A systematic investigation on the theoretical framework of the ultra-fast measurement of temperature by extended X-ray absorption fine structure (EXAFS) applied in laser-driven-compression experiments has been carried out and a new temperature measurement scheme based on the EXAFS cumulant expansion analysis and anharmonic correlated Debye model has been advanced. By considering the anharmonic effect of thermal vibration and avoiding the employment of the empirical model as well as parameters which have large inherent uncertainties in the temperature determination, this new scheme is theoretically more accurate than traditional ones. Then the performance of the new measurement scheme and traditional methods were validated on a synchrotron radiation platform by temperature-dependent EXAFS (TDEXAFS) experiments on Au, Fe, V and Ti; the results showed that the new scheme could provide the most accurate measured temperatures with much lower uncertainties. This accurate scheme gives a firmer physical ground to the EXAFS temperature measurement technique and can expect to be applied in laser-driven compression experiments and promote the development of matter state research at extreme conditions.
