Accurate determination of random pattern phase in structured illumination microscopy with low modulation depth

The initial phase of structured illumination is an important parameter in structured illumination microscopy (SIM). Its estimation accuracy directly affects the reconstruction quality of SIM super-resolution images. However, when the modulation of the system is less than 0.02, the current phase estimation algorithm will cause an estimation error above 0.2 rad. An algorithm based on multi-image correlation processing in frequency domain (MCF) is proposed to solve this problem. Simulation and experimental results show that the MCF algorithm greatly improves both the initial phase estimation accuracy and the reconstruction quality of super-resolution images for low modulation SIM systems with a random phase shift. This means that the MCF algorithm can extend the scope of the SIM technology, especially for low modulation systems or systems lacking precise phase-shifting components.