Any attempt to study matter in extreme conditions encounters severe issues connected with non-linear intensity-dependent phenomena naturally occurring in the interaction process. For the purposes of such fundamental experiments, the laser beam must be well pre-defined before and/or rather well characterized after the irradiation since the non-Gaussian nature of almost all the XUV/X-ray laser beams is responsible for parasitic non-linear effects in the experimental results. It was shown that a considerably better agreement between the simulated and measured data can be achieved if the real beam profile is known. The original method invented by IP-ASCR researchers, for realistic reconstructing the non-Gaussian intensity distribution in the short-wavelength laser beam by investigating its ablation imprints in a suitable material, is reported in this paper. Researchers from other institutions contributed mostly by implementing and proving the method at FEL facilities.