Improving structured illumination microscopy by blind reconstruction and multifocus detection Structured Illumination Microscopy (SIM) is a super resolution microscopy method which enables a two fold resolution enhancement with respect to classical wide field (WF) fluorescence microscopy. In SIM the sample is illuminated by a pattern typically a sinusoidal grid of light. This pattern is typically the result of interference of either two or three plane waves. The wide dissemination of SIM is limited by the difficulties arising during the necessary numerical reconstruction. Artefacts are observed in the SIM reconstructed images if the illumination pattern is distorted or unknown. Blind SIM is a deconvolution based reconstruction approach that enables to reconstruct both the sample and the illumination pattern. Blind SIM is able to reconstruct partially or fully unknown illumination patterns and is therefore robust to distortions. However so far blind SIM was not able to process data from thick samples where the visibility of the fringes is reduced by the presence of out of focus light. In this work we present the thick slice blind SIM algorithm which reconstructs a 3D stack from a 2D measurement thus removing the out of focus light. The acquisition speed in 3D SIM is limited by the axial scanning and sequential focusing. Using a multifocus detection enables to simultaneously acquire a focal series. Merging SIM excitation with multifocus detection (MF SIM) permits to enhance the volumetric acquisition speed of 3D SIM as well as removing the need for axial mechanical scanning a source of sample drift and vibrations. The recorded MF SIM data does not obey the same theoretical description as the conventional scanning 3D SIM data. Hence the classical approach for 3D SIM reconstruction cannot be applied. We developed a deconvolution based algorithm using known 3D illumination pattern that can be applied to the reconstruction of MF SIM data. The results demonstrate enhanced resolution in all three dimensions.