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 $\mu$m) maps obtained with ISOPHOT, the photometer on-board the Infrared Space Observatory. For cirrus fields with $\rm > 5$ MJysr$^{-1}$ the formula based on IRAS data (Helou & Beichman, \cite{Helou+Beichman_90}) predicts confusion noise values within a factor of 2 to our measurements. The dependence of the sky confusion noise on the surface brightness was determined for the wavelength range 90 $\le \lambda \le$ 200 $\mu$m. We verified that the confusion noise scales as N ~ ^{1.5}, independent of the wavelength and confirmed N ~ lambda^{2.5}$ for lambda >= 100$um. The scaling of the noise value at different separations between target and reference positions was investigated for the first time, providing a practical formula. Since our results confirm 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 170um a noise term with a Poissonian spatial distribution was detected in the faintest fields ( <= 3-5 MJysr^{-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 170um, respectively, as supported by model calculations, we achieved a new simultaneous determination of the fluctuation amplitudes and the surface brightness of the CFIRB. The fluctuation amplitudes are 7(+/-)2 mJy and 15(+/-)4 mJy at 90 and 170um, respectively. We obtained a CFIRB surface brightness of B(0)=0.8(+/-)0.2 MJysr^{-1} (nuI_nu=14(+/-)3nWm^-2sr^-1) at 170um and an upper limit of 1.1 MJysr^{-1} (nuI_nu=37 nWm^-2sr^-1) at 90um