We have made a Phase Shift Mode Interferometric Optical Microscope (PSM-IOM) operating in liquid and in real time (video rate). We thus implemented for IOM two of the widely accepted basic advantages of Digital Holography Microscopy. Using a modified Tolansky objective to compensate the phase shift from the liquid cell window, we can measure without immersing any part of the microscope objective. The fringe visibility was reduced by 14% in water compared to air. In order to follow surface nano-topography at video rate, we have implemented a Fourier Transform based algorithm which computes the phase map from a single interferogram. A comparison to the Hariharan algorithm is given. As a proof of concept, the nano-evolution of a surface profile of Cu in sulphuric acid is shown.