DarpanX: A python package for modeling X-ray reflectivity of multilayer mirrors

Abstract

Multilayer X-ray mirrors consist of a coating of a large number of alternate layers of high Z and low Z materials with a typical thickness of 10–100 Å , on a suitable substrate. Such coatings play an important role in enhancing the reflectivity of X-ray mirrors by allowing reflections at angles much larger than the critical angle of X-ray reflection for the given materials. Coating with an equal thickness of each bilayer (constant period multilayers) enhances the reflectivity at discrete energies, satisfying Bragg condition for the given thickness. However, by systematically varying the bilayer thickness in the multilayer stack (depth graded multilayers), it is possible to design X-ray mirrors having enhanced reflectivity over a broad energy range. One of the most important applications of such a depth graded multilayer mirror is to realize hard X-ray telescopes for astronomical purposes. Design of such multilayer X-ray mirrors and their characterization with X-ray reflectivity measurements require appropriate software tools that can compute X-ray reflectivity for the given set of parameters and geometry. We have initiated the development of hard X-ray optics for future Indian X-ray astronomical missions, and in this context, we have developed a program, DarpanX, to calculate X-ray reflectivity for single and multilayer mirrors. It can be used as a stand-alone tool for designing multilayer mirrors with required characteristics. But more importantly, it has been implemented as a local model for the popular X-ray spectral fitting program, XSPEC, and thus can be used for accurate fitting of the experimentally measured X-ray reflectivity data. DarpanX is implemented as a Python 3 module, and an API is provided to access the underlying algorithms. Here we present details of DarpanX implementation and its validation for different types of multilayer structures. We also demonstrate the model fitting capability of DarpanX for experimental X-ray reflectivity measurements of single and multilayer samples.