SR micro-XRF installation on VEPP-3 storage ring. An approach and difficulties in increasing the spatial resolution.
X-ray fluorescence microanalysis on synchrotron radiation beams (SR micro-XRF) is a method to explore the elemental composition of samples and objects of various nature with a typical spatial resolution of 15 to 25 μm. Such resolution, available in qualitative micro-XRF (mapping of fluorescent signal distribution or exploration of area of interest without detailed consideration of effects caused by absorption by a sample) is defined by the transverse size of the focal spot of x-ray optics used. As a rule, up-to-date (monolithic) polycapillary lenses are applied. This qualitative elemental mapping in some cases can provide useful information. It can be in demand, for example, in reconstruction of paleoclimate (layered samples of bottom sediments, so called varves) and conditions of rock formation in deposit occurrences, as well as in examination of biological objects (hair and large cells), particles of earth and meteorite dust and some other objects [1-2].
The SR XRF experimental station on the VEPP-3 storage ring (the SCSTR)  is equipped with the installation "SR micro-XRF", which is intensely used by a number of users in most of these areas of research. The installation was engaged in an extensive series of experiments  using qualitative SR micro-XRF; unique results were obtained in several cases. Two directions of improving the method and installation were selected so far. The first one is development of certified techniques of (semi-) quantitative XRF, and the second one is 1.5-2 time improvement of the spatial resolution due to application of complicated algorithms to process experimental data (so called regularization), including embedded indirect accuracy control.
Regularization is a method of approximate solution to unstable inverse problems. It is based on certain controlled introduction of systematic error into the result. This error is introduced so that its contribution optimally balances [4, p. 52-55] the influence of random noise, because of which the problem cannot be accurately solved by traditional methods. Development of any regularization algorithms implies analysis of feasibility of the above rule (in other words, the convergence of the approximate solution) over the entire range of all input parameters. The algorithm user is assumed to know the rules for use of one or another regularizing procedure (that may expect, for example, normal distribution of noise, absence of systematic errors, special prior constraints to the solution, and others) and adhere to them. Unfortunately, this is not always the case, and application of regularization of algorithms is often blind and inefficient, especially when third-party programs are used.
This work presents an attempt of non-strict but effective practical analysis of the influence of various factors "hindering" the regularization (inaccuracy in the determination of the instrumental function, discretization errors, Gibbs boundary effects etc.) on the process of solving inverse deconvolution problems arising in SR micro-XRF using the Tikhonov algorithm [4, p. 52]. The analysis performed resulted in practical recommendations on the optimal regimes of experiment with improved spatial resolution and highlighted the role of numerical simulation in the control of solving real inverse deconvolution problems.
This work was supported by the RFBR Grants № 14-02-00631, 16-32-00705. The work by D.S. Sorokoletov was supported by a scholarship of the President of the Russian Federation (SP-2761.2016.2).
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