Incoherent digital holographic adaptive optics is a new technology of wavefront sensing and correction. Combined with appropriate numerical algorithm, wavefront sensing and compensation can be achieved by the wavefront recording and reconstruction ability of the holography. Based on the basic principle of the Fresnel incoherent correlation holography (FINCH), the incoherent digital holographic adaptive optics is investigated through theoretical analysis and simulations. Holograms of the guide star and the distorted object are recorded respectively using a modified Michelson interferometer. Aberrations in the distorted hologram can be compensated digitally by using the complex conjugate of the guide star hologram. The effect of the size and position of the guide star on the wavefront compensation are investigated quantitatively through experiments. The aberrations can be well compensated by the guide star chosen from a suitable area which is measured by the parameters of system. Furthermore, the isoplanatic region of the system is demonstrated.