Diagnostic tools used to determine the metallicity of lensed galaxies in the AMAZE sample. In each block, the top-left panel shows the best solution (blue cross) and the 1σ confidence level in the A_V–metallicity plane. In the other panels the solid black line show the average relations between various line ratios and the gas metallicity as inferred by Maiolino et al. (2008). The dashed lines show the associated dispersions. The green error bars show the observed ratios (along the y-axis) and the best-fit metallicity with uncertainty (along the x-axis); the blue cross shows the best-fit metallicity and the de-reddened ratios from adopting the best-fit extinction; the red line shows the projection of the 1σ uncertainty of the fit in the top-left panel. For the lensed AMAZE galaxy LnA1689-2 the metallicity was inferred from the [NeIII]/[OII] line ratio exploiting the anticorrelation (though with high dispersion) between this line ratio and the metallicity found in Maiolino et al. (2008).