Copyright -International Centre for Diffraction Data 2010 ISSN 1097-0002 CALCULATION METHODS OF X-RAY SPECTRA: A COMPARATIVE STUDY B. Chyba, M. Mantler, H. Ebel, R. Svagera Technische Universit Vienna, Austria ABSTRACT The accurate characterization of the spectral distribution of x-rays emitted from X-ray tubes is crucial in many analytical investigations. This includes the primary production of radiation within the tube target as well as absorption by the tube window and eventually applied filters. This paper discusses two calculation methods for tube spectra: an analytical program based on algorithms by H. Ebel and the MCNP software package based on Monte-Carlo code. The calculated data were also compared to measured spectra generated on a SEM with Au and Cu targets at voltages from 10kV to 30kV. INTRODUCTION The most accurate method to simulate x-ray tube spectra is perhaps based on calculating a large number of scattering paths of electrons in the target anode using Monte-Carlo methods (Booth et al., 2003). At each point of interaction bremsstrahlung and/or characteristic radiation can be induced. The varying distances of the photon source to exit points and absorption lead to a direction dependent spectral distribution and intensity of the emitted tube radiation. The accurate calculation is, however, at the cost of computing time. A simplification is to average the electron cloud into a single point inside the target by Figure 1. MC simulation of scattered electron paths inside a target Figure 2. Simplified model using an average penetration depth for impinging electrons introducing an energy dependent mean penetration depth of electrons, shown in Fig. 2. This is accomplished by the analytical calculation model of H. Ebel (1989, 1999, 2003, 2006). 243
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Copyright -International Centre for Diffraction Data 2010 ISSN 1097-0002 244 Calculation times are orders of magnitudes shorter than using MC-methods (about 1s compared to 4h), but the model is currently limited to energies up to 50keV; reliable experimental data for higher energies are extremely rare. Apparently the MC-method is the only alternative to provide spectra at higher energies up to several hundreds of kev. Such tube voltages are common in industrial computed tomography and spectral data are required to support simulations employed for optimizations and improvement of experimental parameters (Chyba et al., 2008). A topical example is computed tomography (CT) where the demand for increased image resolution causes twofold problems: In clinical diagnostics the absorbed dose of the radiation from a CT device by the patient may already come to a critical level according to recommended dose limits, which makes the need for dose calculations obvious. On the other hand, accurate non-destructive material testing in industry based on CT with cone beam geometry requires detailed mathematical modelling of all interactions of the primary beam with the analyzed object including scattering and excitation of secondary radiation; such data can be used for proper interpretation of the measured image as well as for finding optimized conditions for a measurement. This paper investigates the applicability and possible limitations of MC-methods. We used MCNP as well as H.Ebel's analytical model to compute spectra and compared data from both sources with available experimental data within the matching energy ranges which are however limited to 30keV and below. Simulations include also high energy spectra for up to 450kV tube voltage. INSTRUMENTATION The experimental X-ray spectra shown in this work are from two different target materials (Au, Cu); they are part of the collection used for the development of Ebel's model and have been measured on a scanning electron microscope at the Vienna University of Technology with a Si(Li) detector and electron energies from 10 to 30kV. (Detector model: Edax New XL-30 135-10 UTW+; detecting unit: PV 9760/69ME; port: back left upper; active area: 10mm 2 ; amplifier model: 194) The same energy dependent detector efficiency that was used by Ebel was applied to the MC data for comparison of the spectra. It is based on a simple 3 layer absorption model (window, inactive absorbing layer, active crystal). The software used for the analytical calculations of tube spectra has been developed at the Institute of Solid State Physics, Vienna University of Technology. It implements the Ebel formula (2006) and uses cross-section and fluorescence data from Cullen et al. (1997). RESULTS
Copyright -International Centre for Diffraction Data 2010 ISSN 1097-0002 Measured and simulated spectra obtained at 10kV and 30kV for target materials Au and Cu are shown in Fig. 3. While the good agreement between the analytical model and experiment has already been demonstrated elsewhere (Ebel, 1989, 1999, 2003, 2006) the current interest focuses on the Monte-Carlo spectra. At higher energies their match with the others is excellent as well. The differences at low energies are due to the energy cut off at 1keV (affecting all Cu L-lines) and several M-lines (of Au) missing in the database of MCNP. While the Ebel model is specified to work for energies below 50keV, it was also tried to apply the algorithm to higher energies and compare the result with MCNP. Fig. 4 shows the 100kV spectrum of a W-target as well as the region around the K- and L-absorption edges and emission lines in high magnification. Again good agreement is achieved between both computational methods except for the characteristic lines. MCNP seems to replace the many individual L-lines by a few lines summing up their intensities, and omit most or all M-lines. Both programs cut off energies below 1keV. Figure 3: Comparison of measured and computed x-ray spectra for Au and Cu targets at voltages of 10 and 30kV; electron beam is perpendicular to target surface, photon takeoff angle is 30. 245
Copyright -International Centre for Diffraction Data 2010 ISSN 1097-0002 Figure 4: Top: Comparison of theoretical tube spectra (W-target, 100kV) computed with the analytical model and MCNP. Bottom: Enlarged regions near the L- and K- absorption edges. CONCLUSION The important result is that MC models seem to be well suited for simulating the spectral distribution of tube radiation at very high excitation voltages up to several 100 kv. As far as experimental data were available the agreement with the simulation of continuous radiation was very good. For applications where computing times are a limiting factor, the Ebel model may be an alternative; so far it showed good agreement for tungsten targets up to 100keV but a general extension of its validity to higher energies requires further investigations. The MCNP code allows a rather detailed definition of the tube geometry but exhibits serious deficits with respect to individual L- and M-line representations. A general disadvantage is the low energy cut-off at 1 kev. 246
Copyright -International Centre for Diffraction Data 2010 ISSN 1097-0002 247 REFERENCES Booth, T. E., Brown, F. B., Bull, J. S., Forster, R. A., Goorley, J. T., Hughes, H.G.,Mosteller,R.D.,Prael,R.E.,Sood,A.,Sweezy,J.E.,Zukaitis, A., Marsha Boggs, M., and Roger Martz, R. (2003). MCNP - A general Monte Carlo N-particle transport code, Report LAUR 03-1987, Los Alamos National Laboratory, Los Alamos, NM. Chyba, B., Mantler, M., Reiter, M. (2008). Monte-Carlo Simulation of Projections in Computed Tomography, Powder Diffraction 23 (2), 150-153 Cullen, D. E., Hubbel, J. H., Kissel, L. D. (1997): EPDL97: The Evaluated Photon Data Library, '97 Version, Report UCRL-50400, Vol. 6, Rev. 5, Lawrence Livermore National Laboratory, Livermore, CA Ebel, H., Ebel, M.F., Wernisch, J., Poehn, Ch., Wiederschwinger, H. (1989). of continuous and characteristic tube spectra for fundamental parameter analysis, X-Ray Spectrom. 18, 89-100 Ebel,H.(1999). X-ray tube spectra X-Ray Spectrom. 27, 255-266 Ebel,H.(2003). X-Ray Spectrom. 32, 46-51 Ebel,H.(2006). Fundamental Parameter Programs: Algorithms for the Description of K, L andmspectraof X-rayTubes, Adv.X-Ray Anal.49, 267-273 ACKNOWLEDGEMENT This work was supported by the project 812136-SCK/KUG. Correspondence: Michael Mantler Vienna University of Technology Wiedner Hauptstrasse 8-10/138 A 1040 Vienna, Austria Phone (43-1) 58801-13761 Fax: (43-1) 58801-13799 Email: michael.mantler@ifp.tuwien.ac.at