Proof of the equivalence between two-frame and three-frame optical sectioning structured illumination microscopy

Abstract

Structured illumination microscopy (SIM) is capable of optical sectioning (OS), facilitating easy 3D imaging. It normally illuminates samples with three-frame of equi-phase-shifted fringe patterns and then reconstructs an OS image with the Root-Mean-Square (RMS) algorithm. To increase the OS efficiency, two-frame-based OS-SIMs, such as HiLo and SHT schemes, have been developed. However, a trade-off must be made when choosing these OS-SIM algorithms regarding the amount of raw data, the empirical factor determination and adjustment, and the artifacts. In this paper, we propose a two-frame-based OS-SIM method that uses both a fringe and a uniform illumination image, termed the FUIHT method. It has the same raw data as the HiLo microscopy but a different data processing algorithm. FUIHT intrinsically avoids the empirical factor determination and adjustment in HiLo microscopy. Importantly, we have proved that FUIHT is completely equivalent to the RMS method in mathematics. Both simulation and experimental studies validate that FUIHT can output higher-fidelity optically sectioned images as the RMS, with faster reconstruction speed than the HiLo microscopy. To our knowledge, this finding bridges the normal RMS-based OS-SIM and the HiLo microscopy for the first time. We expect the FUIHT method to enable the OS-SIM to be more efficient, rapid, accurate, and robust in 3D imaging.