Based on the rate equations of a two_level system, the analytical solutions of r elaxation of carrier populations with spin_up and spin_down polarization are obt ained under the condition of incomplete initial spin polarization. In the small signal regime, the saturated absorption_change expression of right_ and left_cir cularly polarized probe beam is given. The parameter, initial degree of spin pol arization of electron population, appears in the expression. Therefore, the init ial degree of spin polarization of electron population, which is a very importan t key parameter in the transport of spin polarization, can be extracted by fitti ng the expression to the saturated absorption trace obtained experimentally. Fin ally, the initial degree of spin polarization of photo_injected electron populat ion and its relaxation time constant in GaAs/AlGaAs multiple quantum wells are a cquired in experiments.