Lateral resolution that exceeds the classical diffraction limit by a factor of two is achieved by using spatially structured illumination in a wide-field fluorescence microscope. The sample is illuminated with a series of excitation light patterns, which cause normally inaccessible high-resolution information to be encoded into the observed image. The recorded images are linearly processed to extract the new information and produce a reconstruction with twice the normal resolution. Unlike confocal microscopy, the resolution improvement is achieved with no need to discard any of the emission light. The method produces images of strikingly increased clarity compared to both conventional and confocal microscopes.