Investigation of the concave spherical surface quality by a sliding X-ray beam
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Investigation of the Concave Spherical Surface Quality by a Sliding XRay Beam I. V. Yakimchuka, b, A. V. Buzmakova, A. V. Andreevb, and V. E. Asadchikova a
Shubnikov Institute of Crystallography, Russian Academy of Sciences, Leninskii pr. 59, Moscow, 119333 Russia b Faculty of Physics, Moscow State University, Moscow, 119991 Russia email: [email protected] Received September 5, 2011
Abstract—A new approach to the investigation of the quality of concave spherical surfaces has been proposed and experimentally implemented for the first time. This approach is based on the whispering gallery effect in the Xray wavelength range. One distinctive feature of the technique proposed is the application of algorithms of computed tomography for locating surface defects and describing their shape. It is noteworthy that the sizes of surfaces and their radius of curvature are not restrictive factors for this analysis. DOI: 10.1134/S106377451202023X
INTRODUCTION Analyzing the quality of large concave surfaces remains a very difficult problem. In this study a new approach to this problem is proposed which is based on the whispering gallery effect in the Xray wave length range. The essence of this effect is as follows: an acoustic or electromagnetic wave which is tangentially incident on a concave surface slides along it due to successive reflections. The results of theoretical stud ies of the whispering gallery effect in the Xray wave length range can be found in [1–4]. The experimental data on this phenomenon were reported in [5–11]. The idea of using the whispering gallery effect for studying the roughness of concave surfaces was pro posed in [12–14], where the influence of surface parameters on the angular distribution of intensity in the emerging beam was demonstrated. These parame ters include the rms roughness height and the form of the roughness correlation function. However, only concave cylindrical surfaces were considered in [12– 14] for simplicity. It was shown in [15] that, from the experimental point of view, it is even simpler to observe the whispering gallery effect on concave spherical sur faces. In this case an important requirement is the presence of a source with a wide angular spectrum. In addition, the propagation of an Xray beam sliding along a concave spherical surface (depending on the mutual position of the source and the surface) was analyzed in detail in [15]. The possibility of detecting defects on concave spherical surfaces with the aid of the whispering gal lery effect in the Xray wavelength range is shown in this study. An important feature of the proposed approach is the possibility of determining the position and size of treatment defects on the surface analyzed. Furthermore, the method under consideration is qual
itatively described and the results of the first experi ments, in which the concave spherical mirror was investigated, are analyzed. QUALITATIVE ANALYSIS The essence of the proposed approach is the obser vation of the whispering gallery effect on a spheric
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