Microscope apparatus and methods for imaging an object with a resolution beyond the Abbe limit are disclosed. The apparatus employs an object selectively patterned with a fluorescing material that is induced to fluoresce with one wavelength and inhibited from fluorescing with a second wavelength. Two orthogonal interference-fringe patterns are generated from four diffracted light beams of an inhibiting wavelength and superimposed on the object along with light that induces fluorescence. The interference-pattern image allows only sub-resolution-sized emission areas of the object to fluoresce. Multiple images of the fluorescing object are obtained, each corresponding to a slightly different position of the fringe patterns on the substrate. Each image is processed to yield a sparsely sampled super-resolution image. Multiple sparse images are interwoven to form a complete super-resolution image of the object.