This paper describes how to take advantage of the replacement of an intensity camera with a polarization camera in a standard differential interference contrast (DIC) microscope. Using a polarization camera enables snapshot quantitative phase analysis so that real-time imaging of living transparent tissues become possible. Using our method, we quantify the phase measurement accuracy using a phantom consisting of glass beads embedded in lacquer. In order to demonstrate these advantages, we image the pumping heart and blood flow in a living medaka egg.