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[en] A quadrupole lens-free diagnostic is a simple single shot method which can be used to measure the electron beam transverse emittance. LANEX screens are used as profile monitors due to the high yield of visible photons which can be easily detected by standard camera sensors. This type of minimally destructive diagnostics is particularly suitable for electron beams accelerated by the laser wakefield mechanism where the basic parameters of such beams fluctuate shot-to-shot mainly during the beam optimizing process. It allows to simultaneously measure the beam divergence, position, profile, pointing, and charge. The numerical study of the diagnostics performance and applicability range is presented and its limits are discussed. The influence of the LANEX screen multiple Coulomb scattering is studied by means of GEANT4; the unfolding procedure for multiple scattering contribution is presented.