The backward-compatible stereoscopic display is a technology that a stereoscopic view is perceived with 3D glasses while a 2D version of the 3D image is concurrently available for naked-eye viewers on the same physical display medium. This unique functionality is achieved by an information display technology Temporal Psychovisual Modulation (TPVM), an interesting interplay between high refresh rate optoelectronic display, signal processing and psychophysics. However, the current performance of the system is not satisfactory, and it is a trade-off keeping simultaneously the best performance of the 3D view and the 2D view. The global quality of 3D scene and 2D scene plays a great important impact on user's quality-of-experience. In this paper, we are the first to put forward the concept of global quality, including two components: the quality of 3D view and 2D view. Then we have constructed the display system prototype and first proposed quality assessment criteria to evaluate the quality of both 3D scene and 2D scene, towards as guidance to improve their performances. We conduct subjective experiments to figure out when the system runs the best under the criteria. Experimental results demonstrate that we can effectively calculate the optimal quality of this system using the quality assessment criteria.