Circularly polarized images with high spatial resolution (better than 1 arcsec) of a solar active region, obtained with a tunable filter in the wings of Fe I 5247.1 A and Fe I 5250.2 A, have been analyzed in terms of the magnetic line ratio technique introduced by Stenflo (1973). Whenever a measurable amount of polarization is present, the distribution of the observed magnetic-line ratio is compatible with a unique value, which is randomly blurred by noise due to the photon statistics, the CCD camera, and atmospheric distortions. There is no need for a distribution of field strengths to explain the observed distribution of the magnetic line ratio. Consequently, the observations are compatible with a unique magnetic field strength in solar small-scale magnetic elements of about 1000 G at the level of line formation. For a thin flux tube, this corresponds to a field strength of approximately 2000 G at the level of continuum formation, which is in excellent agreement with previous field strength determinations from low spatial resolution spectra (4-10 arcsec).