Structured illumination applied to imaging interferometric microscopy (IIM) allows extension of the resolution limit of low numerical aperture objective lenses to ultimate linear systems limits (<approximately lambda/4 in air) without requiring a reference beam around the objective lens. Instead, the reference beam is provided by an illumination beam just at the edge of the optical system numerical aperture resulting in a shift of the recorded spatial frequencies (equivalent to an intermediate frequency). The restoration procedure is discussed. This technique is adaptable readily to existing microscopes, since extensive access to the imaging system pupil plane is not required.