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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
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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 [3]. 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. [7], 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. [8] 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. [9] 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-
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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).
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