The operation of a Photo Elastic Modulator (PEM) type ellipsometer is described via Mueller matrix elements. The phase shift (6) and the relative amplitude attenuation ratio (tan ik) between orthogonal polarization components is contained in the Mueller matrix elements and can be obtained via combinations of measured matrix elements. A phase shift measurement accuracy of ±0.2° has been obtained without calibration. A computer controlled implementation is described along with simple algorithms to extract the ellipsometric constants. The Mueller matrix of a magneto optic film media system has been used along with one for a "leaky " beamsplitter to form the optical readout system matrix for an ideal system. One of the Stokes parameters is porportional to the differential detection signal often used in MO data detection schemes.