Issues in energy calibration, nonlinearity, and signal processing for gamma-ray microcalorimeter detectors N. Hoteling, M. K. Bacrania, A. S. Hoover, M. W. Rabin, M. Croce, P. J. Karpius, J. N. Ullom, D. A. Bennett, R. D. Horansky, L. R. Vale, and W. B. Doriese Citation: AIP Conference Proceedings 1185, 711 (2009); View online: https://doi.org/10.1063/1.3292440 View Table of Contents: http://aip.scitation.org/toc/apc/1185/1 Published by the American Institute of Physics Articles you may be interested in A high resolution gamma-ray spectrometer based on superconducting microcalorimeters Review of Scientific Instruments 83, 093113 (2012); 10.1063/1.4754630 An analytical model for pulse shape and electrothermal stability in two-body transition-edge sensor microcalorimeters Applied Physics Letters 97, 102504 (2010); 10.1063/1.3486477 Issues in energy calibration, nonlinearity, and signal processing for gamma-ray microcalorimeter detectors N. Hoteling*, M. K. Bacrania*, A. S. Hoover*, M. W. Rabin*, M. Croce*, P. J. Karpius*, J. N. Ullom''', D. A. Bennett''', R. D. Horansky''', L. R. Vale''' and W. B. Doriese''' *Los Alamos National Laboratory, Los Alamos, NM "^National Institute of Standards and Technology, Boulder, CO Abstract. Issues regarding the energy calibration of high dynamic range microcalorimeter detector arrays are presented with respect to new results from a minor actinide-mixed oxide radioactive source. The need to move to larger arrays of such detectors necessitates the implementation of automated analysis procedures, which turn out to be nontrivial due to complex calibration shapes and pixel-to-pixel variability. Some possible avenues for improvement, including a more physics-based calibration procedure, are suggested. Keywords: microcalorimeter, energy calibration, optimal filter INTRODUCTION times become comparable. This scheme quickly renders the conventional by-hand analysis unfeasible and thus the need for automation arises. This, however, turns out to be a nontrivial step, as will be described in detail in this paper Microcalorimeter detectors offer the promise of significant improvements in energy resolution over traditional methods of 7-ray spectroscopy. Thus, it is clearly important to extend the capabilities of these systems to higher energies where a wealth of new applications can be explored. Recent advances in detector design and fabrication have allowed for the construction of large arrays, including the instrument operated by this group which presently holds a muhiplexed array of 64 pixels, about 35 of which have been successfully operated to date with energy ranges up to '-.'200 keV and energy resolution typically under 100 eV. With this groundbreaking new instrument, new regions of the energy spectrum which include 7 rays and hard x rays have been studied for nuclear materials that are of interest to the nuclear safeguards community, such as highly enriched uranium, mixed plutonium samples, and a minor actinide-mixed oxide (MA-MOX) pellet. The latter is a synthetic reproduction of reprocessed fuel designed for research purposes and will make up the bulk of analysis presented in this work. The spectrum, seen in Figure 1, offers the possibility for an improved quantitative analysis of Pu isotopics since the complex spectral regions are much more easily disentangled with the superior resolution of the microcalorimeter detector. However, this instrument in its present state suffers from a small active area and large signal time constants, so that an HPGe detector requires a significantly reduced counting time. One solution to this is to construct large detector arrays (a 256-pixel array will have comparable active area to a planar HPGe detector) such that the counting ENERGY CALIBRATION The superior energy resolution achievable with microcalorimeter detectors represents this technology's most intriguing property. However, such an excellent quality comes at a price as it mandates an extremely accurate energy calibration, particularly in such cases where many detectors are to be compared or summed. Nowhere is this more evident than in systems with comparatively large dynamic range. In the case described here where the energy range extends to '^200 keV with energy resolution '-.'80 eV, a systematic deviation of 100 eV can produce distinct doublets in summed spectra, and offsets as small as 50 eV will produce noticeably distorted peak shapes, as illustrated in Figure 2. Thus, for a many-pixel array, energy calibration must obtain accuracy better than 0.02%, a requirement that is unparalleled in transition-edge sensor (TES) detectors. At present, most measurements reported in the literature [1, 2] present data fitted to some high-order polynomial, a method that works reasonably well when spectra contain a high density of lines with well-known peak energies, but falls short when peaks are sparse, not well known, or if the dynamic range is large. Figure 3 displays the resuhs of a sixth-order polynomial fit to the MA-MOX data described above. This source is presum- CP1185,Low Temperature Detectors LTD 13, Proceedings of the 13^ International Workshop edited by B. Cabrera, A. Miller, and B. Young © 2009 American Institute of Physics 978-0-7354-0751-0/09/$25.00 711 c > 0) 120 140 Energy (keV) FIGURE 1. Spectrum obtained with the microcalorimeter array for the MA-MOX pellet. Comparison is made to a similar spectrum collected with a planar HPGe detector Peaks used in the energy calibration described in this paper are labeled. ably a good candidate for energy calibration since it produces many 7 ray andx ray peaks that are well distributed over the dynamic range of the detector. For consistency, a set of eight peaks, denoted in Fig. 1, was selected for use in the calibration for each of these pixels. This seemingly minor detail is actually quite important, as the goal of increasingly large detector arrays necessitates the development of automated calibration procedures and, in consequence, a common set of calibration points will be an important asset. Figure 3 a depicts the energy offsets, which are defined as the difference between the calb) offset = 20 eV a) offset = 0 eV 100.0 100.1 100.2 100.3 c) offset = 40 eV 99.9 100.0 100.1 100.1 9.9 100.0 100.1 100.2 100.3 100.2 100.3 d) offset = 60 eV 100.2 100.3 offset = 80 eV 100.0 ibrated energy and the value used in the calibration procedure or declared in the literature. Three of the peaks which are present between calibration points are compared in Figure 3b,c,d for several individual pixels. The distorted summations give clear evidence that the chosen set is not adequate for the calibration of all pixels. In particular, the systematic offsets exceed the limits as determined in Figure 2 for these peaks. A possible solution might be to increase the number of data points and/or the order of polynomial, but this is unsatisfactory since the peaks of Figure 3b,c,d were not used in the calibration due to their weak intensities, and a higher-order polynomial would not solve the problem of offsets between calibration points. One solution that does seem to work is to hand-select calibration points individually for each pixel (as was done for the summed spectrum of Fig. 1) but, again, this method will quickly become unwieldy as the number of pixels is increased. 9.9 100.0 100.1 DATA FILTERING f) offset = 100 eV 100.2 100.3 9.9 100.0 100.1 100.2 Data filtering is often used as a sophisticated and highly effective method for determining peak heights in the presence of non-white noise . This kind of technique is invaluable to applications such as that described here, where an optimal energy resolution is among the most important spectral features, and can typically lead to significant improvements in this value. Nevertheless, the use of an optimal filter introduces the intrinsic assumption of 100.3 FIGURE 2. Simulated peaks for different values of systematic offset. Individual peaks depicted in black and red are simulated with a Gaussian distribution with 2:1 peak areas and 80-eV FWHM. 712 100 120 140 energy (keV) 350 300 [ b) 250 200 150 yX^\ 100 7Y\\V :^V^^ 50 ^ FIGURE 3. a) Energy offsets determined by fitting data to a sixth-order polynomial, and b), c), d) selected regions of the spectrum between calibration points. A portion of the summed spectrum is also included with b), c) and d). a uniform pulse shape. It is well-known that pulses in TES systems are not uniform in shape (see Figure 4 and Refs. [4, 5, 6]), particularly near the end of the superconducting transition region where the dR/dT response becomes less steep and, thus, pulse amplitude is not proportional to deposited energy. Moreover, the application of an optimal fiher under these conditions introduces additional complexities to the data that will need to be deah with later in the energy calibration. To illustrate this, consider the output of fiher F(iJ), where a template pulse with energy / is applied at energy/. Since the "correct" filtered value is obtained only when / = J, it is useful to normalize the output to F(i,i), as depicted in Table 1. These data appear to require only a very small correction, but this small correction turns out to have a rather signif- icant influence when one considers the accuracy limits alluded to in Fig. 2. Hence, these data clearly demonstrate that the application of a data fiher in cases with variable pulse shape can lead to the introduction of new complications in the energy calibration. In principle, a fit to these data can provide an adequate correction to the introduced ambiguity, but the curve shape is not well defined. Thus, a fit would necessarily require the use of an arbitrary function and would likely suffer from the same deficiencies as the energy calibration described above. DISCUSSION It is clear from the previous sections that the analysis of microcalorimeter spectra is a fundamentally complex process that is only exacerbated by the introduction of ambiguities in the data filtering procedure due to nonuniform pulse shapes. The current method of fitting an arbitrary polynomial to a set of designated calibration points is not sufficient for studies in the hard x ray and low energy y ray region. Part of the problem detailed here is that TES detector response for compound systems is extremely complex with respect to pulse shape and pulse height as a function of energy. Even in the best case, the use of an arbitrary polynomial function in the energy calibration only conceals this fact. For example, the choice to increase the order of polynomial or the number of calibration points simply brushes aside the fact that physics may be driving these undesirable effects, and that a physically sound calibration may, at least in part, improve the consistency of such fits. Progress in this direction was recently reported by Hollerith et al. , who have presented a formula for detector response based on a simplified circuit dia- ^0.010 100 120 140 160 180 200 220 240 time (arb. units) xlO' 0.4 0.2 '- ^^ -0.2 -0.4 -0.6 = ^ ^ 100 120 140 160 180 • 200 220 240 time (arb. units) FIGURE 4. Template pulses computed at several energies for a single pixel. Each pulse is normalized to integral 1. The lower panel shows the difference between each pulse and an average pulse computed from those depicted in the top panel. 713 TABLE 1. Filter output for different template pulses (columns) at different energies (rows) for a single pixel. Data given in this table are normalized to the diagonal value. See text for details. gram, which includes TES, shunt resistor, and bias current (their model also assumes a low event rate or complete rejection of pileup events). However, their system differs markedly from the one described here since their TES is also the absorber In contrast, the detectors used in this work have TES and absorber as separate entities. Hence, a proper model of detector response in the current system is considerably more complex. Recent work from Bennett et al.  illustrates this point well in the solution to a set of differential equations in the linear limit. This purely theoretical approach shows significant promise in terms of peak fitting, but an extension to the nonlinear regime is likely to be needed before an adequate fit is to be achieved. Whereas a generalized calibration formula based on the theoretical approach of Bennett et al. would be a big step forward, it is not likely to solve all of the aformentioned problems at once. For instance, the exact shape of the superconducting transition region may contribute small "wiggles" in the calibration curve independent of the detector response. This is likely to vary from pixel to pixel and will require an empirical solution. The recent work of Tan et al.  expresses a similar idea, as those authors report fundamental differences in pulse shape from pixel to pixel in addition to the energy dependence discussed above. Even with a theoretically sound calibration formula the complex nature of the curve will necessarily require the use of several calibration points that are closely spaced in energy. It remains to be seen whether the range and peak density of the MA-MOX spectrum is sufficient or if a larger array of photopeaks will be needed. One alternative to radioactive source calibrants could be the installation of heat pulsers on the absorbers, but this is certainly not feasible for large arrays and the simple presence of additional materials may only further complicate the details of detector response. In spite of the plethora of issues described here, good data can and have been obtained with the present detector array, as evidenced by Fig. 1 and Refs. [10, 11]. Furthermore, the collection of data for several sources and over several magnet cycles indicates that calibration problems consistently appear for the same detectors, meaning that an empirical solution for one dataset should extrapolate to other datasets collected with the same detector with reasonable success. Improvements in detector design are ongoing [12,13], and it is not unreasonable to expect improvements in the consistency of detector response in the near future. In conclusion, we have demonstrated that the analysis of microcalorimeter spectra with large dynamic range is a complex and delicate process in need of a more physics-based approach. The necessary step of automation is nontrivial with current systems due to this and to variability in pixel-to-pixel behavior. Despite these set- 84 98 109 144 186 84 98 109 144 186 1.000 0.996 0.998 1.013 1.027 1.004 1.000 1.002 1.016 1.031 1.002 0.998 1.000 1.015 1.029 0.987 0.983 0.985 1.000 1.014 0.972 0.969 0.971 0.985 1.000 backs, progress continues at a fast pace, making the practical application of microcalorimeter arrays to hard x ray and 7 ray energy regions an exciting prospect for the near future. ACKNOWLEDGMENTS We gratefully acknowledge the support of the Department of Energy, Office of Nonproliferation and Development (DOE/NNSA/NA-22). REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 714 D. A. WoUman, K. D. Irwin, and G. C. H. et al, J. of Microscopy 188, 196-223 (1997). L. Gottardi, Y. Takei, and J. van der Kuur et al., J. Low Temp. Phys. 151, 106-111 (2008). A. E. Szymkowiak, R. L. Kelley, S. H. Moseley, and C. K. Stahle, J. Low Temp. Phys. 93, 281 (1993). E. Figueroa-Feliciano, B. Cabrera, A. J. Miller, S. F. Powell, T. Saab, and A. B. C. Walker, Nucl. Instr. Meth. A 444, 453^56 (2000). C. H. Whitford, Nucl. Instr. Meth. A 555, 255-259 (2005). D. J. Fixsen, S. H. Moseley, B. Cabrera, and E. FigueroaFeliciano, Nucl. Instr Meth. A 520, 555-558 (2004). C. Hollerith, B. Simmnacher, and R. W. et al., Rev. Sci. Instr 11, 053105 (2006). D. A. Bennett, private communication (2009). H. Tan, D. Breus, and W. H. et al., this conference (2009). A. S. Hoover, M. K. Bacrania, N. Hoteling, and R J. K. et al., J. Radioanalytical and Nucl. Chem. (in press). M. W. Rabin, this conference (2009). M. K. Bacrania, A. S. Hoover, and R J. K. et al, IEEE Transactions in Nuclear Science (in press). J. N. UUom, J. A. Beall, and W. B. D. et al, Appl. Phys. Lett 87, 194103 (2005).