We present adivision of focal plane(DoFP)polarimeter based polarization microscope capable of measuring both the Stokes vector simultaneously and the 4×3 Mueller matrix with optimal polarization illumination.Using a calibration protocolproposed in this work and the GPU acceleration,thisDoFPpolarimeteris capable offast Stokes calculations and almost video rate polarization imaging.To test the potential applications of this polarization microscope in clinical diagnosis,4×3 Mueller matrix images ofunstainedhuman carcinoma tissue sliceshave been taken and analyzed using direct observation and Mueller matrix transformation.The preliminary results show that the m24 and m34elements of the Mueller matrix can provide rich microstructural information on the biological samples.Under circularly polarized illuminations,the characteristic features represented bythe m24 and m34elements can be enhanced further and displayed as single frame images with optimum contrasts,which is known as the“polarization staining” technique.Hence,combined with GPU acceleration algorithm,the DoFP polarization microscope is capable of real time polarization stained imaging of fast dynamic processes in living biological specimen.