The relation between loudness and loudness limen of pure tone

Past postulates of relation between loudness and loudness limen of pure tone,which never explicated the physical process of loudness coding and judging and the relation between the physical process and psychological reflection,can not explain psychoacoustic experimental results well.In this paper,based on signal detection theory and postulates about loudness coding which assume that loudness is neural spikes count in duration of T and that temporal distribution of neural spikes rates for steady pure tone is steady normal stochastic,we get a relation between loudness and loudness limen of pure tone,which can explain experimental results of tonal intensity limen well,especially the results that could not be explained such as Weber fraction bump at the moderate level and near miss to Weber's law.The derived relation is that loudness limed-to-loudness ratio of pure tone is independent of signal intensities.