This paper proposes a method for characterizing the linear relationship of sine amplitude grating imaging systems using the apparent transfer function, with the aim of investigating the linear response of grating imaging systems under partially coherent illumination. A spatial-domain mathematical model of the grating imaging system is established, and MATLAB is adopted for simulation. The simulation results indicate that the apparent transfer function of the imaging system approaches linearity within the normalized intrinsic frequency range of the grating as the system's coherence approaches that of a fully incoherent imaging system. An experimental platform was designed and constructed to investigate the linear relationship of the first-order and second-order harmonic components of the imaging system under three different coherence conditions, using seven gratings with different line pairs. The experimental results demonstrate that the apparent transfer function of the grating imaging system approaches linearity as the system becomes closer to a fully incoherent imaging system, which is in good agreement with the theoretical results.