Approaches to the Optimal Nonlinear Analysis of Microcalorimeter Pulses

We consider how to analyze microcalorimeter pulses for quantities that are nonlinear in the data, while preserving the signal-to-noise advantages of lin- ear optimal filtering. We successfully apply our chosen approach to compute the electrothermal feedback energy deficit (the "Joule energy") of a pulse, which has been proposed as a linear estimator of the deposited photon energy.Comment: Accepted by Journal of Low Temperature Physics. Contribution to the proceedings of Low Temperature Detectors 17, (Kurume Japan, 2017

The Practice of Pulse Processing

The analysis of data from x-ray microcalorimeters requires great care; their excellent intrinsic energy resolution cannot usually be achieved in practice without a statistically near-optimal pulse analysis and corrections for important systematic errors. We describe the essential parts of a pulse-analysis pipeline for data from x-ray microcalorimeters, including steps taken to reduce systematic gain variation and the unwelcome dependence of filtered pulse heights on the exact pulse-arrival time. We find these steps collectively to be essential tools for getting the best results from a microcalorimeter-based x-ray spectrometer.Comment: Accepted for publication in J. Low Temperature Physics, special issue for the proceedings of the Low Temperature Detectors 16 conferenc

Filters for High Rate Pulse Processing

We introduce a filter-construction method for pulse processing that differs in two respects from that in standard optimal filtering, in which the average pulse shape and noise-power spectral density are combined to create a convolution filter for estimating pulse heights. First, the proposed filters are computed in the time domain, to avoid periodicity artifacts of the discrete Fourier transform, and second, orthogonality constraints are imposed on the filters, to reduce the filtering procedure's sensitivity to unknown baseline height and pulse tails. We analyze the proposed filters, predicting energy resolution under several scenarios, and apply the filters to high-rate pulse data from gamma-rays measured by a transition-edge-sensor microcalorimeter.Comment: 5 pages, 6 figures, 1 tabl

Optimization and analysis of code-division multiplexed TES microcalorimeters

We are developing code-division multiplexing (CDM) systems for transition-edge sensor arrays with the goal of reaching multiplexing factors in the hundreds. We report on x-ray measurements made with a four-channel prototype CDM system that employs a flux-summing architecture, emphasizing data-analysis issues. We describe an empirical method to determine the demodulation matrix that minimizes cross-talk. This CDM system achieves energy resolutions of between 2.3 eV and 3.0 eV FWHM at 5.9 keV.Comment: 7 pages, 5 figures. Presented at the 14th International Workshop on Low Temperature Detectors, Heidelberg University, August 1-5, 2011, proceedings to be published in the Journal of Low Temperature Physic

A Highly Linear Calibration Metric for TES X-ray Microcalorimeters

Transition-edge sensor X-ray microcalorimeters are usually calibrated empirically, as the most widely-used calibration metric, optimal filtered pulse height (OFPH), in general has an unknown dependance on photon energy, $E_{\gamma}$. Because the calibration function can only be measured at specific points where photons of a known energy can be produced, this unknown dependence of OFPH on $E_{\gamma}$ leads to calibration errors and the need for time-intensive calibration measurements and analysis. A calibration metric that is nearly linear as a function of $E_{\gamma}$ could help alleviate these problems. In this work, we assess the linearity of a physically motivated calibration metric, $E_{Joule}$. We measure calibration pulses in the range 4.5 keV$<$$E_{\gamma}$$<$9.6 keV with detectors optimized for 6 keV photons to compare the linearity properties of $E_{Joule}$ to OFPH. In these test data sets, we find that $E_{Joule}$ fits a linear function an order of magnitude better than OFPH. Furthermore, calibration functions using $E_{J}$, an optimized version of $E_{Joule}$, are linear within the 2-3 eV noise of the data

High-resolution kaonic-atom x-ray spectroscopy with transition-edge-sensor microcalorimeters

We are preparing for an ultra-high resolution x-ray spectroscopy of kaonic atoms using an x-ray spectrometer based on an array of superconducting transition-edge-sensor microcalorimeters developed by NIST. The instrument has excellent energy resolutions of 2 - 3 eV (FWHM) at 6 keV and a large collecting area of about 20 mm^2. This will open new door to investigate kaon-nucleus strong interaction and provide new accurate charged-kaon mass value.Comment: 6 pages, 3 figures, Proceedings of 15th International Workshop on Low Temperature Detectors (LTD-15, Pasadena, California, June 24-28, 2013), To be published in a special issue of the Journal of Low Temperature Physics (JLTP

Transition-Edge Sensors for Particle Induced X-ray Emission Measurements

In this paper we present a new measurement setup, where a transitionedge sensor detector array is used to detect X-rays in particle induced X-ray emission measurements with a 2 MeV proton beam. Transition-edge sensors offer orders of magnitude improvement in energy resolution compared to conventional silicon or germanium detectors, making it possible to recognize spectral lines in materials analysis that have previously been impossible to resolve, and to get chemical information from the elements. Our sensors are cooled to the operation temperature (65 mK) with a cryogen-free adiabatic demagnetization refrigerator, which houses a specially designed X-ray snout that has a vacuum tight window to couple in the radiation. For the best pixel, the measured instrumental energy resolution was 3.06 eV full width at half maximum at 5.9 keV.We discuss the current status of the project, benefits of transition-edge sensors when used in particle induced X-ray emission spectroscopy, and the results from the first measurements.Comment: 6 pages, 3 figure, LTD-15 proceeding

On low-energy tail distortions in the detector responsefunction of x-ray microcalorimeter spectrometers

We use narrow spectral lines from the x-ray spectra of various highlycharged ions to measure low-energy tail-like deviations from a Gaussian responsefunction in a microcalorimter x-ray spectrometer with Au absorbers at energiesfrom 650 eV to 3320 eV. We review the literature on low energy tails in othermicrocalorimter x-ray spectrometers and present a model that explains all thereviewed tail fraction measurements. In this model a low energy tail arises fromthe combination of electron escape and energy trapping associated with Bi x-rayabsorbers

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

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 8,000 eV and achieve an energy resolution of 3.7 eV to 5.0 eV over this range, a more modest (<2X) 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

Eliminating the non-Gaussian spectral response of X-ray absorbers for transition-edge sensors

Transition-edge sensors (TES) as microcalorimeters for high-energy-resolution X-ray spectroscopy are often fabricated with an absorber made of materials with high Z (for X-ray stopping power) and low heat capacity (for high resolving power). Bismuth represents one of the most compelling options. TESs with evaporated bismuth absorbers have shown spectra with undesirable and unexplained low-energy tails. We have developed TESs with electroplated bismuth absorbers over a gold layer that are not afflicted by this problem and that retain the other positive aspects of this material. To better understand these phenomena, we have studied a series of TESs with gold, gold/evaporated bismuth, and gold/electroplated bismuth absorbers, fabricated on the same die with identical thermal coupling. We show that bismuth morphology is linked to the spectral response of X-ray TES microcalorimeters