Based on the performance evaluation method of traditional imaging optical systems, this study reveals that the autocorrelation function of the point hologram can be used to evaluate the imaging performance of incoherent digital holographic adaptive optics (IDHAO) system. Inspired by the fact that the autocorrelation function of the ideal white noise function is approximately a Dirac δ function, we propose that increasing the randomness of the point hologram can make its autocorrelation function close to the Dirac δ function and improve the imaging resolution of the IDHAO system. Accordingly, a practical method which introduces a random phase plate into the IDHAO system, is proposed and implemented to increase the randomness of the point hologram. The proposed method is evaluated through numerical simulations and effects of the pixel number and the standard deviation of phase in the random phase plate on the imaging resolution of the IDHAO system are investigated. Finally, an optical experiment is performed in the laboratory to evaluate the proposed method and experimental results demonstrate that the random phase plate can effectively improve the IDHAO system's imaging resolution.