Theory describing a super-resolution microscopy experiment using temporally and spatially coherent structured illumination was developed, and used to derive a method for processing experimental data. Numerical simulations were performed to verify that the method can, in principle, produce super-resolved images that are exactly equivalent to an image processed by a system with a much larger aperture (that is, the correct weighting between different regions of the image spectrum is maintained). The process was then demonstrated experimentally, showing a factor of two improvement in resolution over a diffraction-limited, coherently illuminated, microscope.