When “Optimal Filtering” Isn’t
Joseph W. Fowler, Bradley K. Alpert, William Bertrand Doriese, James P. Hays-Wehle, Young Il Joe, Kelsey M. Morgan, G. C. O’Neil, C. D. Reintsema, Daniel R. Schmidt, Joel N. Ullom, Daniel S. Swetz · IEEE Transactions on Applied Superconductivity · 2016
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. However, the shapes of pulses from a nonlinear detector can and do depend on the pulse energy. 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 to 4.2 eV at the Cu K$\alpha$line (8.0 keV).