Resolution beyond the rayleigh limit using beam displacement

Two fluorescence microscope systems which claim to achieve resolution beyond the Rayleigh limit have recently been described. These systems operate using two displaced beams focused on the sample and produce the image from the region of overlap. We describe an analogous system, which performs in a similar manner but does not rely on fluorescence. The imaging performance of these systems is analysed and we show that they all give improved resolution although, crucially, the optical bandwidth is not increased. These systems merely attenuate the lower spatial frequencies and, although such systems can be useful and operate in a manner analogous to pupil plane filters, it is important to appreciate that they do not offer true superresolution, contrary to the impression given in previous papers.