The cosmic infrared background (CIRB) consists mainly of the integrated light of distant galaxies. In the far-infrared the current estimates of its surface brightness are based on the measurements of the COBE satellite. Independent confirmation of these results is still needed from other instruments. In this paper we derive estimates of the far-infrared CIRB using measurements made with the ISOPHOT instrument aboard the ISO satellite. The results are used to seek further confirmation of the CIRB levels that have been derived by various groups using the COBE data. We study three regions of very low cirrus emission. The surface brightness observed with the ISOPHOT instrument at 90, 150, and 180 um is correlated with hydrogen 21 cm line data from the Effelsberg radio telescope. Extrapolation to zero hydrogen column density gives an estimate for the sum of extragalactic signal plus zodiacal light. The zodiacal light is subtracted using ISOPHOT data at shorter wavelengths. Thus, the resulting estimate of the far-infrared CIRB is based on ISO measurements alone. In the range 150 to 180 um, we obtain a CIRB value of 1.08+-0.32+-0.30 MJy/sr quoting statistical and systematic errors separately. In the 90 um band, we obtain a 2-sigma upper limit of 2.3 MJy/sr. The estimates derived from ISOPHOT far-infrared maps are consistent with the earlier COBE results.
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