  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.
