We propose a novel microscopy method, called chiral structured illumination microscopy, for fast imaging fluorescent chiral domains at sub-wavelength resolution. This method combines three main techniques, namely structured illumination microscopy, fluorescence-detected circular dichroism and optical chirality engineering. By generating the moir`e effect based on the circular dichroism response of the sample, chiral SIM is able to restore the high spatial frequency information on the chiral domains and reconstruct an image with super resolution. We establish the theoretical framework of chiral SIM and present a numerical demonstration that indicates its superior resolving power over that of diffraction-limited wide-field imaging methods. We also discuss the possibility of applying nanostructures that form the superchiral near fields to boost the circular dichroism response in the proposed chiral SIM method.
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