Zernike phase contrast microscopy is extended and combined with a phase-shifting mechanism to perform quantitative phase measurements of microscopic objects. Dozens of discrete point light sources on a ring are constructed for illumination. For each point light source, three different levels of point-like phase steps are designed, which are alternatively located along a ring on a silica plate to perform phase retardation on the undiffracted (dc) component of the object waves. These three levels of the phase steps are respectively selected by rotating the silica plate. Thus, quantitative evaluation of phase specimens can be performed via phase-shifting mechanism. The proposed method has low "halo" and "shade-off" effects, low coherent noise level, and high lateral resolution due to the improved illumination scheme.