Rocket nozzle performance is critically affected by shock-induced flow separation when operating in over-expanded conditions. This study presents an experimental and quantitative investigation of the unsteady flow phenomena occurring in an over-expanded Thrust Optimized Parabolic (TOP) rocket nozzle. Building upon previous work on the characterization of Free Shock Separation (FSS), Restricted Shock Separation (RSS), and the End-Effect Regime (EER), this research introduces and validates the Background Oriented Schlieren (BOS) technique as a quantitative flow visualization tool for high-speed nozzle flows and combine it with Proper Orthogonal Decomposition (POD), a data-driven modal analysis technique, to describe the flow's main instability structure.