Structured illumination microscopy with unknown patterns and a statistical prior.

Structured illumination microscopy (SIM) improves resolution by down-modulating high-frequency information of an object to fit within the passband of the optical system. Generally, the reconstruction process requires prior knowledge of the illumination patterns, which implies a well-calibrated and aberration-free system. Here, we propose a new algorithmic self-calibration strategy for SIM that does not need to know the exact patterns a priori, but only their covariance. The algorithm, termed PE-SIMS, includes a pattern-estimation (PE) step requiring the uniformity of the sum of the illumination patterns and a SIM reconstruction procedure using a statistical prior (SIMS). Additionally, we perform a pixel reassignment process (SIMS-PR) to enhance the reconstruction quality. We achieve 2× better resolution than a conventional widefield microscope, while remaining insensitive to aberration-induced pattern distortion and robust against parameter tuning.