6th World Conference on NDT and Microanalysis in Diagnostics and Conservation of Cultural and Environmental Heritage, Rome, 1999 May. Published by AIPnD, email: aipnd@numerica.it

TABLE OF CONTENTS

Summary Introduction Method and experimental setup Experimental and results Conclusion Acknowledgement References Appendix

Summary

Energy-dispersive X-ray diffraction tomography [1], also termed coherent X-ray scatter imaging, is a novel technique for the non-destructive determination of the material composition within bulk objects. No sample of material has to be taken from the object and direct comparison of the results to conventional powder diffraction data is possible. Applications of this technique were investigated, e.g. in the fields of industrial production control [2,3] and the detection of explosives and drugs in airport baggage [4]. In this paper the method and the used experimental setup are described in detail, its application to non-destructive testing of works of art is discussed and experiments are presented.

A main characteristic of the technique is the use of a X-ray tube (150 kV) with pencil-beam collimation for irradiation of the object with polychromatic X-rays. A HPGe detector is employed for energy-resolved detection of the photons scattered elastically under a fixed scatter angle. The measured energy spectrum can be regarded as a "fingerprint" of the material within a distinct volume element inside the bulk object.

In order to demonstrate the applicability of the method to the investigation of works of art the identification of pigments used in historical paintings was chosen as an example. The experimental model contained 6 different pigments (azurite, malachite, ultramarine blue, verdigris, lead white, lead tin yellow) all applied upon a chalk/glue ground on canvas or wood. For identification the acquired data were compared visually to the results of measurements made on powdered samples of the same materials. In addition, the experimental process was simulated by means of a software program using diffraction data from literature [5] as input. Good coincidence was found between the measured diffraction patterns and the comparative data. As a characteristic of the measurement process the observed scatter signal is not only representing the material close to the surface but that in deeper layers. This is a major difference between this method and other diffraction techniques applying reflection geometry at low X-ray energy.

Although the experimental demonstration presented here is focused on paintings, the method is not considered as an alternative to means of analyzing the surface of objects. Its advantage is to give spatially resolved material specific information from the inside of extended objects in a non-destructive way.

Introduction

Traditionally the development of methods employing X-rays for to study bulk objects is progressing in two directions: X-ray imaging mainly stimulated by increasing requirements of medical diagnosis but also by the needs of industrial applications, and methods for material science mainly based on X-ray scatter, absorption or fluorescence. In X-ray imaging the local variation in X-ray absorption, which may be divided into photoelectric absorption and scatter, is represented by the gray values of the resulting image. In this class of techniques X-ray scatter is normally regarded as an unwanted effect leading to a reduction in image contrast.

Measurement of coherently scattered X-rays (X-ray diffraction), on the other hand, allows to gain material specific information and may be used for substance identification. Unlike X-ray fluorescence, neutron or photon activation analysis or ion beam techniques [6], where the elements within the material are determined, this method is sensitive to its crystalline structure. Traditionally it is applied to powder samples or crystals in material science or crystallography. Compared with the imaging techniques mentioned above there are significant differences with respect to the experimental procedure and the used setup. In X-ray imaging on bulk objects energies significantly above 100 keV are often required due to high absorption, whereas X-ray diffraction studies on small samples of material are typically performed at much lower energy (e.g. Cu K_a( radiation). Furthermore, in contrast to imaging, methods like powder diffraction can not be regarded as non-destructive, since a sample of material has to be taken from the object. However, X-ray diffraction also allows non-destructive investigations concerning the surface of objects [7]. In both cases the conventional procedure is to use monochromatic X-rays and to measure the angle of the scattered photons (angular dispersive measurement). As a result, the atomic planar spacings (lattice spacings) of the material can be determined allowing substance identification. Due to the reflection geometry and the low X-ray energy used the identification of the material composition within deeper layers of bulk objects is usually impossible. The applicability of transmission geometry, on the other hand, is restricted to very thin layers because of absorption.

In order to observe coherent X-ray scatter from volume elements deep inside an extended object other experimental procedures are required. The method used here represents a possible approach combining features of X-ray imaging with those of X-ray diffraction. Its applicability to various problems of non-destructive testing has been investigated. Examples are the detection of contaminants in production control for the foodstuff industry [2,3] and the detection of explosives and drugs in airport baggage [4]. The technique, that was described by Harding et al. [1], enables determination of the material within the object in a spatially selective way. It further allows imaging by combining the scatter data from all volume elements within a slice of material in the object. Compared with conventional diffraction measurements the resolution of the method with respect to the atomic spacings is usually reduced. Therefore the applicability of the technique to a certain inspection task has to be assessed theoretically and experimentally concerning resolution, sensitivity and spatial resolution.

In this paper an improved setup for coherent scatter measurements on extended objects is described in detail and the influence of various experimental parameters is discussed. In order to demonstrate the experimental procedure and the performance of the method the identification of pigments in paintings was chosen as an example. In this field of non-destructive testing of works of art material discrimination is required and extensive literature data exist.

Method and experimental setup

a

b

Figure 1: a) Schematic diagram of the experimental setup as described in [1]. Figures refer to text. b) Enlarged longitudinal section of the circularly symmetric region-of-interest of the system. Its size is defined by the beam diameter (Dbeam) and the scatter collimator dimensions. The (mean) scatter angle Q is changed by moving the upper diaphragm of the collimator in the vertical direction by means of a step motor. The dimensions of the used collimator were: R1: 7.5 mm, R2: 12.8 mm, A: 0.6 mm, L: depending on scatter angle (see text). The total range of scatter angles Q causing angular blurring is determined by Qmin, Qmax and the angular distribution of the incident photons within the beam. The investigated volume element within the object can be changed by moving it relative to the setup in 3 dimensions. (For clarity the drawing is not true to scale. The beam widening is not shown.)

The experimental setup is schematically shown in Fig.1. The central part of Fig.1a represents a longitudinal section of the incident and scattered X-ray paths. It is intended to illustrate the scatter geometry and is not true to scale. A 150 kV¹ X-ray tube (1) operated at 5 to 10 mA is used as a radiation source. By means of the primary collimator (2) a X-ray pencil beam is formed penetrating the object under investigation (3). Besides photoelectric absorption, the observed interactions comprise Compton scatter and coherent scatter. Due to the high X-ray energy the coherent scatter is concentrated in a small angular range around the central beam. In this low-angle region and for the used X-ray energy coherent scatter dominates Compton scatter such that the latter is neglected [1] in the following. By means of the annular scatter collimator (4), the longitudinal section of which is shown in the figure, a small angular range within the coherent scatter region is selected for energy-dispersive detection using the high-purity Germanium (HpGe) detector (5). Fig.1b shows how the scatter angle as well as the sensitive volume of the apparatus - the so-called region-of-interest - is defined by the dimensions of the system. Only X-ray photons scattered inside this (dotted) region under a scatter angle within a range Q are passing the collimator and can be detected by means of the HpGe detector. Different volume elements within the object can be investigated by moving it relative to the setup. Thus, besides the acquisition of spatially localized diffraction data, the system allows imaging through point-by-point scanning of the object with respect to the apparatus. Within our experiments on pigment layers, however, this imaging capability of the method was not used.
¹ Suitable for objects containing atoms of low or moderate Z depending on thickness.

The signal created by a detected X-ray photon within the Ge-crystal of 5 cm diameter is pre-amplified and further processed by means of a standard NIM pulse amplifier (6) with ADC (7) and PC-based 2048 channel MCA electronics (8). The energy distribution of the scattered X-rays for the given scatter angle is thus gained by pulse height analysis of the detector signals. As in conventional angular dispersive X-ray diffraction lattice spacings are determined from the measured diffractograms.

The Bragg law describes the condition to be fulfilled by the X-ray wavelength l, the scatter angle Q and the lattice spacing d for positive interference:

	(Note: Only first order diffraction is considered).	(1)
It can be rewritten as:	(h: Planck's constant, c: velocity of light)	(2)

where the wavelength of the X-ray radiation is replaced by the photon energy E. From this equation the interrelation between the lattice spacing d the photon energy E and the scatter angle Q can be seen.

The momentum transfer defined as:

(3)

is determined from the position of a point of maximum intensity (E) within the energy spectrum of the scattered radiation. It can be converted directly into the corresponding lattice spacing d by means of equation (2). The d values determined from the peak positions in the diffraction pattern may be compared with literature data for material identification. For quantitative comparison of peak intensities several corrections of the measured data are required. First, a calibration procedure is necessary in order to compensate for the non-uniform energy spectrum of the incident X-ray radiation as well as the energy dependent absorption within the object itself. For that purpose the energy spectrum of the transmitted X-rays is measured by removing the beam stop (9, see Fig.1b) and, if necessary, covering the scatter collimator aperture. The correction is performed by dividing the diffraction spectrum by the transmission spectrum. Using this kind of calibration procedure an error is introduced because of the fact that the X-ray paths between the diffraction and the absorption measurement slightly differ from one another. However, in view of the small scatter angles used here (see below) this error can usually be considered as small, at least for flat objects like paintings, and is thus neglected. For the comparison of measured peak intensities with literature data from powder diffraction a second correction is necessary allowing for the differences with respect to the scatter geometry and the experimental procedure. It is taken into account in the simulation program described below.

Sensitivity and resolution of the measured diffraction data as well as the accuracy of the volume localization are influenced by various experimental parameters. These are the emission voltage and current of the X-ray tube, the (mean) scatter angle Q, the diameter of the pencil beam D_beam and the measures of the scatter collimator. These parameters influence the position and size of the region of interest within the object and well as the energy position, width and height of the measured diffraction peaks for a given material. Whilst the emission voltage is mainly determined by the absorption of the investigated object and the current is chosen as high as possible in order to reduce the measurement time, the role of the collimator dimensions is more difficult to assess. Sensitivity, spatial resolution and line width are interrelated.

According to Fig.1b the maximum range of scatter angles Q to be detected is defined by the scatter collimator together with the diameter of the X-ray beam and the focus dimensions of the X-ray tube. Usually the extent of this angular range is representing the dominant effect causing line broadening of the diffraction peaks. This angular blurring is limiting the "spectral" resolution of the method. We shall use this term to denote the capability to distinguish different lattice spacings d based on their peaks in the energy spectrum. Corresponding to the Bragg condition (2) any change in the scatter angle Q results in a shift of the whole diffraction pattern on the energy scale. Consequently, the energy position of the spectrum can be adjusted by changing Q. For the choice of the most suitable angle different criteria concerning the corresponding peak positions have to be considered. On the one hand peak positions are desired leading to high signal intensities. These are obtained if the peak energy falls into the region of high spectral intensity of the X-ray tube. On the other hand a small line width is obtained for a peak at a low energy value. It can be seen from equation (2) that the (maximum) line width E of a peak corresponding to a fixed lattice spacing d is increasing approximately with the square of its energy position E in the spectrum as long as the diffraction angleQ remains small and Q is kept constant. Since the energy difference of two diffraction peaks belonging to adjacent lattice spacings is rising approximately linearly with E, the resolution is improved significantly if the corresponding diffraction peaks fall in the low-energy part of the spectrum or can be transformed into it by changing the diffraction angle. A main limitation in lowering the peak energies is the decreasing line intensity due to absorption within the object. Although this effect is basically taken into account by means of the described calibration procedure, it may lead to a significant decrease in sensitivity that could only be compensated by a corresponding increase in measurement time. A detailed consideration of the effects of angular blurring is given in [8].

As stated above, the observable line broadening is mainly caused by the range of scatter angles Q defined by various system parameters. On the other hand it depends on the material distribution within the region-of-interest if the maximum line width is actually observed in the experiment, since crystallites with suitable orientations have to be present in the corresponding points in space. Thus, the system parameters only set the lower limit of resolution.

Another important aspect of scatter collimator design is its influence on the spatial resolution. The diameter of the region-of-interest is given by the value of D_beam, which in our system usually ranges between 0.4 and 3 mm. Due to the small scatter angle its vertical dimension is considerably larger (see Fig.1b). Thus the spatial resolution of the method in the vertical direction is significantly worse compared with that in the plane perpendicular to it. For the measurements on paintings presented here the height of the investigated pigment layer was always much smaller than that of the region-of interest of the system. For this limiting case the aspect of spatial resolution in the vertical direction does not need further attention. For applications to other inspection tasks, however, careful consideration of the limiting influence of the mentioned system parameters on spatial resolution in the vertical direction is required. Usually the height of the region-of-interest lies above 1 to 1.5 cm in our system. The following example explains the relationship between resolution and sensitivity: Decreasing the scatter collimator aperture A leads to an improvement in both spectral and spatial resolution. As a consequence of the smaller region-of-interest the signal intensity is generally reduced.

As a result of the above considerations the definition of both the scatter angle and the collimator sizes for a given inspection task must be based on a compromise between spectral and spatial resolution on the one hand and sensitivity on the other. In order to facilitate the choice of the various mentioned parameters within the experiment the used setup allows to change the scatter angle by shifting the upper diaphragm of the scatter collimator in the vertical direction by means of a step motor under remote control. Thereby, for a given material, diffraction patterns with different peak energy positions are simply obtained experimentally. For the experimental work presented here a primary collimator of 2 mm diameter and a scatter collimator aperture of 0.6 mm were used. Taking into account the focus dimensions of the X-ray tube (0.8 mm ( 1.2 mm) and the geometrical measures of the apparatus a region-of-interest of approximately 3 mm diameter is obtained. Thus the diffraction data acquired from a painting represent the material composition within a 3 mm spot of the pigment and ground layers.

In view of the large number of experimental parameters influencing the quality and significance of the measured diffractograms we decided to simulate the whole measurement procedure numerically based on literature data. By means of the simulation program diffraction patterns can be generated either from a known crystalline structure or based on spectra from powder diffraction data bases. The simulated patterns reflect the experimental procedure and geometry used in this work. Their calculation is mainly based on the evaluation of possible geometrical traces of X-ray photons (ray tracing) as well as a recalculation of line intensities incorporating the geometrical conditions of both powder diffraction and the method used here.

In contrast to the energy positions of the diffraction peaks, which are governed by the Bragg condition (2), their measured relative intensities may significantly differ from the theoretical prediction if the material within the investigated volume element displays texture. Therefore, the comparison of the diffraction patterns measured in this work with simulated data based on powder diffraction is focused on the values of the lattice spacings d, i. e. on the line positions, and less on the relative line intensities of the peaks.

Experimental and results

For the non-destructive identification of pigments in paintings several substances were studied. The material was supplied by the "Restaurierungzentrum der Landeshauptstadt Düsseldorf, Schenkung Henkel", Düsseldorf, Germany. It comprised the following six pigments:
azurite, malachite, ultramarine blue, verdigris, lead white and lead tin yellow.
In addition to powder samples a single layer of each pigment had been applied with a brush on both canvas and wooden supports. The thickness of the wooden panels was 11mm. All paint layers were applied on a chalk/glue ground as used in traditional medieval north-alpine panel painting. Reference data regarding the chemical composition and structure of the pigments were taken from [5].

For the identification of pigments in paintings very thin layers of material have to be investigated leading to data sets with low signal intensity that may also display texture. The identification is based on the comparison of the measured diffraction patterns with reference data. Within our experiments these were taken from two sources: simulation using literature data and measurements performed on the powder samples. First, for each pigment the diffraction pattern was calculated theoretically by means of the simulation program using its known lattice spacings as input. Besides comparison with the experimental data, the purpose of this step was to find an estimate for the optimum scatter angle. The criterion for a suitable angle was that all major diffraction peaks of the pigment fall within the favorable energy range of approx. 40 to 140 keV². For comparison the diffraction patterns were now determined experimentally using the powder samples placed in the center of the region-of-interest of the system. Apart from differences concerning the measured relative peak intensities (see above) the experimental data turned out to be in good agreement with the simulations. Fig.2 shows a simulated data set for malachite (scatter angle Q @ 2.6°) as an example. Note the good agreement between the peak energy values in Fig.2 and the result of the corresponding measurement shown in Fig.3b³ . However, in some cases (e.g. verdigris) the chemical composition of the pigment may vary [5] leading to different lattice spacings. As a result not all of the diffraction data from literature were verified in our measurements. For the purpose of this experiment, however, the powder measurements were regarded as the more relevant reference since they reflect exactly the same material composition as the pigments in the paint layers.
² At the moment the lower limit of the usable X-ray photon energy is set to approx. 25 keV by built-in filtering of the X-ray tube.
³ The results of all measurements concerning pigment powder samples and paint layers are summarized in the appendix

Fig 2: Simulated diffraction pattern for malachite at a scatter angle Q @ 2.6°. The peak energies calculated from the Bragg condition (2) are: 46.0, 54.5, and 74.6 keV, 96.6, 97.6 and 99.2 keV (observed as one peak at 97.5 keV) and 109.4, 111.3 and 111.8 keV (observed as one peak at 110.5 keV).

In the next step of the experimental procedure the scatter angle was further optimized experimentally aiming at the highest possible resolution. This is illustrated in Fig.3 showing malachite powder measured under different scatter angles. Once for a pigment the optimum angle was defined up to 6 diffraction measurements were performed with respect to different points of the layer in order to minimize the influence of texture. The object plane was placed vertically in the center of the region-of-interest. After these measurements the data were added in order to increase the signal-to-noise ratio. The total measurement time ranged between 60 and 100 minutes. The absorption measurements necessary for the described calibration procedure were generally taken from one position of the paint layer only, since no significant changes between different points were observed.

It is a characteristic of the measurement process that diffraction data are not only acquired from the surface but also from layers below it. Thus, apart from the peaks belonging to the pigments the measured diffraction patterns contain also those belonging to the ground layer from chalk/glue on canvas or wood, respectively. The contribution of the ground layer was measured in a separate step using points from an area of the object without a pigment layer. Later on this data set was subtracted from the sum spectra containing the pigment patterns. This subtraction also eliminates the influence of background radiation on the spectra resulting from incomplete screening of the detector in combination with multiple scatter processes within the apparatus. However, since this procedure is not feasible for real paintings, the diffraction pattern of the lower layers may also be incorporated into the evaluation and only the background radiation has to be measured and subtracted separately. Furthermore it is a prerequisite for the described subtraction technique that no significant spatial variation in thickness or texture within the ground layers is present. To verify this condition for the given object diffraction patterns were taken from different points of the ground layers yielding no visible differences.

The used diffraction angles ranged from 2.0° to 4.3°. Based on the experimental procedure described above the following angles were assigned to the different pigments: azurite (2.6°), malachite (2.6°), ultramarine blue (4.3°), verdigris (2.6°), lead white (3.3°) lead tin yellow (4.3°).

Fig.4 shows a comparison of results concerning the powder sample (a) and the paint layers (b and c) for the case of lead white as an example. Note the good agreement between the measured diffraction patterns. Due to the energy-dispersive detection technique X-ray fluorescence from the investigated object is also observed within this type of measurement. It can be regarded as an additional source of information. In the experimental work on pigments fluorescence lines from lead and tin were found.

An example illustrating the subtraction procedure allowing to separate the pigment layer from the ground layer is given in Fig.5 for lead tin yellow. The diffraction data set from the mere chalk/glue ground layer applied on canvas is shown (5b). It is subtracted from the measured sum spectrum (5a) to give the pigment spectrum (5c).

Fig.6a-c and Fig.6d-f comprise the results for the remaining pigments applied on canvas or wood, respectively. Good coincidence with the results from the powder samples (upper traces) is found. The slight difference between the measured peak positions from ultramarine blue on canvas and the corresponding powder result may be due to residuals of the contribution from the chalk/glue ground layer indicating the limits of the subtraction procedure described above. As observed for lead white (Fig.4c), also lead tin yellow (6a) and azurite (6c) gave significant results also for the layers applied on wood. However, due to the smaller signal intensity of azurite as compared to pigments containing lead (Figs.4, 5) its identification on wood is less conclusive within the measurement time spent in the experiment. In Figs.5 and 6a again lead fluorescence lines are visible.

The reproducibility of the pigment measurements concerning different points of the paint layers as well as their agreement with the powder measurements were good as long as sufficient signal-to-noise ratio (SNR) was obtained (see Figs.3-6 [appendix]). In particular none of the major diffraction peaks known from the powder experiments was unobserved due to texture in the paint layers. Among all measurements those of ultramarine blue turned out to be the most difficult to interpret. Because of many similar lattice spacings and low scatter signal intensity well resolved diffraction peaks were not observed in the measurements on pigment layers at angles below 4.3°.

Layers on wood gave insufficient SNR in three cases resulting from absorption of the small scatter signals caused by the wooden panels. This problem might be overcome by the use of a brighter X-ray source. Significant improvements regarding the task of identifying the diffraction patterns can further be expected from the application of data processing methods for pattern recognition suitable for low SNR data. This should also enable to reduce the measurement time. Further extensions of the experimental procedure may be helpful in order to simplify the interpretation of the measured data sets in more complicated cases: The identification could be based on a combination of measurements carried out under different diffraction angles each being optimized for a certain range of lattice spacings. Also a combination with results from conventional diffraction measurements concerning the surface of the painting as well as X-ray imaging could help to identify deeper pigment layers covered up by others.

Conclusion

Within these first experiments six pigments were distinguished from one another based on their coherent X-ray scatter data. Although more complicated paint layers and pigment mixtures still have to be investigated, we expect that the method of energy-dispersive X-ray diffraction tomography can yield additional significant information with respect to the identification of pigments and ground layers in real paintings. The investigation of paintings was chosen as a first application of the technique to non-destructive testing on works of art and it may be followed by others.

The method is not considered as an alternative to means of analyzing the surface of objects. Instead, it may be used complimentary to these. Its main feature is to deliver information on the crystalline structure from the inside of objects in a non-destructive way. Thereby it could provide answers to scientific questions in the field of non-destructive testing on works of art or archaeological findings where the material within extended objects is to be determined and its spatial distribution is to be analyzed.

Acknowledgement

I wish to thank Herrn Gunnar Heydenreich, Restaurierungszentrum der Landeshauptstadt Düsseldorf, Schenkung Henkel, for the preparation of the powder and brushed pigment samples as well as for helpful discussions. Furthermore I wish to thank Herrn Thorsten Müller for carrying out most of the measurements and Herrn Lars Hild for providing the simulation program.

References

1. G. Harding, M. Newton and J. Kosanetzky, Phys. Med. Biol. 35, p. 33, 1990
2. R.D. Luggar and W.B. Gilboy, Nucl. Instrum. Methods Phys. Res. A 353, p. 650, 1994
3. G. Martens, H. Bomsdorf, G. Harding, J. Kanzenbach and R. Linde, SPIE Vol. 2092, Substance Detection Systems, p. 387, 1993
4. H. Strecker, G. Harding, H. Bomsdorf, J. Kanzenbach, R. Linde and G. Martens,SPIE Vol. 2092, Substance Detection Systems, p. 399, 1993
5. Ashok Roy [Ed.], Artists` Pigments, Vol. 2, Oxford University Press, 1993
6. Ch. Neelmeijer and W. Wagner, 4^th Intl. Conf. on Non-Destructice Testing of Works of Art, Berlin, Oct. 3.-8. 1994, book of abstracts p. 296
7. R. Fuchs, 4^th Intl. Conf. on Non-Destructice Testing of Works of Art, Berlin, Oct. 3.-8.1994, book of abstracts p. 441
8. R.D. Luggar, J.A. Horrocks, R.D. Speller and R.J. Lacey, Nucl. Instrum. Methods Phys.Res. A 383, p. 610, 1996

Appendix: results of measurements on pigment powders and paint layers

Figure 3: Diffraction patterns from malachite powder at 3 different diffraction angles (2.0°, 2.6° and 3.3°). The dotted lines indicate the energy values of 5 major diffraction peaks as obtained in the simulations. (For the simulation result corresponding to (b) see Fig.2.) The strong reduction in line width resulting from an increase of the diffraction angle is visible. For malachite, an angle of 2.6° was chosen for the investigation enabling observation of signals from 5 lattice spacings within the favourable energy range between 40 and 140 keV.

Figure 4: Comparison of diffraction patterns of lead white acquired from the powder sample and from paint layers. The high signal intensity enables identification of the diffraction pattern for both wooden and canvas supports. Lead fluorescence lines are observed between 70 and 90 keV.

Figure 5: Diffraction Patterns from a paint layer of lead tin yellow on canvas before and after subtraction of the contribution from the ground layer (chalk, glue and canvas) measured separately. The dotted lines indicate the energy values of the major peaks. The contribution of the ground layer in (a) is strongly suppressed by the subtraction procedure leaving the diffraction pattern of the mere pigment (c). Again lead fluorescence lines are observed.

Figure 6a-c: Diffraction patterns from paint layers of lead tin yellow on wood, and azurite on both canvas and wood. The results from powder measurements (upper traces) are shown for comparison.

Figure 6d-f: Diffraction patterns from paint layers of malachite, verdigris and ultramarine blue applied on canvas. The results from powder measurements (upper traces) are shown for comparison.