X-ray propagation through hollow channel: PolyCAD – a ray tracing code

Abstract

“PolyCAD”, a CAD program designed for X-ray photon tracing in polycapillary optics, is described. To understand the PolyCAD code and its results, the theoretical bases of X-ray transmission by a single cylindrical channel (monocapillary) are discussed first. Then cases of cylindrical, lens and semi-lens shaped polycapillary optics are examined. PolyCAD allows any type of X-ray source to be used: an X-ray tube of finite beam dimensions or an astrophysical object can be simulated in combination with the polycapillary optics. The radiation density distribution images formed on a screen located at various focal distances are discussed. The good agreement of the PolyCAD results with experimental and previous theoretical calculations validate the code.

Introduction

The use of polycapillary optics to control X-ray beams in analytical X-ray apparatuses for diffraction and fluorescence analysis is becoming increasingly important. In the near future polycapillary optics will be widely used in many different fields, e.g. aerospace research, medicine, biology and so on [1]. Our strong interest in the development of these devices led to the idea of creating a ray tracing program that allows us to simulate the process of radiation propagation through polycapillary optical systems and to visualize the radiation distributions at the optical output.

At present there are few procedures available for evaluating X-ray transmission by capillary structures in the case of peculiar configurations, see for instance [2], [3], [4], [5], [6], [7], [8], [9], [10], [11]. One of the first papers [2] reported X-ray radiation transmission by a hollow glass pipe. This code also considered (i) the presence of a rough surface as an X-ray anomalous dispersion effect, (ii) radiation penetration into the channel wall and (iii) the possible presence of micro-dust inside the channel.

Another algorithm [3] for X-ray transmission by capillaries of various shapes runs in the geometrical optics approximation; for this reason it is simpler and more flexible than the previous model.

The first X-ray tracing codes were developed in 1992 by Hoffman et al. [4], Thiel [5] and by the Institute for Roentgen Optics, for a review look at [12]. However, these simulations used a number of simplifications based either on capillary system with cylindrical symmetry or on the meridional ray approximation, which is valid only for describing radiation propagation through a bundle of channels or a monocapillary concentrator.

To the authors’ knowledge, the most advanced and complete softwares for X-ray tracing inside capillary channels are four. The first code [6], [9] traces the trajectory of each photon including the corrections of absorption and roughness; according to some experimental results, the authors are able to evaluate the roughness of the channel. The second one [7] uses the SHADOW ray tracing software, adapting it to the channel shape. In addition, recently some new works based on SHADOW ray tracing were published [13], [14]. The last code [8], [10] uses a Monte Carlo simulation for X-ray radiation propagation through hollow channels. The theoretical results obtained by this code agree quite well with the experimental data, although the algorithm is rather simple due to the geometrical optics approximation and to the circular cross section of the channel’s shape.

The main aim of all these simulation codes is to optimize both the channel size and the optical shape in order to obtain highly efficient optical systems. Obviously, this is very important from the viewpoint of the development of capillary optics technology. However, analysis of the radiation distribution features, reported in a number of papers [15], [16], [17] is particularly interesting. (Some of the earlier publications are cited in [17].) In these papers the experimental data were validated by means of analytical estimations based on the wave theory of radiation propagation.

Before we continue any further, let us clarify the terminology used in this work: (1) a monocapillary is a single capillary; (2) a polycapillary is a set of closely packed monocapillaries; (3) a lens is a device that concentrate the radiation in a point or in a small region; (4) a semi-lens, or a half-lens is a device that can concentrate a quasi-parallel beam in a point and vice versa by reversing the geometry.

Here, we introduce an X-ray tracing code for polycapillary optics, named PolyCAD. A previous version was designed for cylindrical optics only [18], [19]. Now, the software can simulate monocapillary and polycapillary optics with any shape. The advantage of the code lies in its precise mathematical solutions for each given optical shape. Comparison of the results of PolyCAD and of the previous algorithms [5], [6], [7], [8], [12] revealed some differences, due to the fact that PolyCAD is free of many of the algorithmic constraints.

In the first part of our paper the theoretical basis of a cylindrical monocapillary is explained; in the second part numerical results and simulations are reported. In the last part we compare experimental data with our predictions.