Structured illumination microscopy with unknown patterns and a statistical prior

TL;DR

This paper introduces PE-SIMS, a novel SIM reconstruction algorithm that self-calibrates using only pattern covariance, achieving doubled resolution and robustness without prior pattern knowledge or calibration.

Contribution

The paper presents a new self-calibration algorithm for SIM that eliminates the need for known illumination patterns, using statistical priors and covariance information.

Findings

Achieves 2x resolution improvement over widefield microscopy.

Insensitivity to aberration-induced pattern distortions.

Robustness against parameter tuning.

Abstract

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 \textit{algorithmic self-calibration} strategy for SIM that does not need to know the exact patterns {\it 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$\times$ better resolution than a conventional widefield microscope, while remaining insensitive to aberration-induced pattern distortion and robust against parameter tuning.