Optical systems based on compound refractive lenses (CRLs) with rotationally parabolic profile  are amongst the most advanced optical components at the novel synchrotrons worldwide . Methods and technologies of their production one of the most rapidly progressing areas of modern synchrotron instrumentation techniques. Manufacturing of CRLs is closely related to the analysis of technological errors affecting on quality of their optical characteristics. The most important problem is the geometric deviations of the CRL refractive profile from the calculated shape . Therefore, in addition to the improvement of lens manufacturing methods, the development of metrological diagnostic methods which provide accurate measurements of the geometric characteristics of the parabolic profile of the CRL are also required.
This work presents a comparison of various methods of metrological studies of profiles of X-ray refractive lenses. Application of the regression analysis allows to assess the adequacy of the of proposed model of geometrical description of the lens profile and coaxial alignment of the refracting surfaces which determine the quality of the optical system for x-ray imaging. The developed a comprehensive laboratory metrological approach allows controlling the quality of the profile shape of refractive lenses and thus significantly improve their quality characterization, by a proper adjustment of the CRL production process.
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