An investigation is made for a four-aperture, sparse optical synthetic aperture imaging system. The characteristics of both the diffraction-limited performance and the effects of aberrations on this system are obtained. According to the coverage range of optical transfer function, the space distribution's restrictive condition of sub-apertures and the diffraction-limited performance are deduced. The wavefront aberrations are classed as three types based on the relationship between the Strehl ratio and the sub-apertures' aberrations with the exponential approximation. The tolerance limits of piston error, tilt error and defocus error are calculated in terms of the Maréchal criterion,
Shengqian Wang ab, Changhui Rao a,Wenhan Jiang a. Diffraction-limited performance and aberration tolerance of a sparse optical synthetic aperture imaging system with four sub-apertures[J]. Journal of Modern Optics,2008,55(11):1771 - 1785.