Coherent structured illumination microscopy using hexagonal-lattice illumination fields for enhancing the isotropy of 2D super-resolution

摘要

We present a method to improve the isotropy of 2D super-resolution in the coherent structured illumination microscopy (SIM) that can be implemented for imaging non-fluorescent samples. To alleviate the problem of anisotropic lateral resolution in the coherent SIM which previously employed the two orthogonal standing-wave illumination fields (referred to as the orthogonal SIM), we make use of a hexagonal-lattice illumination comprising three standing-wave fields that are simultaneously superimposed at the orientations equally divided in the lateral plane. A theoretical formulation is derived to rigorously model the coherent image formation with such simultaneous multiple-beam illuminations and a Fourier-domain framework is established to reconstruct an image with enhanced spatial resolution. Using a computer-synthesized resolution target to serve as a 2D coherent sample, we carried out numerical simulations to examine the imaging characteristics of our three-angle SIM compared with the orthogonal SIM. The investigation on the 2D resolving power for the various test patterns of different periods and orientations reveal that the orientation-dependent undulation of lateral resolution can be reduced from 27% to 8% in our three-angle SIM while the best resolution (0.54 times the resolution limit of conventional coherent imaging) in the directions of structured illumination is slightly deteriorated by 4.6% from that of the orthogonal SIM.