Confidence intervals for the encircled energy fraction and the half energy width

TL;DR

This paper introduces non-parametric statistical methods to quantify the uncertainty in the encircled energy fraction and half energy width, improving the characterization of X-ray optical systems.

Contribution

It presents a novel approach to estimate statistical errors for encircled energy metrics, enhancing the accuracy of X-ray system characterization.

Findings

Non-parametric methods provide reliable error estimates.

Statistical errors can accelerate X-ray system testing.

Improved characterization accuracy for X-ray optics.

Abstract

The Encircled Energy Fraction and its quantiles, notably the Half Energy Width, are routinely used to characterize the quality of X-ray optical systems. They are however always quoted without a statistical error. We show how non-parametric statistical methods can be used to redress this situation, and we discuss how the knowledge of the statistical error can be used to speed up the characterization efforts for future X-ray observatories.