Self-referenced spectral interferometry with extended time excursion (SRSI-ETE) is a powerful method for single-shot characterization of the temporal contrast of a high peak power laser, which has high temporal resolution but a low dynamic range. Here, a temporal contrast reduction method is proposed that uses the cascaded Kerr lens process in two thin glass plates. Combined with the SRSI-ETE method, the measurement dynamic range of the method is increased about two orders of magnitude while having a 20 fs temporal resolution and a 40 ps time window in single shot.