By use of the Fourier decomposition of a low-coherence optical image field into two spatial components that can be controllably shifted in phase with respect to each other, a new high-transverse-resolution quantitative-phase microscope has been developed. The technique transforms a typical optical microscope into a quantitative-phase microscope, with high accuracy and a path-length sensitivity of lambda/5500, which is stable over several hours. The results obtained on epithelial and red blood cells demonstrate the potential of this instrument for quantitative investigation of the structure and dynamics associated with biological systems without sample preparation.