Investigating the performance of reconstruction methods used in structured illumination microscopy as a function of the illumination pattern's modulation frequency

Surpassing the resolution of optical microscopy defined by the Abbe diffraction limit, while simultaneously achieving optical sectioning, is a challenging problem particularly for live cell imaging of thick samples. Among a few developing techniques, structured illumination microscopy (SIM) addresses this challenge by imposing higher frequency information into the observable frequency band confined by the optical transfer function (OTF) of a conventional microscope either doubling the spatial resolution or filling the missing cone based on the spatial frequency of the pattern when the patterned illumination is two-dimensional. Standard reconstruction methods for SIM decompose the low and high frequency components from the recorded low-resolution images and then combine them to reach a high-resolution image. In contrast, model-based approaches rely on iterative optimization approaches to minimize the error between estimated and forward images. In this paper, we study the performance of both groups of methods by simulating fluorescence microscopy images from different type of objects ( ranging from simulated two-point sources to extended objects). These simulations are used to investigate the methods' effectiveness on restoring objects with various types of power spectrum when modulation frequency of the patterned illumination is changing from zero to the incoherent cut-off frequency of the imaging system. Our results show that increasing the amount of imposed information by using a higher modulation frequency of the illumination pattern does not always yield a better restoration performance, which was found to be depended on the underlying object. Results from model-based restoration show performance improvement, quantified by an up to 62% drop in the mean square error compared to standard reconstruction, with increasing modulation frequency. However, we found cases for which results obtained with standard reconstruction methods do not always follow the same trend.