The optical transfer function (OTF) of an optical system with partially coherent illumination was developed according to the theory of image formation. This function is the same as the incoherent OTF of optical system. So the permissible tolerances of the wave aberrations of optical system are identical for illumination either incoherent or partially coherent. This conclusion explained the customary rule of optical system design of microscope that the tolerances of wave aberrations are the same for both the incoherent and partially coherent illumination, no difference for various forms of illumination.