Far-infrared detection limits - II. Probing confusion including source confusion

We present a comprehensive analysis for the determination of the confusion levels for the current and the next generation of far-infrared surveys assuming three different cosmological evolutionary scenarios. We include an extensive model for diffuse emission from infrared cirrus in order to derive absolute sensitivity levels taking into account the source confusion noise due to point sources, the sky confusion noise due to the diffuse emission, and instrumental noise. We use our derived sensitivities to suggest best survey strategies for the current and the future far-infrared space missions Spitzer, AKARI (ASTRO-F), Herschel and SPICA. We discuss whether the theoretical estimates are realistic and the competing necessities of reliability and completeness. We find the best estimator for the representation of the source confusion and produce predictions for the source confusion using far-infrared source count models. From these confusion limits considering both source and sky confusions, we obtain the optimal, confusion limited redshift distribution for each mission. Finally, we predict the cosmic far-infrared background (CFIRB), which includes information about the number and distribution of the contributing sources.