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Context. The deuterium fraction in low-mass prestellar cores is a gooddiagnostic indicator of the initial phases of star formations, and it is also afundamental quantity to infer the ionisation degree in these objects.  Aims. With the analysis of multiple transitions of $\rm N_2H^+$, $\rmN_2D^+$, $\rm HC^{18}O^+$ and $\rm DCO^+$ we are able to determine themolecular column density maps and the deuterium fraction in $\rm N_2H^+$ and$\rm HCO^+$ toward the prototypical prestellar core L1544. This is thepreliminary step to derive the ionisation degree in the source.  Methods. We use a non-local thermodynamic equilibrium (non-LTE) radiativetransfer code, combined with the molecular abundances derived from a chemicalmodel, to infer the excitation conditions of all the observed transitions,which allows us to derive reliable maps of each molecule's column density. Theratio between the column density of a deuterated species and its non-deuteratedcounterpart gives the searched deuteration level.  Results. The non-LTE analysis confirms that, for the analysed molecules,higher-J transitions are characterised by excitation temperatures $\approx1-2\,$K lower than the lower-J ones. The chemical model that provides the bestfit to the observational data predict the depletion of $\rm N_2H^+$ and to alesser extent of $\rm N_2D^+$ in the innermost region. The peak values for thedeuterium fraction that we find are $\mathrm{D/H_{N_2H^+}} =0.26^{+0.15}_{-0.14}$ and $\mathrm{D/H_{HCO^+}} = 0.035^{+0.015}_{-0.012}$, ingood agreement with previous estimates in the source.

High sensitivity maps of molecular ions in L1544: I. Deuteration of N2H+ and HCO+ and first evidence of N2D+ depletion