It is known that the phase-shift intererometry is promising measurement method for the precise optical test. Liquid crystal (LC) phase shifter is very attractive as an electrically tunable phase sifter for the key component of the test system. We adopt here a bend aligned liquid crystal cell for the fast phase shifting, and mount it on the optical system of polarization microscope. A potential application for precise 2D birefringence measurement system is investigated and as high as a few tenths of a wavelength resolution can be obtained by the simple 4-step phase shifting technique. Obtained image data show the phase profile which corresponds to retardation distribution of the prepared sample, and then it becomes possible to perform quantitative analysis of 2D birefringence distribution in planar sample. Since there is basically a setting angle dependency of the test sample, measurement phase data have information of birefringence sign (positive or negative) and we can distinguish between the direction parallel and perpendicular to the anisotropic axis. We observe tiny marine zooplankton as a weakly anisotropic actual sample, and the birefringence of the muscle can be clearly detected. It is also successfully pick up that the elongated direction of muscles show higher index value.