Optimal binning of X-ray spectra and response matrix design

TL;DR

This paper presents a theoretical framework for optimally binning X-ray spectra and designing response matrices, significantly reducing computational complexity while maintaining accuracy.

Contribution

It introduces a method to determine optimal bin sizes and response matrix structure considering photon counts and energies, improving spectral analysis efficiency.

Findings

Response matrix can be reduced by a factor of 10-100.

Including response derivatives improves spectral modeling.

Guidelines for constructing optimal energy grids are provided.

Abstract

A theoretical framework is developed to estimate the optimal binning of X-ray spectra. We derived expressions for the optimal bin size for model spectra as well as for observed data using different levels of sophistication. It is shown that by taking into account both the number of photons in a given spectral model bin and their average energy over the bin size, the number of model energy bins and the size of the response matrix can be reduced by a factor of $10-100$. The response matrix should then contain the response at the bin centre as well as its derivative with respect to the incoming photon energy. We provide practical guidelines for how to construct optimal energy grids as well as how to structure the response matrix. A few examples are presented to illustrate the present methods.