Benefiting from the development of increasingly advanced high speed cameras, flow visualization and analysis nowadays yield detailed data of the flow field in many applications. Notwithstanding this progress, for high speed and supersonic flows it is still not trivial to capture high quality images. In this study we present a Schlieren setup that uses pulsed LEDs with high currents (up to 18 Ampere) to increase the optical output to sufficient levels. The bright and short pulses, down to 130 nanoseconds, allow detailed and sharp imaging of the flow with a high spatial resolution adequate for supersonic flow. The pulse circuit and pulse width determination are explained in detail. As a test case we studied the near field of a 2 mm diameter sonic jet injected transversely into a supersonic cross flow. This is a model flow for fuel injection in scramjet engines, which is not yet fully understood. Owing to the high resolution and accuracy of the images produced by the newly developed system we prove the existence of a large (density) gradient wave traveling in the windward subsonic region between the Mach barrel and the bowshock, which hitherto was observed only in some numerical studies but not yet shown in experiments. Furthermore, we demonstrate with this Schlieren setup that time-correlated images can be obtained, with an interframe time of 2 microseconds, so that also flow unsteadiness can be studied such as the movement of shock waves and trajectories of vortices. The obtained results of the jet penetration height are presented as a power law correlation. The results of this study show that the designed setup using a low-cost LED and low-cost control system is a high potential option for application in visualization studies of high speed flows.