When the digital micromirror device (DMD) is applied in the convergent path of the imaging optical system, the deflection movement of the micromirrors on the DMD surface around their respective rotation axes and the non-continuous distribution with respect to the plane mirror directly result in an optical path difference (OPD) between the off-axis chief ray and the on-axis chief ray. Based on the geometrical optics and the aberration theory, the relationship between the final OPD and the image height on the DMD surface, the incident angle, the DMD pixel size and the DMD tilt angle is obtained in the DMD-based convergent imaging path. The factors influencing the image quality of optical system and the compensation method are analyzed. The correctness of the theory is verified by simulation and experiments. The research results have a great significance to the design and adjustment of optical systems with DMD devices.