Out-of-focus background subtraction for fast structured illumination super-resolution microscopy of optically thick samples.

We propose a structured illumination microscopy method to combine super resolution and optical sectioning in three-dimensional (3D) samples that allows the use of two-dimensional (2D) data processing. Indeed, obtaining super-resolution images of thick samples is a difficult task if low spatial frequencies are present in the in-focus section of the sample, as these frequencies have to be distinguished from the out-of-focus background. A rigorous treatment would require a 3D reconstruction of the whole sample using a 3D point spread function and a 3D stack of structured illumination data. The number of raw images required, 15 per optical section in this case, limits the rate at which high-resolution images can be obtained. We show that by a succession of two different treatments of structured illumination data we can estimate the contrast of the illumination pattern and remove the out-of-focus content from the raw images. After this cleaning step, we can obtain super-resolution images of optical sections in thick samples using a two-beam harmonic illumination pattern and a limited number of raw images. This two-step processing makes it possible to obtain super resolved optical sections in thick samples as fast as if the sample was two-dimensional.