Using the Sparrow criterion, the resolution of small double-bar targets placed in a bright background is investigated for an optical system under partially coherent illumination. The analysis is performed in one dimension. It is shown that the best resolution can be attained under the illumination condition that the ratio of the numerical aperture of the condenser to that of the objective is unity. It is further shown that the resolution of small double-bar targets with unequal complex transmittance becomes poorer compared with that for the case of equal transmittance.