We use aberration theory to derive a generalized pupil function of the Golay3 imaging system when astigmatisms exist in its submirrors. Theoretical analysis and numerical simulation using ZEMAX show that the point spread function (PSF) and the modulation transfer function (MTF) of the Golay3 sparse aperture system have a periodic change when there are piston errors. When the peak-valley value of the wavefront (PV(tilt)) due to the tilt error increases from zero to λ, the PSF and the MTF change significantly, and the change direction is determined by the location of the submirror with the tilt error. When PV(tilt) becomes larger than λ, the PSF and the MTF remain unvaried. We calculate the peaks of the signal-to-noise ratio (PSNR) resulting from the piston and tilt errors according to the Strehl ratio, and show that the PSNR decreases when the errors increase.