- Email: [email protected]
First results on ion micro-tomography at LIPSION
Nuclear Instruments and Methods in Physics Research B 268 (2010) 2001–2005
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
First results on ion micro-tomography at LIPSION M. Rothermel *, T. Reinert, T. Andrea, T. Butz Institute for Experimental Physics II, Department of Nuclear Solid-State Physics, University of Leipzig, Linnéstraße 5, 04103 Leipzig, Germany
a r t i c l e
i n f o
Article history: Available online 26 February 2010 Keywords: STIM PIXE Tomography
a b s t r a c t At the nanoprobe LIPSION ion micro-tomography can be used to determine the 3D distribution information of a sample’s mass density and elemental composition. For ion micro-tomography the two analytical techniques scanning transmission ion microscopy tomography (STIM-T) and particle induced X-ray emission tomography (PIXE-T) are combined. The required data are collected in two consecutive series of measurements, during which the sample is rotated by 180°/360° in small steps. Because all ions have to traverse the sample, the upper limit of the sample size is given by the range of the ions in the material. The tomogram is obtained using the discrete image space reconstruction algorithm (DISRA) by Sakellariou (1997) [1]. This algorithm iteratively corrects a sketchy initial tomogram estimated from the experimental reconstruction – obtained by backprojection of filtered projections (BFP) – and an a priori elemental composition. The necessary correction factors are calculated comparing the reconstruction of the experimental data with the reconstruction of simulated data. For the simulated data sets of STIM projections and PIXE maps are computed from the tomogram. These data sets are proceeded with the BFP algorithm to get simulated reconstruction data. Using the DISRA for ion micro-tomography, one can benefit from the high resolution of STIM-T by transferring it to the elemental distribution given by PIXE-T. This article presents first results of this technique applied on a phantom at the LIPSION facility. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction The technique of ion micro-tomography (IMT) provides 3D information about a sample’s mass density and elemental composition. Although applications still remain scarce, reaching a spatial resolution of less than a 1 lm this technique becomes more and more interesting for lots of applications in materials research as well as life sciences. Whereas some micro-tomographical techniques need to cut the sample into slices, the sole preparation step for IMT is to mount the sample freestanding, thus enabling a nondestructive analysis. The very recent development of limited angle tomography [2] with ion beams [3] even allows mounting the samples on thin foils or Si3N4-windows. Despite the larger efforts – compared to commercially available X-ray tomography devices – the additional elemental information as well as the better density resolution demonstrate the advantages of this technique. Ion micro-tomography combines the two analytical techniques scanning transmission ion microscopy tomography (STIM-T) and particle induced X-ray emission tomography (PIXE-T). In combination with a computer algorithm suited to ion micro-tomography to
* Corresponding author. Address: Fakultät für Physik und Geowissenschaften, Universität Leipzig, Linnéstr. 5, D-04103 Leipzig, Germany. Tel.: +49 341 97 32709; fax: +49 341 97 32708. E-mail address: [email protected] (M. Rothermel). URL: http://www.uni-leipzig.de/~nfp (M. Rothermel). 0168-583X/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2010.02.117
reconstruct the data, the technique can benefit from the high spatial resolution of STIM-T by transferring it the elemental distribution given by PIXE-T. Nevertheless, the spatial resolution in STIM and PIXE mode need to be comparable. This is available at the high energy nanoprobe in the LIPSION laboratory [4,5]. The required data are collected in two consecutive series of measurements, during which the sample is rotated in small steps. The large range of high energy ions in matter allows the measurement of information deep inside the sample. The only restriction is that the ions have to traverse the sample, giving an upper limit of typically some tens of micrometers using 2.25 MeV protons. Although the need for tomography was mainly driven by medical applications, the principle can easily be transferred to focused ion beam techniques. Starting with Cormack and Koehler in 1976 (128 MeV proton beam with a diameter of 2 mm) [6], this technique was progressed to ion micro beams by Pontau and Fischer [7,8]. In the 1990s computational power and the availability of sub-micron ion beams boost the possibilities of ion tomography, reaching practical biological applications [9–11]. This experience of other laboratories [12,13] (especially Melbourne) paved the way for STIM-T experiments at the Leipzig high energy nanoprobe LIPSION [11,14]. Whereas STIM-T nowadays is well established in several groups [12–16], there remained some obstacles regarding PIXE-T [17,18]. In contrast to STIM-T, where simple median filtering of few detected energy loss events suffices for adequate statistics, the physical phenomena in PIXE-T are more complex. Besides
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M. Rothermel et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 2001–2005
variations of the X-ray production cross section along an ion’s trajectory, a major problem to obtain quantitative information in PIXE-T is the need to correct the X-ray yields because of attenuation and attenuation variations inside the sample. Since X-rays emitted from one point in the sample may undergo different attenuations on their path to the detector, the total detector solid angle needs to be subdivided for simulation purposes, thus taking into account the cone-beam geometry of the X-ray detection. To overcome this problem caused by the sample geometry and local composition variations in quantitative analysis, a successive approximation to the real composition of the sample is necessary. A reconstruction code including the most important physical effects as well as taking into consideration convergence criteria of the iteration process was proposed and tested by Sakellariou’s DISRA [1,19]. This article enlightens the procedure to derive a 3D tomogram from the measured data using a phantom consisting of a ZnO micro-wire and oxide grains and introduces to the interactive, real-time 3D visualization possibilities of the IDL software [20]. 2. Experimental and data processing Due to different experimental setups for STIM and PIXE, the measurements for ion micro-tomography have to be conducted in two series of experiments. Thereby, the sample is rotated stepwise over an angular range of 180° (STIM) and 360° (PIXE). Each projection is done by scanning a parallel ion beam over the sample and detecting the desired information. Mathematically, with the measurement a Radon transform of the specimen is performed. Thus, the original data can be obtained by the inverse operation. The method of choice is the BFP, an algorithm where the filter is Fourier transformed and then convoluted with the sinograms. Since discrete Fourier transformations always produce sidelobes a data set without disturbances is desired. 2.1. Sample preparation The phantom was prepared as follows: Since the range of 2.25 MeV protons in ZnO is close to 30 lm, a thick ZnO micro-wire of about 13 lm with a thin, triangular flag at its side was chosen from a pile. Simple electrostatics attached the wire to a steel needle, where it was fixed under a stereo-microscope with varnish by hand using a wooden toothpick. The varnish (division of superconductivity and magnetism, Universität Leipzig) is soluble in alcohol, thus the consistency was easily controllable. A mixture of varnish with oxide grains (SiO2, MnO2, Co3O4, Fe2O3, and K2Cr2O7) was prepared on an optical microscope slide. Again, using the toothpick a droplet of this mixture was put on the tip of the micro-wire. The needle is attached to a tomography sample holder and, with the help of the integrated microscope in the specimen chamber, is shifted and tilted to align the rotational axis with respect to the long axis of the specimen. During the experiment the projection angle of the specimen axis is controlled via a piezo driven rotary stage with an encoder resolution of 0.0001°. In case the specimen moves out of the field of view during rotation piezo driven linear stages in x- and z-direction with an encoder resolution of 0.1 lm and a stepper motor driven y stage (51,200 steps per revolution with 1 mm screw pitch) are used to correct the specimen position. 2.2. Data acquisition Since the expected sample damage by a STIM-T experiment is negligible (fluence of 50 protons per lm2), the STIM projection set was recorded first. The residual energy of the protons after traversing the sample was detected using a windowless PIN photodi-
ode (Hamamatsu 1223-01) with a resolution of 12 keV at full width at half-maximum (FWHM). The preamplifier Amptek A250 was mounted just beside the PIN-diode on the same circuit board directly into the vacuum chamber. The STIM projection set was measured over a 180° angular range with a step width of 1° resulting in 181 projections. The scan width of 40 40 lm2 was covered by 128 128 pixels. As object diaphragm micro-slits were used, thus the measurements were performed at a count rate of the PIN-diode of about 3000–4000 ions per second. Recording five events per pixel, the pure measurement time of all projections took about an hour. As the photodiode suffers from damage during the experiment due to ion implantation into the depletion area, the diode needs to be shifted slightly from time to time to expose a fresh region. The set of PIXE maps was recorded with an EG&G Ortec HPGedetector of the IGLET-X series with a detector area size of 95 mm2 at a crystal thickness of 10 mm. The measurement set covers an angular range of 360° in 22 steps (step width 16.363°). Each measurement was performed at a beam current of 200 pA to avoid electric charging of the sample. The scan width was again 40 40 lm now covered by 64 64 pixels. To apply the charge of 60 pC per pixel, the beam was scanned 200 times over the sample to reduce external influences and sample damage. This took about 20 min pure measurement time per map. The fast scan speed did not lead to any disturbances in the maps, due to a novel glass beam tube inside the scan coils. Since in usual beam tubes fast alternating magnetic fields induce eddy-currents the changing magnetic field is delayed. The new glass beam tube is coated with a silver layer inside. This layer avoids charging effects in the tube affecting the beam and due to linearly scratched paths circumvents the eddy-currents. 2.3. Pre-processing At the entrance point to the DISRA iteration procedure fully preprocessed data are needed. That is, aligned energy loss data for STIM and aligned PIXE maps with element marks of the contained elements. First, an overall energy spectrum of the STIM data is extracted from the event files, where each detected event is stored with its position and energy channel. Then, by identifying a maximum channel number, the spectra are cut off for further processing. Thus artificial counts caused by pile up are removed. Now, the projections are median filtered, excluding spurious and random events to contribute to the measured energy loss. With appropriate calibration parameters the channel data are converted to energy loss. Since the detector damage causes artifacts due to locally reduced sensitivity a threshold has been set. Pixel with an energy loss below this value are set to zero energy loss, thus artifacts due to detector damage are removed. From case to case one has to decide whether thresholding is necessary, because real, small energy loss data might get lost. If still some data artifacts exist in the projection data, they can be removed by an algorithm searching for spikes and plateaus. The parameters for this algorithm need to be adjusted manually to find the best result. On the one hand side, the corrections enhance the consistency of the reconstruction. On the other hand side, each correction step of the data may remove real data and reduce the accuracy of the reconstruction. Thus, one has to adjust the parameters carefully. The alignment of the STIM projections has been done manually, since the automatic alignment program did not succeed. However, the automatic alignment of the sinograms using the center-ofmass shifted on a sine curve enhanced the quality of the reconstruction. This was the final step for the STIM data pre-processing. Since the DISRA needs the data of each beam position consecutively, the list mode PIXE files had to be sorted, due to the recoding
M. Rothermel et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 2001–2005
procedure with 200 scans per map. As for the STIM data, an overall spectrum is extracted and a maximum channel identified. To identify the channels corresponding to the contained elements, the overall spectrum is deconvoluted. That is, the entire spectrum is reproduced by Gaussian curves. The characteristic X-ray lines of the contained elements have to be assigned to the main peaks and this information is stored in a file. Thus, the DISRA can assign the respective channels to the elements. Of course, the PIXE maps need to be aligned, too. Now the automatic part of the DISRA can be started. 2.4. Data-processing by the DISRA The pre-processed data are used to initiate a first sketchy tomogram that will be approximated to the real sample in the iteration steps. For the initial tomogram, the STIM projections are rearranged to a sinogram data set. Due to the different resolutions of Table 1 The parameters (here, exemplary the for the STIM data) used by the reconstruction procedures in the DISRA. The BFP algorithm just requires the angle range and bandwidth information (a lower bandwidth parameter leads to a smoother tomogram, but reduces details). The other parameters are used for the iteration process: consecutive projections sets are compared numerically by the normalized absolute error (comparison type 2) and the iteration process is stopped when this error is below the limit given by the convergence factor. The parameter ‘convergence name’ is not implemented, hence requires NULL or an arbitrary filename. The file specified for ‘iteration data’ just contains the number of the current iteration. A scaling of the mass density of the initial tomogram has not been necessary (init scale execution commented out in the DISRA-script). The mass density and mass fractions in the tomogram are initialized by combining the reconstructed energy loss data with a global a priori elemental composition. This contains the number of elements present, a specification of these elements and its relative amounts. Optionally, knowledge of a local elemental composition can be inserted from an extra file (local a priori name). By applying a MDL – calculated from the negative values in a radius of MDL spread size around the voxel – vacuum voxels are identified, thus even enhancing the convergence properties of the DISRA. Reconstruction parameters for STIM-T Convergence factor Convergence name Comparison type Angle range Bandwidth Init scale MDL spread size Iteration data Local apriori name Global apriori elements Global apriori data ...
0.01 NULL 2 180 0.5 0.00001 16 Iter.dat NULL 15 30,0.976 ...
2003
the projection sets (128 128 for STIM and 64 64 for PIXE) the PIXE data need to be scaled to the same extends as the STIM data to get reconstructions of the same size. Then, the PIXE data are rearranged to sinograms as well. The sinogram data are now reconstructed using the BFP algorithm. Corresponding parameters are listed in Table 1. From the resulting reconstructions the reconstruction noise is removed by setting a minimum detection limit (MDL). Afterwards, the reconstructions are merged into one data set. In the PIXE reconstruction data set the information for each element was stored in an array using the atomic number of the contained elements. Here, the atomic number ‘‘zero” remained free and the merging program simply overwrites this channel with the STIM data. With the complete reconstruction set containing the elemental distribution and the energy loss information the sketchy tomogram containing mass and weight fraction data is initialized, including a priori information about the sample composition. For convergence reasons the mass density of the initial tomogram is checked by simulating one STIM projection set and comparing it with the measured one, thus the mass density is scaled to be more realistic. Iterations: In each iteration step a complete set of STIM projections and PIXE maps is simulated with the parameters given in Table 2. This is a crucial point in the whole tomography data reconstruction, since the precision of the final tomogram depends on the physical phenomena included in the simulation. More details will be given in the next paragraph. The simulated data sets are rearranged to sinograms and reconstructed by the BFP algorithm. Thus, the comparison of the reconstruction of the simulated data and the reconstruction of the measured data delivers correction factors for each voxel and a new tomogram is calculated. Designating the initial tomogram as Ti, the reconstruction data of the measured data as Rexp and the reconstruction data of the simulated as Rsim, the new tomogram Ti+1 is T iþ1 ¼ T i Rexp =Rsim . To check whether the iteration should stop, the next projection data sets are calculated and compared with the measured data. This procedure numerically compares the projection data. A visual comparison is given in Fig. 1. If the error between the files is lower than a predefined convergence factor, the program indicates the DISRA to stop. Then, the last tomogram is accepted to represent the samples composition. The DISRA includes the following physical phenomena and data: The electronic stopping powers semi-empirical tabulated by Ziegler et al. [21]. Wherever more than one element is present, the stopping power is calculated using Bragg’s additivity rule [22]. Based
Table 2 The parameters used by the simulation procedures in the DISRA. Simulation parameters for STIM-T Experiment type (–) Projection angles (–) Angle range (–) Proton beam energy (MeV) Charge per pixel (pC) Proton beam width (lm) Proton beam height (lm) Scan pixels width (–) Scan pixels height (–) Energy low (keV) Energy high (keV) Sili diameter (mm) Sili distance (mm) Sili angle (deg) Detector type (–) Detector area size (–) X-ray step size (–) Proton step size (–)
Simulation parameters for PIXE-T STIM_only 181 180 2.25 0.0000008 0.3125 0.3125 128 128 250 2250 4.0 40.0 180 Point 1.0 1.0 1.0
Experiment type (–) Projection angles (–) Angle range (–) Proton beam energy (MeV) Charge per pixel (pC) Proton beam width (lm) Proton beam height (lm) Scan pixels width (–) Scan pixels height (–) Energy low (keV) Energy high (keV) Sili diameter (mm) Sili distance (mm) Sili angle (deg) Detector type (–) Detector area size (–) X-ray step size (–) Proton step size (–)
PIXE 22 360 2.25 60 0.625 0.625 64 64 1.0 20.0 9.75 25.0 45 Area 1.0 1.0 1.0
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M. Rothermel et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 2001–2005
Zn
Fe
sim. 0°
exp. 0°
sim. 0°
exp. 0°
sim. 82°
exp. 82°
sim. 82°
exp. 82°
Co
STIM
sim. 0°
exp. 0°
sim. 0°
epx. 0°
si m. 82°
exp. 82°
si m. 82°
exp. 82°
Fig. 1. Comparison of simulated and measured maps/projections. The exemplary mappings show the elemental distributions for Zn, Fe, and Co and the energy loss for the STIM projections at selected projections angles of 0° and 82°. Each projection has the dimension of 40 40 lm2.
on the energy of the proton beam at a specific voxel (from STIM simulation), the amount of characteristic X-ray quanta produced at this voxel is calculated. On their path through the sample the X-rays may undergo absorption as well as produce new X-rays in fluorescence processes. Both processes are taken into account using X-ray production cross section data and fluorescence yields as well as absorption coefficients from the GeoPIXE software package [23]. Furthermore, the detector is placed near to the sample to get a maximum solid angle. This causes the problem that X-ray quanta of the same emission voxel may be detected with different intensities due to their different paths through the sample. Up to now, the DISRA is the only algorithm taking into consideration the non-point-like geometry of the PIXE detector.
3. Results and discussion The computational power concerning 3D visualization has increased very fast the last years. Taking advantage of this progress we can visualize our tomography data interactively. That is, rotating the tomogram data freely or around fixed axes, reducing the opacity of each element and uncover hidden structures, moving along slices through the tomogram and investigate the slices in automatically refreshing windows, and more. Some images shown in Figs. 2 and 3 give an impression of the power of these possibilities. The DISRA code includes lots of important physical effects, e.g. X-ray attenuation and sophisticated mathematical processing,
Fig. 2. Visualization of the tomogram after 12 iteration steps. The colors represent the distribution of Zn (blue), Si (yellow), K (magenta), Mn (cyan), Fe (red), Co (green), and glue (grey, translucent). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
e.g. limitations on correction factors for convergence stability. However, it suffers from some limitations:
M. Rothermel et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 2001–2005
2005
increase, thus allowing the analysis of quantitative (trace) element distributions in biological specimens. Furthermore, a second PIXE detector is bought. The enlarged detection solid angle allows reducing the measurement time for a constant amount of detected X-ray events. Of course, the DISRA must be adapted to the new detector arrangement. Very recent development has reached to introduce even limited angle tomography to ion beam techniques, thus allowing even more practical applications where samples could not be mounted free-standing. In this case the sinograms must be interpolated to angular range where the projections could not be measured. This may be included to the DISRA as well. Acknowledgements We thankfully acknowledge A. Sakellariou (Australian National University, Canberra) for the DISRA source code and C. Czekalla (Universität Leipzig, Semiconductor Physics Group) for the ZnO micro-wires. M. Rothermel and T. Andrea are funded by the DFG graduate school 185 ‘‘Leipzig School of Natural Sciences – Building with Molecules and Nano-objects” (BuildMoNa). We like to acknowledge the advice and support of M.A. Jakob, Ch. Meinecke and D. Spemann. References
Fig. 3. (a) The rings indicate the fixed angle rotation possibility, (b) the light cyan parallelograms indicate the present slice that can be investigated in a dependent window. The color code is the same as in Fig. 2.
– Just one X-ray line of an element can be used. The introduction of dynamic analysis for Ka/Kb ratio would be desirable, enabling a more precise analysis of the spectra, especially if heavier elements are present, from which mainly L-lines are detected. – Improvements in the alignment procedure [24] need to be included. Up to now the data sets of STIM and PIXE are aligned separately. The conjoint alignment may increase the consistency of the tomogram and may lead to better convergence. Furthermore, measurement automation needs to be implemented at LIPSION. A new overall user-friendly interface for data accumulation and analysis needs to be developed to make this technique available and interesting to more ion beam laboratories which have the requirements for tomography. Concerning instrumentation, advances in performance are underway, aiming on resolution enhancements and beam current
[1] A. Sakellariou, M. Cholewa, A. Saint, G.J.F. Legge, Meas. Sci. Technol. 8 (1997) 746–758. [2] J.L. Prince, A.S. Willsky, Opt. Eng. 29 (1990) 534–544. [3] T. Andrea, M. Rothermel, R. Werner, T. Butz, T. Reinert, Nucl. Instr. Meth. B 268 (2010) 1884–1888. [4] J. Vogt, R.-H. Flagmeyer, J. Heitmann, D. Lehmann, T. Reinert, S. Jankuhn, D. Spemann, W. Tröger, T. Butz, Mikrochim. Acta 133 (2000) 105–111. [5] T. Reinert, U. Reibetanz, J. Vogt, T. Butz, A. Werner, W. Gründer, Nucl. Instr. Meth. Phys. Res. B 181 (2001) 511–515. [6] A.M. Cormack, A.M. Koehler, Phys. Med. Biol. 21/4 (1976) 560–569. [7] A. Pontau, A.J. Antolak, D.H. Morse, A.A. Ver Berkmoes, J.M. Brase, D.W. Heikkinen, H.E. Martz, I.D. Procter, Nucl. Instr. Meth. B 40/41 (1989) 646– 650. [8] B.E. Fischer, C. Mühlbauer, Nucl. Instr. Meth. B 47 (1990) 271–282. [9] G.S. Bench, K.A. Nugent, Nucl. Instr. Meth. B 54 (1991) 390–396. [10] C. Michelet, PhD thesis, Université Bordeaux I, 1998. [11] M. Schwertner, A. Sakellariou, T. Reinert, T. Butz, Ultramicroscopy 106 (2006) 574–581. [12] A. Sakellariou, D.N. Jamieson, G.J.F. Legge, Nucl. Instr. Meth. B 181 (2001) 211– 218. [13] C. Michelet, Ph. Moretto, Nucl. Instr. Meth. B 150 (1999) 173–178. [14] T. Andrea, M. Rothermel, T. Butz, T. Reinert, Nucl. Instr. Meth. B 267 (2009) 2098–2102. [15] D. Beasley, N.M. Spyrou, J. Rad. Nucl. Chem. 264 (2) (2005) 289–294. [16] M. Wegdén, M. Elfman, P. Kristiansson, N. Arteaga Marrero, V. Auzelyte, K.G. Malmqvist, C. Nilsson, J. Pallon, Nucl. Instr. Meth. B 249 (2006) 756–759. [17] C. Habchi, D.T. Nguyen, Ph. Barberet, S. Incerti, Ph. Moretto, A. Sakellariou, H. Seznec, Nucl. Instr. Meth. B 267 (2009) 2107–2112. [18] C. Habchi, D.T. Nguyen, G. Devès, S. Incerti, L. Lemelle, P. Le Van Vang, Ph. Moretto, R. Ortega, H. Seznec, A. Sakellariou, C. Sergeant, A. Simionovici, M.D. Ynsa, E. Gontier, M. Heiss, T. Pouthier, A. Boudou, F. Rebilla, Nucl. Instr. Meth. B 249 (2006) 653–659. [19] A. Sakellariou, M. Cholewa, A. Saint, G.J.F. Legge, Nucl. Instr. Meth. B 130 (1997) 253–258. [20] http://www.ittvis.com/ProductServices/IDL.aspx. [21] J.F. Ziegler, J.B. Biersack, U. Littmark, The Stopping and Range of Ions in Matter, Pergamon Press, New York, 1985. [22] W.H. Bragg, R. Kleeman, Philos. Mag. 10 (1905) 318–340. [23] C.G. Ryan, D.R. Cousens, S.H. Sie, W.L. Griffin, G.F. Suter, E. Clayton, Nucl. Instr. Meth. B 47 (1990) 55. [24] T. Andrea, Diploma thesis, Universität Leipzig, 2009.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
First results on ion micro-tomography at LIPSION M. Rothermel *, T. Reinert, T. Andrea, T. Butz Institute for Experimental Physics II, Department of Nuclear Solid-State Physics, University of Leipzig, Linnéstraße 5, 04103 Leipzig, Germany
a r t i c l e
i n f o
Article history: Available online 26 February 2010 Keywords: STIM PIXE Tomography
a b s t r a c t At the nanoprobe LIPSION ion micro-tomography can be used to determine the 3D distribution information of a sample’s mass density and elemental composition. For ion micro-tomography the two analytical techniques scanning transmission ion microscopy tomography (STIM-T) and particle induced X-ray emission tomography (PIXE-T) are combined. The required data are collected in two consecutive series of measurements, during which the sample is rotated by 180°/360° in small steps. Because all ions have to traverse the sample, the upper limit of the sample size is given by the range of the ions in the material. The tomogram is obtained using the discrete image space reconstruction algorithm (DISRA) by Sakellariou (1997) [1]. This algorithm iteratively corrects a sketchy initial tomogram estimated from the experimental reconstruction – obtained by backprojection of filtered projections (BFP) – and an a priori elemental composition. The necessary correction factors are calculated comparing the reconstruction of the experimental data with the reconstruction of simulated data. For the simulated data sets of STIM projections and PIXE maps are computed from the tomogram. These data sets are proceeded with the BFP algorithm to get simulated reconstruction data. Using the DISRA for ion micro-tomography, one can benefit from the high resolution of STIM-T by transferring it to the elemental distribution given by PIXE-T. This article presents first results of this technique applied on a phantom at the LIPSION facility. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction The technique of ion micro-tomography (IMT) provides 3D information about a sample’s mass density and elemental composition. Although applications still remain scarce, reaching a spatial resolution of less than a 1 lm this technique becomes more and more interesting for lots of applications in materials research as well as life sciences. Whereas some micro-tomographical techniques need to cut the sample into slices, the sole preparation step for IMT is to mount the sample freestanding, thus enabling a nondestructive analysis. The very recent development of limited angle tomography [2] with ion beams [3] even allows mounting the samples on thin foils or Si3N4-windows. Despite the larger efforts – compared to commercially available X-ray tomography devices – the additional elemental information as well as the better density resolution demonstrate the advantages of this technique. Ion micro-tomography combines the two analytical techniques scanning transmission ion microscopy tomography (STIM-T) and particle induced X-ray emission tomography (PIXE-T). In combination with a computer algorithm suited to ion micro-tomography to
* Corresponding author. Address: Fakultät für Physik und Geowissenschaften, Universität Leipzig, Linnéstr. 5, D-04103 Leipzig, Germany. Tel.: +49 341 97 32709; fax: +49 341 97 32708. E-mail address: [email protected] (M. Rothermel). URL: http://www.uni-leipzig.de/~nfp (M. Rothermel). 0168-583X/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2010.02.117
reconstruct the data, the technique can benefit from the high spatial resolution of STIM-T by transferring it the elemental distribution given by PIXE-T. Nevertheless, the spatial resolution in STIM and PIXE mode need to be comparable. This is available at the high energy nanoprobe in the LIPSION laboratory [4,5]. The required data are collected in two consecutive series of measurements, during which the sample is rotated in small steps. The large range of high energy ions in matter allows the measurement of information deep inside the sample. The only restriction is that the ions have to traverse the sample, giving an upper limit of typically some tens of micrometers using 2.25 MeV protons. Although the need for tomography was mainly driven by medical applications, the principle can easily be transferred to focused ion beam techniques. Starting with Cormack and Koehler in 1976 (128 MeV proton beam with a diameter of 2 mm) [6], this technique was progressed to ion micro beams by Pontau and Fischer [7,8]. In the 1990s computational power and the availability of sub-micron ion beams boost the possibilities of ion tomography, reaching practical biological applications [9–11]. This experience of other laboratories [12,13] (especially Melbourne) paved the way for STIM-T experiments at the Leipzig high energy nanoprobe LIPSION [11,14]. Whereas STIM-T nowadays is well established in several groups [12–16], there remained some obstacles regarding PIXE-T [17,18]. In contrast to STIM-T, where simple median filtering of few detected energy loss events suffices for adequate statistics, the physical phenomena in PIXE-T are more complex. Besides
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M. Rothermel et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 2001–2005
variations of the X-ray production cross section along an ion’s trajectory, a major problem to obtain quantitative information in PIXE-T is the need to correct the X-ray yields because of attenuation and attenuation variations inside the sample. Since X-rays emitted from one point in the sample may undergo different attenuations on their path to the detector, the total detector solid angle needs to be subdivided for simulation purposes, thus taking into account the cone-beam geometry of the X-ray detection. To overcome this problem caused by the sample geometry and local composition variations in quantitative analysis, a successive approximation to the real composition of the sample is necessary. A reconstruction code including the most important physical effects as well as taking into consideration convergence criteria of the iteration process was proposed and tested by Sakellariou’s DISRA [1,19]. This article enlightens the procedure to derive a 3D tomogram from the measured data using a phantom consisting of a ZnO micro-wire and oxide grains and introduces to the interactive, real-time 3D visualization possibilities of the IDL software [20]. 2. Experimental and data processing Due to different experimental setups for STIM and PIXE, the measurements for ion micro-tomography have to be conducted in two series of experiments. Thereby, the sample is rotated stepwise over an angular range of 180° (STIM) and 360° (PIXE). Each projection is done by scanning a parallel ion beam over the sample and detecting the desired information. Mathematically, with the measurement a Radon transform of the specimen is performed. Thus, the original data can be obtained by the inverse operation. The method of choice is the BFP, an algorithm where the filter is Fourier transformed and then convoluted with the sinograms. Since discrete Fourier transformations always produce sidelobes a data set without disturbances is desired. 2.1. Sample preparation The phantom was prepared as follows: Since the range of 2.25 MeV protons in ZnO is close to 30 lm, a thick ZnO micro-wire of about 13 lm with a thin, triangular flag at its side was chosen from a pile. Simple electrostatics attached the wire to a steel needle, where it was fixed under a stereo-microscope with varnish by hand using a wooden toothpick. The varnish (division of superconductivity and magnetism, Universität Leipzig) is soluble in alcohol, thus the consistency was easily controllable. A mixture of varnish with oxide grains (SiO2, MnO2, Co3O4, Fe2O3, and K2Cr2O7) was prepared on an optical microscope slide. Again, using the toothpick a droplet of this mixture was put on the tip of the micro-wire. The needle is attached to a tomography sample holder and, with the help of the integrated microscope in the specimen chamber, is shifted and tilted to align the rotational axis with respect to the long axis of the specimen. During the experiment the projection angle of the specimen axis is controlled via a piezo driven rotary stage with an encoder resolution of 0.0001°. In case the specimen moves out of the field of view during rotation piezo driven linear stages in x- and z-direction with an encoder resolution of 0.1 lm and a stepper motor driven y stage (51,200 steps per revolution with 1 mm screw pitch) are used to correct the specimen position. 2.2. Data acquisition Since the expected sample damage by a STIM-T experiment is negligible (fluence of 50 protons per lm2), the STIM projection set was recorded first. The residual energy of the protons after traversing the sample was detected using a windowless PIN photodi-
ode (Hamamatsu 1223-01) with a resolution of 12 keV at full width at half-maximum (FWHM). The preamplifier Amptek A250 was mounted just beside the PIN-diode on the same circuit board directly into the vacuum chamber. The STIM projection set was measured over a 180° angular range with a step width of 1° resulting in 181 projections. The scan width of 40 40 lm2 was covered by 128 128 pixels. As object diaphragm micro-slits were used, thus the measurements were performed at a count rate of the PIN-diode of about 3000–4000 ions per second. Recording five events per pixel, the pure measurement time of all projections took about an hour. As the photodiode suffers from damage during the experiment due to ion implantation into the depletion area, the diode needs to be shifted slightly from time to time to expose a fresh region. The set of PIXE maps was recorded with an EG&G Ortec HPGedetector of the IGLET-X series with a detector area size of 95 mm2 at a crystal thickness of 10 mm. The measurement set covers an angular range of 360° in 22 steps (step width 16.363°). Each measurement was performed at a beam current of 200 pA to avoid electric charging of the sample. The scan width was again 40 40 lm now covered by 64 64 pixels. To apply the charge of 60 pC per pixel, the beam was scanned 200 times over the sample to reduce external influences and sample damage. This took about 20 min pure measurement time per map. The fast scan speed did not lead to any disturbances in the maps, due to a novel glass beam tube inside the scan coils. Since in usual beam tubes fast alternating magnetic fields induce eddy-currents the changing magnetic field is delayed. The new glass beam tube is coated with a silver layer inside. This layer avoids charging effects in the tube affecting the beam and due to linearly scratched paths circumvents the eddy-currents. 2.3. Pre-processing At the entrance point to the DISRA iteration procedure fully preprocessed data are needed. That is, aligned energy loss data for STIM and aligned PIXE maps with element marks of the contained elements. First, an overall energy spectrum of the STIM data is extracted from the event files, where each detected event is stored with its position and energy channel. Then, by identifying a maximum channel number, the spectra are cut off for further processing. Thus artificial counts caused by pile up are removed. Now, the projections are median filtered, excluding spurious and random events to contribute to the measured energy loss. With appropriate calibration parameters the channel data are converted to energy loss. Since the detector damage causes artifacts due to locally reduced sensitivity a threshold has been set. Pixel with an energy loss below this value are set to zero energy loss, thus artifacts due to detector damage are removed. From case to case one has to decide whether thresholding is necessary, because real, small energy loss data might get lost. If still some data artifacts exist in the projection data, they can be removed by an algorithm searching for spikes and plateaus. The parameters for this algorithm need to be adjusted manually to find the best result. On the one hand side, the corrections enhance the consistency of the reconstruction. On the other hand side, each correction step of the data may remove real data and reduce the accuracy of the reconstruction. Thus, one has to adjust the parameters carefully. The alignment of the STIM projections has been done manually, since the automatic alignment program did not succeed. However, the automatic alignment of the sinograms using the center-ofmass shifted on a sine curve enhanced the quality of the reconstruction. This was the final step for the STIM data pre-processing. Since the DISRA needs the data of each beam position consecutively, the list mode PIXE files had to be sorted, due to the recoding
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procedure with 200 scans per map. As for the STIM data, an overall spectrum is extracted and a maximum channel identified. To identify the channels corresponding to the contained elements, the overall spectrum is deconvoluted. That is, the entire spectrum is reproduced by Gaussian curves. The characteristic X-ray lines of the contained elements have to be assigned to the main peaks and this information is stored in a file. Thus, the DISRA can assign the respective channels to the elements. Of course, the PIXE maps need to be aligned, too. Now the automatic part of the DISRA can be started. 2.4. Data-processing by the DISRA The pre-processed data are used to initiate a first sketchy tomogram that will be approximated to the real sample in the iteration steps. For the initial tomogram, the STIM projections are rearranged to a sinogram data set. Due to the different resolutions of Table 1 The parameters (here, exemplary the for the STIM data) used by the reconstruction procedures in the DISRA. The BFP algorithm just requires the angle range and bandwidth information (a lower bandwidth parameter leads to a smoother tomogram, but reduces details). The other parameters are used for the iteration process: consecutive projections sets are compared numerically by the normalized absolute error (comparison type 2) and the iteration process is stopped when this error is below the limit given by the convergence factor. The parameter ‘convergence name’ is not implemented, hence requires NULL or an arbitrary filename. The file specified for ‘iteration data’ just contains the number of the current iteration. A scaling of the mass density of the initial tomogram has not been necessary (init scale execution commented out in the DISRA-script). The mass density and mass fractions in the tomogram are initialized by combining the reconstructed energy loss data with a global a priori elemental composition. This contains the number of elements present, a specification of these elements and its relative amounts. Optionally, knowledge of a local elemental composition can be inserted from an extra file (local a priori name). By applying a MDL – calculated from the negative values in a radius of MDL spread size around the voxel – vacuum voxels are identified, thus even enhancing the convergence properties of the DISRA. Reconstruction parameters for STIM-T Convergence factor Convergence name Comparison type Angle range Bandwidth Init scale MDL spread size Iteration data Local apriori name Global apriori elements Global apriori data ...
0.01 NULL 2 180 0.5 0.00001 16 Iter.dat NULL 15 30,0.976 ...
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the projection sets (128 128 for STIM and 64 64 for PIXE) the PIXE data need to be scaled to the same extends as the STIM data to get reconstructions of the same size. Then, the PIXE data are rearranged to sinograms as well. The sinogram data are now reconstructed using the BFP algorithm. Corresponding parameters are listed in Table 1. From the resulting reconstructions the reconstruction noise is removed by setting a minimum detection limit (MDL). Afterwards, the reconstructions are merged into one data set. In the PIXE reconstruction data set the information for each element was stored in an array using the atomic number of the contained elements. Here, the atomic number ‘‘zero” remained free and the merging program simply overwrites this channel with the STIM data. With the complete reconstruction set containing the elemental distribution and the energy loss information the sketchy tomogram containing mass and weight fraction data is initialized, including a priori information about the sample composition. For convergence reasons the mass density of the initial tomogram is checked by simulating one STIM projection set and comparing it with the measured one, thus the mass density is scaled to be more realistic. Iterations: In each iteration step a complete set of STIM projections and PIXE maps is simulated with the parameters given in Table 2. This is a crucial point in the whole tomography data reconstruction, since the precision of the final tomogram depends on the physical phenomena included in the simulation. More details will be given in the next paragraph. The simulated data sets are rearranged to sinograms and reconstructed by the BFP algorithm. Thus, the comparison of the reconstruction of the simulated data and the reconstruction of the measured data delivers correction factors for each voxel and a new tomogram is calculated. Designating the initial tomogram as Ti, the reconstruction data of the measured data as Rexp and the reconstruction data of the simulated as Rsim, the new tomogram Ti+1 is T iþ1 ¼ T i Rexp =Rsim . To check whether the iteration should stop, the next projection data sets are calculated and compared with the measured data. This procedure numerically compares the projection data. A visual comparison is given in Fig. 1. If the error between the files is lower than a predefined convergence factor, the program indicates the DISRA to stop. Then, the last tomogram is accepted to represent the samples composition. The DISRA includes the following physical phenomena and data: The electronic stopping powers semi-empirical tabulated by Ziegler et al. [21]. Wherever more than one element is present, the stopping power is calculated using Bragg’s additivity rule [22]. Based
Table 2 The parameters used by the simulation procedures in the DISRA. Simulation parameters for STIM-T Experiment type (–) Projection angles (–) Angle range (–) Proton beam energy (MeV) Charge per pixel (pC) Proton beam width (lm) Proton beam height (lm) Scan pixels width (–) Scan pixels height (–) Energy low (keV) Energy high (keV) Sili diameter (mm) Sili distance (mm) Sili angle (deg) Detector type (–) Detector area size (–) X-ray step size (–) Proton step size (–)
Simulation parameters for PIXE-T STIM_only 181 180 2.25 0.0000008 0.3125 0.3125 128 128 250 2250 4.0 40.0 180 Point 1.0 1.0 1.0
Experiment type (–) Projection angles (–) Angle range (–) Proton beam energy (MeV) Charge per pixel (pC) Proton beam width (lm) Proton beam height (lm) Scan pixels width (–) Scan pixels height (–) Energy low (keV) Energy high (keV) Sili diameter (mm) Sili distance (mm) Sili angle (deg) Detector type (–) Detector area size (–) X-ray step size (–) Proton step size (–)
PIXE 22 360 2.25 60 0.625 0.625 64 64 1.0 20.0 9.75 25.0 45 Area 1.0 1.0 1.0
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Zn
Fe
sim. 0°
exp. 0°
sim. 0°
exp. 0°
sim. 82°
exp. 82°
sim. 82°
exp. 82°
Co
STIM
sim. 0°
exp. 0°
sim. 0°
epx. 0°
si m. 82°
exp. 82°
si m. 82°
exp. 82°
Fig. 1. Comparison of simulated and measured maps/projections. The exemplary mappings show the elemental distributions for Zn, Fe, and Co and the energy loss for the STIM projections at selected projections angles of 0° and 82°. Each projection has the dimension of 40 40 lm2.
on the energy of the proton beam at a specific voxel (from STIM simulation), the amount of characteristic X-ray quanta produced at this voxel is calculated. On their path through the sample the X-rays may undergo absorption as well as produce new X-rays in fluorescence processes. Both processes are taken into account using X-ray production cross section data and fluorescence yields as well as absorption coefficients from the GeoPIXE software package [23]. Furthermore, the detector is placed near to the sample to get a maximum solid angle. This causes the problem that X-ray quanta of the same emission voxel may be detected with different intensities due to their different paths through the sample. Up to now, the DISRA is the only algorithm taking into consideration the non-point-like geometry of the PIXE detector.
3. Results and discussion The computational power concerning 3D visualization has increased very fast the last years. Taking advantage of this progress we can visualize our tomography data interactively. That is, rotating the tomogram data freely or around fixed axes, reducing the opacity of each element and uncover hidden structures, moving along slices through the tomogram and investigate the slices in automatically refreshing windows, and more. Some images shown in Figs. 2 and 3 give an impression of the power of these possibilities. The DISRA code includes lots of important physical effects, e.g. X-ray attenuation and sophisticated mathematical processing,
Fig. 2. Visualization of the tomogram after 12 iteration steps. The colors represent the distribution of Zn (blue), Si (yellow), K (magenta), Mn (cyan), Fe (red), Co (green), and glue (grey, translucent). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
e.g. limitations on correction factors for convergence stability. However, it suffers from some limitations:
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increase, thus allowing the analysis of quantitative (trace) element distributions in biological specimens. Furthermore, a second PIXE detector is bought. The enlarged detection solid angle allows reducing the measurement time for a constant amount of detected X-ray events. Of course, the DISRA must be adapted to the new detector arrangement. Very recent development has reached to introduce even limited angle tomography to ion beam techniques, thus allowing even more practical applications where samples could not be mounted free-standing. In this case the sinograms must be interpolated to angular range where the projections could not be measured. This may be included to the DISRA as well. Acknowledgements We thankfully acknowledge A. Sakellariou (Australian National University, Canberra) for the DISRA source code and C. Czekalla (Universität Leipzig, Semiconductor Physics Group) for the ZnO micro-wires. M. Rothermel and T. Andrea are funded by the DFG graduate school 185 ‘‘Leipzig School of Natural Sciences – Building with Molecules and Nano-objects” (BuildMoNa). We like to acknowledge the advice and support of M.A. Jakob, Ch. Meinecke and D. Spemann. References
Fig. 3. (a) The rings indicate the fixed angle rotation possibility, (b) the light cyan parallelograms indicate the present slice that can be investigated in a dependent window. The color code is the same as in Fig. 2.
– Just one X-ray line of an element can be used. The introduction of dynamic analysis for Ka/Kb ratio would be desirable, enabling a more precise analysis of the spectra, especially if heavier elements are present, from which mainly L-lines are detected. – Improvements in the alignment procedure [24] need to be included. Up to now the data sets of STIM and PIXE are aligned separately. The conjoint alignment may increase the consistency of the tomogram and may lead to better convergence. Furthermore, measurement automation needs to be implemented at LIPSION. A new overall user-friendly interface for data accumulation and analysis needs to be developed to make this technique available and interesting to more ion beam laboratories which have the requirements for tomography. Concerning instrumentation, advances in performance are underway, aiming on resolution enhancements and beam current
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