The Fourier ptychographic microscopy (FPM) algorithm provides a method for reconstructing a high resolution image by stitching together the Fourier spectra of a number of low resolution intensity images, which are taken under various inclined illumination angles. However, the quality of the reconstructed image can be distorted by the optical aberrations of the illumination system. In this paper we investigate the influence of the optical aberrations on the reconstructed intensity images by using the FPM algorithm and discuss whether is it possible to remove the optical aberrations of the illumination system.