Optical diffraction tomography (ODT) is a recent imaging technique that combines the experimental methods of phase microscopy and synthetic aperture with the mathematical tools of inverse scattering theory. We show experimentally that this approach permits us to obtain the map of permittivity of highly scattering samples with axial and transverse resolutions that are much better than that of a microscope with the same numerical aperture.

Structured illumination microscopy (SIM) is a powerful technique for obtaining super-resolved fluorescence maps of samples, but it is very sensitive to aberrations or misalignments affecting the excitation patterns. Here, we present a reconstruction algorithm that is able to process SIM data even if the illuminations are strongly distorted. The approach is an extension of the recent blind-SIM technique, which reconstructs simultaneously the sample and the excitation patterns without a priori information on the latter. Our algorithm was checked on synthetic and experimental data using distorted and nondistorted illuminations. The reconstructions were similar to that obtained by up-to-date SIM methods when the illuminations were periodic and remained artifact-free when the illuminations were strongly distorted.