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 $\text{Å }$, 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.

多层X射线反射镜由大量高Z和低Z材料的交替层组成，典型厚度为10–100 $\text{一个 }$在合适的基材上。这样的涂层通过允许以比给定材料的X射线反射的临界角大得多的角度进行反​​射，从而在增强X射线镜的反射率中起重要作用。在每个双层（恒定周期多层）上具有相同厚度的涂层可增强在离散能量下的反射率，从而满足给定厚度下的布拉格条件。然而，通过系统地改变多层堆叠（深度分级的多层）中的双层厚度，可以设计在宽的能量范围内具有增强的反射率的X射线反射镜。这种深度渐变多层反射镜最重要的应用之一是实现用于天文目的的硬X射线望远镜。这种多层X射线反射镜的设计及其通过X射线反射率测量进行表征需要适当的软件工具，这些软件工具可以针对给定的参数和几何形状集计算X射线反射率。我们已经开始为未来的印度X射线天文任务开发硬X射线光学器件，在这种情况下，我们开发了DarpanX程序来计算单面和多层反射镜的X射线反射率。它可以用作设计具有所需特性的多层反射镜的独立工具。但更重要的是，它已被实现为流行的X射线光谱拟合程序XSPEC的局部模型，因此可用于对实验测量的X射线反射率数据进行精确拟合。DarpanX被实现为Python 3模块，提供API来访问基础算法。在这里，我们介绍了DarpanX实施的细节及其对不同类型的多层结构的验证。我们还演示了DarpanX用于单个和多层样品的实验X射线反射率测量的模型拟合能力。