When 'Optimal Filtering' Isn't

摘要

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