The spread function of a x-ray polycapillary lens may be approximated very accurately by a laterally symmetrical gaussian function . However it is true statement for the spacial fields whose are near to a focus of the lens only. We carried out the research to clarify a specifics of the lateral spacial distribution of the intensity of x-ray radiation around more spacious areas (placed more farly from lens' focus along axial directions). As the result we found that in many cases a range of characteristical features of nonstandard behavior for the spread function are exist. They may be asymmetrical behavior of gaussian peak (most frequently), superposition of two peaks (whose are respectively big and small), strong nongauss behavior, etc.
We consider for all these effects to be explained fully by a nonaccuracy adjustment of angles and position of the polycapillary lens because of a limited precision of applied piesomechanics. Herewith most acceptable of the quality of the adjustment of the lens refers to cases of asymmetrical behavior of gaussian peak of the spread function of the lens. In the frame of this research a range of series of scanning experiments for detecting the spread function of the x-ray lens was carried out. The numbers of these series and the experiments of each series were be about 10. (Each series corresponded to an individual case of adjustment of the polycapillary lens, whereas a single experiments in each series referred to an individual case of spacial position of interesting field of spread function along the axial direction.)
We selected the range of the cases of the detected spread functions in order to be proceed by the quantitative analysis (approximation) those refer to the cases of most good quality of lens' adjustment. After that a various of approximation models (asymmetrical gaussians, extreme, logistpk, lorentz peaks , some our models) were tested by us. As the result it was shown that most good results refer to the cases of the extreme peaks approximation model additionally modified by us.
The scanning experiments were carried out at Synchrotron and Terahertz Research (INP SB RAS, Novosibirsk) and the Kurchatov Complex of Synchrotron-Neutron Research (KISI, Moscow) using a confocal X-ray microscope. The work was carried out in the framework of the RFBR projects no. 19-05-50046. The work was partly done at the shared research center SSTRC on the basis of the VEPP-4-VEPP-2000 complex at BINP SB RAS, using equipment supported by project RFMEFI62119X0022.
 Mantouvalou, W. Malzer, and B. Kanngiesber, “Quantification for 3D Micro X-ray Fluorescence,” Spectrochimica Acta. Pt. B 77, 9–18 (2012).