NLTE determination of the calcium abundance and 3D corrections in extremely metal-poor stars

(Abridged) Extremely metal-poor stars contain the fossil records of the chemical composition of the early Galaxy. The NLTE profiles of the calcium lines were computed in a sample of 53 extremely metal-poor stars with a modified version of the program MULTI. With our new model atom we are able to reconcile the abundance of Ca deduced from the Ca I and Ca II lines in Procyon. -We find that [Ca/Fe] = 0.50 $\pm$ 0.09 in the early Galaxy, a value slightly higher than the previous LTE estimations. -The scatter of the ratios [X/Ca] is generally smaller than the scatter of the ratio [X/Mg] where X is a "light metal" (O, Na, Mg, Al, S, and K) with the exception of Al. These scatters cannot be explained by error of measurements, except for oxygen. Surprisingly, the scatter of [X/Fe] is always equal to, or even smaller than, the scatter around the mean value of [X/Ca]. -We note that at low metallicity, the wavelength of the Ca I resonance line is shifted relative to the (weaker) subordinate lines, a signature of the effect of convection. -The Ca abundance deduced from the Ca I resonance line (422.7 nm) is found to be systematically smaller at very low metallicity, than the abundance deduced from the subordinate lines.