7)the absorption of primary and secondary radiations inside theconfocal volume modifies the original sensitivity function η′jðxÞ in away that for ζox the sensitivity profile is enhanced by theexponent term which becomes 41, whereas for ζ4x the expo-nent term becomes o1 and the sensitivity profile is attenuated.The distortion of the original sensitivity function depends on theeffective linear absorption coefficient as well as on the size of theconfocal volume. In the case of weakly absorbing matrices and

small probing volumes

expZ x

ζμlin;jðξÞdξ

� �≈1⇒Gj ζ; xð Þ≈η′jðζ−xÞ: ð8Þ

In such a case Eq. (6) can be simplified to

ΦjðxÞ ¼ exp −Z x

0μlin;jðξÞdξ

� �Z D

0η′jðζ−xÞρjðζÞdζ

¼ exp −Z x

0μlin;jðξÞdξ

� �ðη′jnρjÞðxÞ: ð9Þ

where operators * and � are convolution and multiplication,respectively. The derived Eq. (9) opens up a possibility fordetermining the local density depth profile of the j-th elementby a direct deconvolution of the observed X-ray fluorescencesignal ΦjðxÞ with known sensitivity function η′jðxÞ followed by theabsorption correction of the deconvolved profile Φj;deconvolvedðxÞ

ΦjðxÞ; η′jðxÞ -deconvolution

Φj;deconvolvedðxÞ ¼ exp −Z x

0μlin;jðξÞdξ

� �ρjðxÞ;

ð10Þ

ρjðxÞ ¼Φj;deconvolvedðxÞexpZ x

0μlin;jðξÞdξ

� �ð11Þ

Φj;deconvolvedðxÞ is a dimension of density. The function η′jðxÞ mustbe known in advance, it can be determined by fitting Eq. (4) to themeasured depth profile of a thin film standard sample. As shownin Eq. (11) the local density profile of the analyzed element iscalculated by multiplying the deconvolved intensity profile by theexponential term determined at each probing position. This termis responsible for correcting the absorption effects due to thepresence of absorbing layers of the sample between the currentposition of the probing volume and the sample surface. To convertthe local density profiles ρjðxÞ into profiles of the concentration weassume a known density of the matrix and known densities of theelements (or chemical compounds containing given element)mixed with the matrix. Assuming that the elements (compounds)are not diluted but mixed with the matrix one can calculate theoverall sample density at given depth and use it to obtainconcentration depth profiles.

The deconvolution with regularization procedure [17,18] wasused to deconvolve the intensity profiles. In this procedure theanalyzed signal h (the measured characteristic peak intensityprofile) is a convolution of the known point spread function(PSF) g (the spectrometer sensitivity function) and the real signalf (the absorption modified element density profile) with super-imposed noise n (statistical fluctuations of the measured intensityprofile). The relation between these functions can be written inthe following form:

h¼ fng þ n ð12Þwhere ∗ is a convolution operator. Function f is approximated by f̂which minimizes the following expression:

∑x

ððf̂ngÞðxÞ−hðxÞÞ2n2ðxÞ þ λ∑

x

���Δf̂ ðxÞΔx

���: ð13Þ

The dimensionless λ parameter controls the strength of theregularization (smoothing). For given problem the value of thisparameter has to be chosen empirically to get the best compro-mise between the smoothing and the maximization of goodness offit. The first term in this sum governs how accurately theconvolution of the approximated function f̂ and the sensitivityfunction g fits to the signal h. The second term avoids solutionsaffected with high noise.

In the numerical implementation used in this work themeasured and deconvolved signals were discrete functions ofprobing positions. The sample was divided into a stack of layers

P. Wrobel, M. Czyzycki / Talanta 113 (2013) 62–6764

with number of layers equal to the number of probing points. Thethickness of each layer was equal to the step size of the confocalscan, Δx. The local densities of all detectable elements insideindividual layers were calculated subsequently starting from thefirst layer (the surface layer of the sample facing the detector) forwhich there were no other absorbing layers on the paths towardthe source and the detector. In the case of the first layer theabsorption correction term in Eq. (11) was equal to 1 and the localdensity of the j-th element was calculated using

ρjðx1Þ ¼Φj;deconvolvedðx1Þ: ð14ÞFor all subsequent layers the element density values were

calculated taking into account absorption in all preceding layers

ρjðxnÞ ¼Φj;deconvolvedðxnÞexp Δx ∑n−1

k ¼ 1∑iρiðxkÞ

μ0;icos ϕ

þ μj;icos φ

� � !:

ð15ÞTo calculate the absorption correction for element j inside n-th

layer the local densities of all elements in the preceding layers(detected elements and elements of dark matrix) have to beknown. For this reason the composition and density of the samplematrix as well as chemical form of detected elements wereassumed to be known. All calculations were performed withfundamental parameters taken from the xraylib library [19,20].

3. Experimental

The set of hypothetical single layer and multi-layered sampleswith assumed parameters/excitation conditions and two in-houseproduced multi-layered standards, measured at a synchrotronbeam line, were used to validate the developed model. Themulti-layered samples with low absorption of X-rays were chosenin order to allow the analysis within large range of depths.

The set of hypothetical single layer samples was based onhomogenous layer containing zinc in polyethylene matrix withdifferent effective linear absorption coefficients. The nominalcomposition and mass density of the samples are presented inTable 1. The synthetic intensity profiles of Zn-Kα line weregenerated for these samples by applying theoretical models givenby Eqs (1) and (9) and utilizing two values of the sx parameter:5 mm and 15 mm. The thickness of all samples was assumed to beequal to 150 mm. The energy of the exciting radiation was set to20.5 keV, the values of the parameters ~η, and Φ0 were set to 1.

Table 1Quantitative comparison of full and simplified formula for X-ray fluorescence intensity

Zinc concentration [%] 31.1 50.1Mean mass density of sample [g/cm3] 1.23 1.6Effective linear absorption coefficient [cm−1] 50 100Chi-square for sx¼5 mm 1.3 �10−4 3.3 � 10−4Chi-square for sx¼15 mm 8.5 �10−4 4.4 � 10−3

Table 2The input and reconstructed structure of the hypothetical layered sample.

Layer # Input values

Thickness [μm] Cu concentration [%] Zn concentration [%

1 100 – 52 50 10 –

3 25 – –

4 100 2.5 –

5 50 – 15

A multi-layered hypothetical standard was defined to verify thereliability of the derived model given by Eq. (15). The sample wasassumed to be composed of five layers containing differentconcentrations of copper and zinc in polyethylene matrix. Theeffective linear absorption coefficients varied from 4.3 cm−1 to22.8 cm−1 for Zn-Kα line and from 5.2 cm−1 to 25.9 cm−1 for Cu-Kαline. The theoretical profiles of Cu-Kα and Zn-Kα peaks werecalculated assuming 2.5 μm step size and utilizing the multi-layered sample formula derived in [12] based on the generalmodel given by Eq. (1). The nominal composition of layers ispresented in Table 2. The parameters ~η and Φ0 were set to 1, whilesx;Cu�Kα and sx;Zn�Kα parameters were set to 6.5 mm and 6.0 mm,respectively.

The two in-house developed standards consisted of nine layersmade of the Engage™ 8003 polyolefin elastomer doped with zincor copper oxide powders with the nominal weight fractions of4.5% for Cu2O (4% of Cu) and 4.98% for ZnO (4% of Zn). The firstsample consisted of five ZnO doped layers (odd numbered layers)separated with pure polymer matrix (even numbered layers),whereas the second one consisted of five ZnO doped layers (oddnumbered layers) separated with Cu2O doped layers (even num-bered layers). The thicknesses of all layers were determined by theobservation of cross sections of samples with an optical micro-scope. The effective linear absorption coefficient for Zn-Kα linevaried from 4.3 cm−1 (pure matrix) to 8.7 cm−1 (ZnO doped layer)whereas for Cu-Kα line this quantity varied from 5.2 cm−1 (purematrix) to 10.1 cm−1 (ZnO doped layer). The full description ofthese standards was given in [14]. The confocal experiment ofthese standards was performed at the beamline L [21] of thesynchrotron storage ring DORIS III in the Hamburger Synchrotron-strahlungslabor (HASYLAB) at DESY, Hamburg, Germany. Themonochromatic beam of exciting radiation with an energy of20.5 keV was focused with a polycapillary half-lens to a spot sizeof 6.7 mm FWHM. A probing volume was formed by attachingpolycapillary half-lens [22] to the detection channel in 451/451geometry. The spatial resolution of the probing volume (expressedas the sx of the registered depth-sensitive profile of infinitely thinstandard sample) was 6.06 mm at the energy of Zn-Kα line and6.42 mm at the energy of Cu-Kα. The fluorescence radiation wasregistered with a Vortex silicon drift detector with a crystalthickness of 350 μm, an active area of 50 mm2 and the energyresolution of 140 eV at the Mn-Kα line. The flux of primaryradiation impinging onto the focusing optics was monitored withan ionization chamber. The current of the ionization chamber was

for different absorbing samples.

62.1 70.3 76.3 80.81.96 2.33 2.7 3.06150 200 250 3006.5 �10−4 1.1 � 10−3 1.8 � 10−3 2.7 �10−31.3 �10−2 3.0 � 10−2 5.9 �10−2 1.1 � 10−1

Reconstructed values

] Thickness [μm] Cu concentration [%] Zn concentration [%]

100.270.4 – 4.9970.0550.070.4 10.070.2 –

24.870.4 – –

100.170.4 2.5170.06 –

50.070.9 – 14.870.2

Fig. 1. (a) Averaged depth-sensitive intensity profiles of zinc for ZnO multi-layersample. (b) Averaged depth-sensitive intensity profiles of zinc and copper forCu2O–ZnO multi-layer sample.

Fig. 2. (a) The comparison of general (dotted line) and simplified (solid line) formulasfor the intensity of fluorescence radiation in confocal geometry for sx equal to 5 mm anddifferent composition of the samples. The front of the sample is on the left side. (b) Thecomparison of general (dotted line) and simplified (solid line) formulas for the intensityof fluorescence radiation in confocal geometry for sx equal to 15 mm and differentcomposition of the samples. The front of the sample is on the left side.

P. Wrobel, M. Czyzycki / Talanta 113 (2013) 62–67 65

used for the normalization of experimental results. The standardswere scanned in depth perpendicularly to the surface with acounting time of 5 s per point and with a step size of 5 mm indepth. A number of 36 lateral scans was executed in an area of250 mm�250 mm encompassing 4716 probing points for eachsample. For each standard, the collected intensity depth profileswere averaged. The measured intensity profiles for both standardsare presented in Fig. 1a,b. Analytical parameters of the confocalspectrometer were estimated by the measurements of thin multi-element NIST SRM 1832 and NIST SRM 1833 standards [23]. Thesereference materials were scanned in depth with a counting time of10 s and a step size of 1 mm.

Fig. 3. Results of the quantification of synthetic sample. The front of the sample ison the left side.

4. Results and discussion

The applicability range of the simplified model was examinedby comparing the predicted profiles obtained with Eq. (9) to thosegenerated with the general model given by Eq. (1) for the set ofhypothetical single layer samples containing zinc in polyethylenematrix. The results of comparison are presented in Fig. 2a,b. Thecalculated reduced chi-square values for all compositions at bothspatial resolutions are presented in Table 1. The results confirmedgood agreement between the two models for samples with low

effective linear coefficient (low density). Due to the fact that theexponential term in Eq. (7) was neglected in the simplified modelgiven by Eq. (9) it was expected that significant discrepancy would

P. Wrobel, M. Czyzycki / Talanta 113 (2013) 62–6766

appear for large probing volumes and strong absorbing samples.The latter case may occur for samples with high mean atomicnumber and high mass density. The absorption is also stronger forlow excitation energy and/or low fluorescent energy of analyzedelement. For this reason the applicability of this simplified modelmay be limited for low energy X-ray fluorescence lines for whichlarger probing volumes are also introduced.,

For all multi-layer samples the positions of the layer borders withtheir uncertainties were estimated by fitting Gaussian functions to

Fig. 4. (a) The reconstruction of the composition of ZnO multi-layer sample. Thefront of the sample is on the left side. (b) The reconstruction of the composition ofCu2O–ZnO multi-layer sample. The front of the sample is on the left side.

Table 3The reconstruction of thickness and composition of ZnO multi-layer sample obtained w

Layer # Thickness [mm]

Optical microscopy General model MC simulation Direct deconvo

1 80.370.3 79.070.7 80.570.7 78.670.62 62.470.5 62.271.0 63.270.5 62.470.53 45.270.4 45.571.0 45.870.4 46.570.64 43.570.5 43.071.1 43.870.4 42.170.75 38.870.9 38.071.1 38.770.3 38.270.76 46.570.6 45.071.1 45.870.4 43.870.67 51.371.1 49.071.2 49.970.4 49.670.48 54.870.5 53.671.2 55.070.5 54.370.49 97.370.6 94.771.2 96.870.8 93.870.7

the first derivative of the concentration function of a given element.These values were then used to evaluate the thicknesses of layers andtheir uncertainties. The uncertainties of the chemical compositionwere estimated from the dispersion of the results within each layer.

The concentration profiles obtained for the multi-layeredhypothetical standard, reconstructed by using the elaboratedmodel given by Eq. (15), are shown in Fig. 3. The deconvolutionprocedure was carried out with the λ parameter equal to 0.0005.Reconstructed thicknesses and the mean composition of layers areshown in Table 2. As can be seen almost all estimates were in goodagreement with input quantities. The concentration profiles of ZnOand Cu2O in two in-house made multi-layered standards, werereconstructed by using the developed model and the averagemeasured intensity profiles. The results are shown in Fig. 4a,b.The deconvolution was performed with λ parameter equal to 0.02.The results were compared with the results obtained with theMonte-Carlo simulation [13] and the general model given by Eq.(1) extended to multi-layered structures in [12]. The comparison ofthe nominal concentrations, thicknesses measured by an opticalmicroscope and reconstructed quantities is presented inTables 3 and 4. The reconstructed concentrations profiles of zincand copper oxides obtained by the approach proposed in this workagreed very well with the estimates determined by existingquantification procedures and the nominal quantities. In almostall cases the determined estimates could be considered equalwithin the uncertainty interval. Relative uncertainties varied from0.6% to 1.8% for ZnO doped layers and from 3.0% to 7.0% for Cu2Odoped layers. Greater uncertainties in the latter case resulted fromless homogenous lateral distribution of copper oxide as comparedto zinc. Due to the high counting statistics and the use of theaveraged experimental depth-sensitive profiles, the contributionfrom the uncertainty of the measurement to the uncertainty ofconcentration was negligible. The deconvolution technique pro-duced very small non-zero concentration estimates (equal to zerowithin uncertainty range) within the layers where the givenelement was not present The significant non-zero concentrationappeared mainly for ZnO in Cu2O doped layers—copper was notdetected in ZnO doped layers. For this reason this effect could notbe explained by any defect of the method—is such a case, it wouldbe observable for both elements. Very likely explanation of thiseffect could be the diffusion of ZnO powder into Cu2O doped layersthat could be introduced during the sample preparation process.

5. Conclusions

A new quantification procedure for the determination ofelemental concentration profiles in multi-layer samples examinedby confocal X-ray fluorescence spectroscopy was derived andvalidated. The experimental verification proved very good perfor-mance of the proposed approach for weakly absorbing matrices.

ith three competitive quantification procedures.

Dopant concentration [%]

lution Nominal General model MC simulation Direct deconvolution

4.98 4.271.0 5.070.1 5.070.1– – – –

4.98 5.571.3 5.170.1 4.870.1– – – –

4.98 5.771.1 4.870.2 5.070.1– – – –

4.98 6.271.4 4.870.1 4.970.1– – – –

4.98 7.271.2 4.970.1 4.970.1

Table 4The reconstruction of thickness and composition of Cu2O–ZnO multi-layer sample obtained with three competitive quantification procedures.

Layer # Thickness [mm] Dopant concentration [%]

Optical microscopy General model MC simulation Direct deconvolution Nominal General model MC simulation Direct deconvolution

1 67.570.6 66.970.6 69.370.6 67.670.6 4.98 5.170.2 5.070.1 4.970.12 43.7570.5 45.170.8 46.570.4 48.870.7 4.5 4.370.5 4.770.2 4.570.33 42.370.4 41.670.8 43.470.4 40.770.4 4.98 4.570.8 4.770.2 4.970.14 49.670.6 48.370.8 49.670.5 45.671.0 4.5 4.870.8 4.870.2 4.670.25 51.971.0 52.270.8 53.87 0.5 50.670.4 4.98 6.271.0 5.270.2 4.970.16 39.470.9 38.070.8 39.370.4 40.371.3 4.5 5.470.8 4.670.1 4.770.47 52.171.0 52.670.8 54.870.5 51.770.7 4.98 6.471.9 5.270.1 4.970.18 48.270.6 47.370.8 48.670.5 49.271.0 4.5 6.271.1 4.870.2 4.570.39 98.070.4 96.670.9 100.370.9 95.470.5 4.98 7.671.0 5.170.2 5.070.1

P. Wrobel, M. Czyzycki / Talanta 113 (2013) 62–67 67

As compared to other methods of quantitative analysis theadvantage of the proposed method is its simplicity. Moreoverthe direct deconvolution approach does not assume any structureof the sample and initial values are unnecessary. Furthermore, thedirect deconvolution of position dependent X-ray fluorescencesignal can be extended into the case of generally heterogeneousstructures where the absorption correction is performed on avoxel by voxel way [24].

Acknowledgments

The authors would like to cordially acknowledge the advice andhelp received from Dr. Dariusz Wegrzynek, a staff member of theFaculty of Physics and Applied Computer Science, AGH Universityof Science and Technology, Krakow, Poland in verifying the under-lying theoretical assumptions of the proposed model, and hiswillingness in reviewing our work.

The research was financially supported and realized under theauspices of the International Atomic Energy Agency, Vienna,Austria within the frame of research Contract no. 16023.

Portions of this research were carried out at the light sourceDORIS III at DESY, Hamburg, Germany, a member of the HelmholtzAssociation. Authors kindly thank Dr. Karen Appel for her assis-tance during the measurement session.

The computational part of the research was performed in theACC CYFRONET AGH, Krakow, Poland within computational Grantno. MNiSW/IBM_BC_HS21/AGH/095/2009.

The research has received funding from the European Commu-nity's Seventh Framework Programme (FP7/2007-2013) undergrant agreement no. 226716. The research was also supported bythe Polish Ministry of Science and Higher Education and its grantsfor scientific research.

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