A two-coupler-type Er-doped-fiber ring resonator is proposed which compensates for the round-trip optical loss by optical amplification thereby attaining a high finesse. Also proposed is a mode-filtered heterodyne method for resonant-linewidth measurements which does not demand narrow-linewidth light sources but uses the beat noise between two uncorrelated lights filtered by the resonator passband. With the proposed measurement method, a finess greater-than-or-equal-to 500 and a resonant linewidth less-than-or-equal-to 17 kHz are confirmed from the Er-doped fiber ring resonator. The ring resonator is operated as a high-resolution optical spectrum analyzer.