Chandra deep fields represent the deepest look at the X–ray sky .
We analyzed the Chandra Deep Field South ( CDFS ) with the aid of a dedicated wavelet-based algorithm .
Here we present a detailed description of the procedures used to analyze this field , tested and verified by means of extensive simulations .
We show that we can safely reconstruct the Log N–Log S source distribution of the CDFS down to limiting fluxes of 2.4 \times 10 ^ { -17 } and 2.1 \times 10 ^ { -16 } erg s ^ { -1 } cm ^ { -2 } in the soft ( 0.5–2 keV ) and hard ( 2–10 keV ) bands , respectively , fainter by a factor \lower 2.15 pt \hbox { $ \buildrel > \over { \sim } $ } 2 than current estimates .
At these levels we can account for \lower 2.15 pt \hbox { $ \buildrel > \over { \sim } $ } 90 \% of the 1–2 keV and 2–10 keV X–ray background .