Infrared luminosities as a function of redshift for Herschel sources situated in the GOODS-S-ultradeep field (red squares) and situated in the GOODS-S-deep and GOODS-N fields (open circles). The blue line on a white background shows the L_IR limits above which the GOODS-S-ultradeep sample could be considered as a unbiased sample of the star-forming galaxy population at this redshift. These limits are inferred in Fig. 9, and “steps” correspond to the redshift bins used for the LF analysis. For the GOODS-S-deep and GOODS-N fields, these limits are shifted by ~0.2  dex towards higher L_IR.