The model independent procedure of extracting charge density distribut
ions from elastic electron scattering data is investigated. The charge
density distributions are expanded on an orthonormal basis and the pa
rameters of the expansions are fixed by the comparison with the experi
mental data. Two bases with different analytical properties (Fourier-B
essel and Hermite) are used. This allows us to disentangle the uncerta
inties coming from the choice of the expansion basis from those intrin
sic to the extraction procedure. We design a set of tests to select th
e number of the expansion coefficients adequate for a proper descripti
on of the data. The procedure is applied to elastic data measured on C
-12, Ca-40 and Pb-208 nuclei.