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Optimal Energy Measurement in Nonlinear Systems - An Application of Differential Geometry



Dale J. Fixsen, Harvey Moseley, Thomas Gerrits, Adriana Lita, Sae Woo Nam


Design of TES microcalorimeters requires a tradeoff between resolution and dynamic range. Often, experimenters will require linearity for the highest energy signals, which requires additional heat capacity be added to the detector. This results in a reduction of low energy resolution in the detector. We derive and demonstrate an algorithm that allows operation far into the nonlinear regime with little loss in spectral resolution. We use a least squares optimal filter that varies with photon energy to accommodate the nonlinearity of the detector and the non-stationarity of the noise. The fitting process we use can be seen as an application of differential geometry. This recognition provides a set of well-developed tools to extend our work to more complex situations. The proper calibration of a nonlinear microcalorimeter requires a source with densely spaced narrow lines. A pulsed laser multi-photon source is used here, and is seen to be a powerful tool for allowing us to develop practical systems with significant detector nonlinearity. The combination of our analysis techniques and the multi-photon laser source create a powerful tool for increasing the performance of future TES microcalorimeters.
Journal of Low Temperature Physics


transition edge sensor, single photon counting, optimal filter, non-stationary noise


Fixsen, D. , Moseley, H. , Gerrits, T. , Lita, A. and Nam, S. (2014), Optimal Energy Measurement in Nonlinear Systems - An Application of Differential Geometry, Journal of Low Temperature Physics, [online],, (Accessed June 15, 2024)


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Created June 30, 2014, Updated October 12, 2021