The theory of optical synthetic aperture imaging system with emphasis on the characteristics of the spatial frequency is described. The cut-off spatial frequency is got higher at the cost of the mid-spatial frequency, and the sidelobes of point spread function (PSF) are higher. The image quality evaluation for diffraction-limited optical synthetic aperture imaging system is analyzed with two-point resolution and optical transmission function (OTF). The disadvantages of Rayleigh criterion, Sparrow criterion and threshold criterion are given. When the sidelobe is 0.5 times of the maximum, the imaging quality of synthetic aperture system is no better than that of the single aperture system. Based on the OTF, relations between the effective diameter of three operture system and pupil parameters including the diameter of sub-apertures and spacing parameter are analyzed. When the pupil diameter is fixed, practical cut-off spatial frequency becomes larger first, and then reduces with the augmentation of the distance between pupils.