An object to be imaged is illuminated with a structured (e.g., sinusoidal) illumination at a plurality of phase shifts to allow lateral superresolution and axial sectioning in images. When an object is to be imaged in vitro or in another situation in which the phase shifts cannot be accurately determined a priori, the images are taken, and the phase shifts are estimated a posteriori from peaks in the Fourier transforms. The technique is extended to the imaging of fluorescent and non-fluorescent objects as well as stationary and non-stationary objects.