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. Lay description Structured illumination microscopy is a method used to build optical sections that reveal details closest together than the fundamental Abbe resolution limit. Fifteen images are classically required to compute the final super resolved section when the sample is three dimensional, while only seven are sufficient in the two dimensional case. The need for extra images in the three dimensional case is explained by the necessity to disentangle the information contained in optical section from the out of focus content. In this paper we show that by estimating and subtracting the out of focus content from the images before combining, then only seven images are sufficient to build super resolved optical sections of three dimensional samples. The main difficulty lies in the evaluation of the weight of the out of focus part. We evaluate the efficiency of our approach using simulated data. We show that it is insensitive to the illumination pattern structure and contrast. We then present results obtained in a 100 micrometre thick C-elegans worm. We compare optical sections computed using a limited number of images, with or without background subtraction, that clearly demonstrate the enhancement brought by our approach.