Abstract: The history and achievements on the minimum resolvable temperature difference(MRTD)mathematical model are researched.The most representative ten kinds of MRTD equations are transformed and deduced.The inherentrelations and difference of these equations are analyzed.Based on the match filtering model,the new MRTD equation,in which the too much approximately sampling is eliminated,tree dimension noise model has been described completely,and the effect of scan effenciency and over scan ratio has been included in the spatial integral of eye/brain,is deduced.