An uncooled infrared focal plane array (FPA) for a multiband optical imaging system monitoring small gas leakages is low in cost but limited by its frame rate and sensitivity. We propose the concept of Archimedean spiral push-broom filtering (ASPBF), where the trajectory of an Archimedean spiral over the FPA is approximated as a straight line. The ASPBF precisely matches the electronic pulse scanning of the uncooled infrared FPA row by row to improve the frame rate. We applied differential imaging to promote gas detection sensitivity. Prototype can detect 11 ml/min of ethylene gas at ΔT = 3 °C with frame rate of 8 fps.