The European Large Area ISO Survey - IX. The 90-mu m luminosity function from the Final Analysis sample

We present the 90-mum luminosity function of the Final Analysis of the European Large Area ISO Survey (ELAIS), extending the sample size of our previous analysis (Paper IV) by about a factor of 4. Our sample extends to z = 1.1, similar to50 times the comoving volume of Paper IV, and 10(7.7) < h(-2) L/Lcircle dot < 10(12.5). From our optical spectroscopy campaigns of the northern ELAIS 90-mum survey (7.4 deg(2) in total, to S-90 (mum) > 70 mJy), we obtained redshifts for 61 per cent of the sample (151 redshifts) to B < 21 identified at 7 mum, 15 mum, 20 cm or with bright (B < 18.5) optical identifications. The selection function is well-defined, permitting the construction of the 90-mum luminosity function of the Final Analysis catalogue in the ELAIS northern fields, which is in excellent agreement with our Preliminary Analysis luminosity function in the ELAIS S 1 field from Paper IV. The luminosity function is also in good agreement with the recent IRAS-based prediction of Serjeant and Harrison - which, if correct, requires luminosity evolution of (1 + z)(3.4 +/- 1.0) for consistency with the source counts. This implies an evolution in comoving-volume-averaged star formation rate at z less than or similar to 1 consistent with that derived from rest-frame optical and ultraviolet surveys.