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Fowler JW, Alpert BK, O’Neil GC, Swetz DS, Ullom JN. Energy Calibration of Nonlinear Microcalorimeters with Uncertainty Estimates from Gaussian Process Regression. J Low Temp Phys 2022; 209:10.1007/s10909-022-02740-w. [PMID: 37427309 PMCID: PMC10327436 DOI: 10.1007/s10909-022-02740-w] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2021] [Accepted: 04/21/2022] [Indexed: 07/11/2023]
Abstract
The nonlinear energy response of cryogenic microcalorimeters is usually corrected through an empirical calibration. X-ray or gamma-ray emission lines of known shape and energy anchor a smooth function that generalizes the calibration data and converts detector measurements to energies. We argue that this function should be an approximating spline. The theory of Gaussian process regression makes a case for this functional form. It also provides an important benefit previously absent from our calibration method: a quantitative uncertainty estimate for the calibrated energies, with lower uncertainty near the best-constrained calibration points.
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Affiliation(s)
- J. W. Fowler
- National Institute of Standards and Technology, 325
Broadway, Boulder, CO 80305, USA
- Department of Physics, University of Colorado, Boulder, CO
80309, USA
| | - B. K. Alpert
- National Institute of Standards and Technology, 325
Broadway, Boulder, CO 80305, USA
| | - G. C. O’Neil
- National Institute of Standards and Technology, 325
Broadway, Boulder, CO 80305, USA
| | - D. S. Swetz
- National Institute of Standards and Technology, 325
Broadway, Boulder, CO 80305, USA
| | - J. N. Ullom
- National Institute of Standards and Technology, 325
Broadway, Boulder, CO 80305, USA
- Department of Physics, University of Colorado, Boulder, CO
80309, USA
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Fowler JW, O’Neil GC, Alpert BK, Bennett DA, Denison EV, Doriese WB, Hilton GC, Hudson LT, Joe YI, Morgan KM, Schmidt DR, Swetz DS, Szabo CI, Ullom JN. Absolute energies and emission line shapes of the L x-ray transitions of lanthanide metals. Metrologia 2021; 58:10.1088/1681-7575/abd28a. [PMID: 34354301 PMCID: PMC8335601 DOI: 10.1088/1681-7575/abd28a] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
We use an array of transition-edge sensors, cryogenic microcalorimeters with 4 eV energy resolution, to measure L x-ray emission-line profiles of four elements of the lanthanide series: praseodymium, neodymium, terbium, and holmium. The spectrometer also surveys numerous x-ray standards in order to establish an absolute-energy calibration traceable to the international system of units for the energy range 4 keV to 10 keV. The new results include emission line profiles for 97 lines, each expressed as a sum of one or more Voigt functions; improved absolute energy uncertainty on 71 of these lines relative to existing reference data; a median uncertainty on the peak energy of 0.24 eV, four to ten times better than the median of prior work; and six lines that lack any measured values in existing reference tables. The 97 lines comprise nearly all of the most intense L lines from these elements under broad-band x-ray excitation. The work improves on previous measurements made with a similar cryogenic spectrometer by the use of sensors with better linearity in the absorbed energy and a gold x-ray absorbing layer that has a Gaussian energy-response function. It also employs a novel sample holder that enables rapid switching between science targets and calibration targets with excellent gain balancing. Most of the results for peak energy values shown here should be considered as replacements for the currently tabulated standard reference values, while the line shapes given here represent a significant expansion of the scope of available reference data.
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Affiliation(s)
- J W Fowler
- Department of Physics, University of Colorado, Boulder, CO 80309, United States of America
- Quantum Electromagnetics Division, National Institute of Standards and Technology, Boulder, CO 80305, United States of America
| | - G C O’Neil
- Quantum Electromagnetics Division, National Institute of Standards and Technology, Boulder, CO 80305, United States of America
| | - B K Alpert
- Applied & Computational Mathematics Division, National Institute of Standards and Technology, Boulder, CO 80305, United States of America
| | - D A Bennett
- Quantum Electromagnetics Division, National Institute of Standards and Technology, Boulder, CO 80305, United States of America
| | - E V Denison
- Quantum Electromagnetics Division, National Institute of Standards and Technology, Boulder, CO 80305, United States of America
| | - W B Doriese
- Quantum Electromagnetics Division, National Institute of Standards and Technology, Boulder, CO 80305, United States of America
| | - G C Hilton
- Quantum Electromagnetics Division, National Institute of Standards and Technology, Boulder, CO 80305, United States of America
| | - L T Hudson
- Radiation Physics Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, United States of America
| | - Y-I Joe
- Department of Physics, University of Colorado, Boulder, CO 80309, United States of America
- Quantum Electromagnetics Division, National Institute of Standards and Technology, Boulder, CO 80305, United States of America
| | - K M Morgan
- Department of Physics, University of Colorado, Boulder, CO 80309, United States of America
- Quantum Electromagnetics Division, National Institute of Standards and Technology, Boulder, CO 80305, United States of America
| | - D R Schmidt
- Quantum Electromagnetics Division, National Institute of Standards and Technology, Boulder, CO 80305, United States of America
| | - D S Swetz
- Quantum Electromagnetics Division, National Institute of Standards and Technology, Boulder, CO 80305, United States of America
| | - C I Szabo
- Radiation Physics Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, United States of America
- Theiss Research, 7411 Eads Ave, La Jolla, CA 92037, United States of America
| | - J N Ullom
- Department of Physics, University of Colorado, Boulder, CO 80309, United States of America
- Quantum Electromagnetics Division, National Institute of Standards and Technology, Boulder, CO 80305, United States of America
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Szypryt P, O’Neil GC, Takacs E, Tan JN, Buechele SW, Naing AS, Bennett DA, Doriese WB, Durkin M, Fowler JW, Gard JD, Hilton GC, Morgan KM, Reintsema CD, Schmidt DR, Swetz DS, Ullom JN, Ralchenko Y. A transition-edge sensor-based x-ray spectrometer for the study of highly charged ions at the National Institute of Standards and Technology electron beam ion trap. Rev Sci Instrum 2019; 90:123107. [PMID: 31893849 PMCID: PMC8772522 DOI: 10.1063/1.5116717] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2019] [Accepted: 11/20/2019] [Indexed: 05/31/2023]
Abstract
We report on the design, commissioning, and initial measurements of a Transition-Edge Sensor (TES) x-ray spectrometer for the Electron Beam Ion Trap (EBIT) at the National Institute of Standards and Technology (NIST). Over the past few decades, the NIST EBIT has produced numerous studies of highly charged ions in diverse fields such as atomic physics, plasma spectroscopy, and laboratory astrophysics. The newly commissioned NIST EBIT TES Spectrometer (NETS) improves the measurement capabilities of the EBIT through a combination of high x-ray collection efficiency and resolving power. NETS utilizes 192 individual TES x-ray microcalorimeters (166/192 yield) to improve upon the collection area by a factor of ∼30 over the 4-pixel neutron transmutation doped germanium-based microcalorimeter spectrometer previously used at the NIST EBIT. The NETS microcalorimeters are optimized for the x-ray energies from roughly 500 eV to 8000 eV and achieve an energy resolution of 3.7 eV-5.0 eV over this range, a more modest (<2×) improvement over the previous microcalorimeters. Beyond this energy range, NETS can operate with various trade-offs, the most significant of which are reduced efficiency at lower energies and being limited to a subset of the pixels at higher energies. As an initial demonstration of the capabilities of NETS, we measured transitions in He-like and H-like O, Ne, and Ar as well as Ni-like W. We detail the energy calibration and data analysis techniques used to transform detector counts into x-ray spectra, a process that will be the basis for analyzing future data.
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Affiliation(s)
- P. Szypryt
- Quantum Electromagnetics Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA
| | - G. C. O’Neil
- Quantum Electromagnetics Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA
| | - E. Takacs
- Quantum Measurement Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
- Department of Physics and Astronomy, Clemson University, Clemson, South Carolina 29634, USA
| | - J. N. Tan
- Quantum Measurement Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - S. W. Buechele
- Quantum Measurement Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - A. S. Naing
- Quantum Measurement Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
- Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA
| | - D. A. Bennett
- Quantum Electromagnetics Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA
| | - W. B. Doriese
- Quantum Electromagnetics Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA
| | - M. Durkin
- Quantum Electromagnetics Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - J. W. Fowler
- Quantum Electromagnetics Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - J. D. Gard
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - G. C. Hilton
- Quantum Electromagnetics Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA
| | - K. M. Morgan
- Quantum Electromagnetics Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - C. D. Reintsema
- Quantum Electromagnetics Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA
| | - D. R. Schmidt
- Quantum Electromagnetics Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA
| | - D. S. Swetz
- Quantum Electromagnetics Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA
| | - J. N. Ullom
- Quantum Electromagnetics Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Yu. Ralchenko
- Quantum Measurement Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
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Fowler JW, Alpert BK, Joe YI, O’Neil GC, Swetz DS, Ullom JN. A Robust Principal Component Analysis for Outlier Identification in Messy Microcalorimeter Data. J Low Temp Phys 2019; 199:10.1007/s10909-019-02248-w. [PMID: 33364637 PMCID: PMC7754256 DOI: 10.1007/s10909-019-02248-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/2019] [Accepted: 11/01/2019] [Indexed: 06/12/2023]
Abstract
A principal component analysis (PCA) of clean microcalorimeter pulse records can be a first step beyond statistically optimal linear filtering of pulses toward a fully nonlinear analysis. For PCA to be practical on spectrometers with hundreds of sensors, an automated identification of clean pulses is required. Robust forms of PCA are the subject of active research in machine learning. We examine a version known as coherence pursuit that is simple and fast and well matched to the automatic identification of outlier records, as needed for microcalorimeter pulse analysis.
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Affiliation(s)
- J. W. Fowler
- Quantum Sensors Group, National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80305, USA
- Department of Physics, University of Colorado, Boulder, CO 80309, USA
| | - B. K. Alpert
- Quantum Sensors Group, National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80305, USA
| | - Y.-I. Joe
- Quantum Sensors Group, National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80305, USA
- Department of Physics, University of Colorado, Boulder, CO 80309, USA
| | - G. C. O’Neil
- Quantum Sensors Group, National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80305, USA
| | - D. S. Swetz
- Quantum Sensors Group, National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80305, USA
| | - J. N. Ullom
- Quantum Sensors Group, National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80305, USA
- Department of Physics, University of Colorado, Boulder, CO 80309, USA
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Fowler JW, Alpert BK, Doriese WB, Fischer DA, Jaye C, Joe YI, O’Neil GC, Swetz DS, Ullom JN. MICROCALORIMETER SPECTROSCOPY AT HIGH PULSE RATES: A MULTI-PULSE FITTING TECHNIQUE. ACTA ACUST UNITED AC 2015. [DOI: 10.1088/0067-0049/219/2/35] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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