ISO deep far-infrared survey in the Lockman Hole - III. Catalogs and source counts at 90 & 170 mu m

We present the catalogs and source counts for the C_90 (reference wavelength of 90 mum) and C_160 (170 mum) bands, which were extracted from our analysis of an ISO deep far-infrared survey conducted as part of the Japan/UH ISO cosmology project. The total survey area is similar to0.9 deg(2) in two fields within the Lockman Hole. The analysis consists of source extraction using the IRAF DAOPHOT package and simulations carried out by adding artificial sources to the maps to estimate the detection rate, the flux bias, the positional accuracy, and the noise. The flux calibration was performed using the Sb galaxy UGC 06009-the photometric error was estimated to be similar to50% at C_90 and similar to65% at C_160. The total noise estimated from the simulation is dominated by the confusion noise due to the high source density. The confusion noise is similar to20 mJy at C_90 and similar to35 mJy at C_160, which is much larger than the instrumental noise which is at the level of a few mJy or less. The catalogs were constructed by selecting 223 C_90 sources and 72 C_160 sources with a Signal to Noise Ratio (SNR) of three or greater. The distribution of the observed associations between C_90 and C_160 sources indicates that the 1sigma positional errors are similar to20 and similar to35 at C_90 and C_160, respectively. The corrections for the detection rate and the flux bias are significant for sources fainter than 200 mJy at C_90 and 250 mJy at C_160. Most of the sources detected both at C_90 and C_160 have a F(C_160)/F(C_90) color redder than the Sb galaxy UGC 06009. Such a red color could result from reddening due to the flux bias or a K-correction brightening due to the effect of redshift. Red sources brighter than 200 mJy at C 160 may be very luminous galaxies like Arp 220 at moderate redshift. The source counts are derived by applying the corrections for the detection rate and flux bias. The resultant counts are quite consistent with the constraints derived from the fluctuation analysis performed in Paper II. The C 160 counts are also consistent with the results from the FIRBACK project. Our C 90 survey, which is 2-3 times deeper than those previously published, reveals an upturn in the count slope at around 200 mJy. While recent models give a reasonable fit to the C 160 counts, none of them are successful in accounting for the upturn in the C 90 counts. If the upturn is caused by ultraluminous IR galaxies, their redshifts would need to be at zsimilar to0.5, implying a major event in galaxy evolution at moderate redshift.