When "Optimal Filtering" Isn't

TL;DR

This paper introduces tangent filtering, a pulse-fitting method that accounts for energy-dependent pulse shapes in nonlinear detectors, leading to improved energy resolution in x-ray microcalorimetry.

Contribution

The paper presents a geometric approach to pulse fitting that incorporates energy-dependent pulse shapes, enhancing resolution over traditional optimal filtering methods.

Findings

Resolution improved from 4.9 eV to 4.2 eV at Cu Kα line

Method predicts potential resolution gains based on pulse shape analysis

Demonstrated with case study on transition metal fluorescence

Abstract

The so-called "optimal filter" analysis of a microcalorimeter's x-ray pulses is statistically optimal only if all pulses have the same shape, regardless of energy. The shapes of pulses from a nonlinear detector can and do depend on the pulse energy, however. A pulse-fitting procedure that we call "tangent filtering" accounts for the energy dependence of the shape and should therefore achieve superior energy resolution. We take a geometric view of the pulse-fitting problem and give expressions to predict how much the energy resolution stands to benefit from such a procedure. We also demonstrate the method with a case study of K-line fluorescence from several 3d transition metals. The method improves the resolution from 4.9 eV to 4.2 eV at the Cu K$\alpha$ line (8.0keV).