Sky confusion noise in the far-infrared: Cirrus, galaxies and the cosmic far-infrared background

We examined the sky confusion noise in 40 sky regions by analysing 175 far- infrared (90-200 mum) maps obtained with ISOPHOT, the photometer on-board t he Infrared Space Observatory. For cirrus fields with (B) > 5 MJy sr(-1) th e formula based on IRAS data (Helou & Beichman 1990) predicts confusion noi se values within a factor of 2 of our measurements. The dependence of the s ky confusion noise on the surface brightness was determined for the wavelen gth range 90 less than or equal to lambda less than or equal to 200 mum. We verified that the confusion noise scales as N proportional to (B)(1.5), in dependent of the wavelength and confirmed N proportional to lambda (2.5) fo r lambda greater than or equal to 100 mum.The scaling of the noise value at different separations between target and reference positions was investiga ted for the first time, providing a practical formula. Since our results co nfirm the applicability of the Helou & Beichman (1990) formula, the cirrus confusion noise predictions made for future space missions with telescopes of a similar size can be trusted. At 90 and 170 mum a noise term with a Poi ssonian spatial distribution was detected in the faintest fields ((B) less than or equal to 3-5 MJy sr(-1)), which we interpret as fluctuations in the Cosmic Far-Infrared Background (CFIRB). Applying ratios of the fluctuation amplitude to the absolute level of 10% and 7% at 90 and 170 mum, respectiv ely, as supported by model calculations, we achieved a new simultaneous det ermination of the fluctuation amplitudes and the surface brightness of the CFIRB. The fluctuation amplitudes are 7 +/- 2 mJy and 15 +/- 4 mJy at 90 an d 170 mum, respectively. We obtained a CFIRB surface brightness of B-0 = 0. 8 +/- 0.2 MJy sr(-1) (vI(v) = 14 +/- 3 nWm(-2) sr(-1)) at 170 mum and an up per limit of 1.1 MJy sr(-1) (vI(v) = 37 nWm(-2) sr(-1)) at 90 mum.