X-ray propagation through polycapillary optics studied through a ray tracing approach☆

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Editor's abstract

Single and polycapillary optics has obtained in recent times increasing attention for its potential high efficiency as device for focusing high-energy photons and thermal neutrons. The actually developed and future applications depend strongly on a detailed knowledge of the optical characteristics of such devices. Nevertheless, an exhaustive theoretical treatment of the polycapillary properties is extremely complicated due both to the intrinsic complexity of the structure and of the interaction between the X-ray photon beam and the mono- and polycapillary surfaces.

Using PolyCAD, a ray-tracing original package developed by our group, here we report a wide study concerning single and polycapillary optics properties. The software allows easily to simulate the optical path inside cylindrical, conical and curved mono- and polycapillary structures; their focusing properties are also presented and discussed.

Introduction

Since the mid-1980s the X-ray optical elements (capillary lenses, capillary/polycapillary optics) formed by a bundle of monocapillaries able to focalize the X radiation have been developed [1], [2]. X-ray transmission through these lenses was based on the phenomenon of total external reflection (TER) of radiation by a surface. Any X-ray quantum, which strikes the channel's wall (typically, the wall substance is a glass composition) at the incidence glancing angle less than the Fresnel angle θc (the critical angle of TER), propagates along a channel by multiple reflections. The number of reflections can vary from one to a few tens and even hundreds, that is why this optics is called multiple reflection optics.

Nowadays, the use of polycapillary optics to handle X-ray beams in analytical instruments for μ-diffraction and μ-fluorescence analysis is becoming increasingly important [3]. Due to the following features: (i) rather wide acceptable requirements for the source parameters (from conventional X-ray tubes up to synchrotron radiation sources); (ii) the high efficiency of radiation bending through large angles (up to 30° at 10–15 cm); (iii) possibility for the radiation density increase (up to 104 times); (iv) the broadband spectral working regime (from about 1 keV up to 50–70 keV) — these optical devices are more suitable for instrumental applications and development based on X-ray diffraction and fluorescence. In many cases it becomes more preferable than other existing X-ray optical devices such as zone plates and multi-layer mirrors. Presently polycapillary optics, as nondestructive technique, is widely used in many different research fields, namely, in material sciences, geology, archeometry, biology and so on [3]; it presents a specific interest for the future studies in aerospace and medicine.

Actually, in order to evaluate the X-ray transmission by capillary structures there are many procedures/codes available that deal only with some peculiar configurations. The first ray-tracing codes were developed by D.J. Thiel [4], [5] and by the Institute for Rontgen Optics (Moscow) [6]. These simulations used a number of simplifications based on the cylindrical symmetry of capillary systems, the last is valid only for estimation of the radiation propagation through a bundle of channels or through a monocapillary concentrator. In the paper [7] the coherent radiation transmission by a hollow glass pipe is studied. Its evaluation takes into account: (i) the presence of a rough surface treated like an X-ray anomalous dispersion effect, (ii) the radiation penetration into the channel wall, and (iii) the possible presence of micro-dust inside the channel. The author of the paper [8] considered the case of X-ray propagation through capillaries of various shapes using the geometrical optics approximation. In such a way a simple and flexible algorithm was proposed. The code described in [9], [10] simulates the trajectory of each X-ray photon including the corrections for absorption. According to some experimental results, the authors were also able to evaluate the roughness inside the channel. The SHADOW ray tracing was utilized in [11], adapting it to the channel shape. Recently some new works based on SHADOW ray tracing were published [12], [13], [14]. The code of the paper [15], [16], [17] uses a Monte Carlo simulation for the X-ray propagation through hollow channels. Even the algorithm is rather simple due to the geometrical optics approximation and the circular cross-section of the channel's shape used, the results obtained by this code have found a good agreement with the experimental data.

To summarize, most of the abovementioned software based on various approximations/simplifications takes into consideration only specific aspects of X-ray propagation, while the others use the SHADOW, a ray tracing code developed for more conventional optical elements.

Our interest in the development and application of polycapillary optics led us to the idea for creating a flexible and complete ray-tracing program named PolyCAD that allows the processes of radiation propagation through any kind of polycapillary optical systems and the radiation distributions at the optics output to be simulated and visualized.

The first PolyCAD version considered only cylindrical optics [18], [19]. Presently, the last version can simulate any kind of monocapillary and polycapillary lenses, providing exact mathematical solutions for any lens shape (for complete details on the PolyCAD radiation propagation algorithm see [20]). Moreover, now it is possible to evaluate rather precisely the real transmission. The comparison between PolyCAD results and those of previous algorithms [5], [9], [11], [15] reveals notable differences due to the various approaches used.

Section snippets

Contour maps for different sources and polycapillary configurations

Our ray-tracing code is based on the exact calculation of each photon path by solving a system of equations that combines the photon path and the exact capillary surface equation. This procedure allows describing the photons trajectory inside any generic capillary optical element. Below some results obtained for polycapillary full lens and semi-lens (sometimes in the literature one uses “a half-lens”) having an “elliptical toroid” shape will be presented. Each channel is cylindrical bent along

Conclusions

PolyCAD is an original software package developed for polycapillary optics simulations. Actually the program uses the ray optics approximation in the ideal case of total external reflection, without absorption effects by the optics channel walls. With such approach PolyCAD allows one: (i) to simulate the propagation of X-ray beam inside capillary channels for the optics of various geometrical shapes using both point or extended sources; (ii) to visualize the spot images formed on a screen at

Acknowledgments

We are grateful to M.A. Kumakhov for his continuous interest and support. This work was done within the frame of the FSSRIS Project ‘Multipurpose Innovative Plants for the UV and X-ray Production’ (CNR–MIUR, Legge 449/97).

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References (27)

  • M.A. Kumakhov

    Selected papers on kumakhov optics and application 1998–2000: Part II. “Application of capillary optics”

    Proc. SPIE Int. Soc. Opt. Eng.

    (2000)
  • D.J. Thiel

    Ray-tracing analysis of capillary concentrators for macromolecular crystallography

    J. Synchrotron Radiat.

    (1998)

    • Cited by (15)

    • An X-ray ray tracing simulation code for mono- and polycapillaries: Description, advances and application

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      Furthermore, this approach potentially ignores the energy dependent acceptance of the (poly)capillary optic when the dimensions of the reference material differ considerably from the sample of interest, i.e. when operating outside of the infinitely thin or thick sample boundary conditions. In order to account for this unknown energy and position dependent response, X-ray ray tracing simulations can be used, as previously reported by the groups of Gibson, Furuta, Vincze, Lin, Hampai and Peng [10–16]. Gibson's model assumes that photons are transmitted along the capillaries' meridian plane, while Lin's model assumes a constant radius for bent capillaries, and Furuta's model is aimed at simulating a single capillary.

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      Half-lens and full-lens transform the divergent X-ray beam in a quasi-parallel beam and in a focused beam, respectively. X radiation propagation in capillary optical elements is of great relevance due to potential applications in X-ray optics and imaging [12,14,15]. The complete characterization of X-ray optics performances is a critical task.

    • X-ray micro-imaging by capillary optics

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    ☆

    This paper was presented at the “18th International Congress on X-ray Optics and Microanalysis” (ICXOM-18) held in Frascati, Rome (Italy), 25–30 September 2005, and is published in the Special Issue of Spectrochimica Acta Part B, dedicated to that conference.

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