  Recently, chiral structured illumination microscopy has been proposed to
image fluorescent chiral domains at sub-wavelength resolution. Chiral
structured illumination microscopy is based on the combination of structured
illumination microscopy, fluorescence-detected circular dichroism, and optical
chirality engineering. Since circular dichroism of natural chiral molecules is
typically weak, the differential fluorescence is also weak and can be easily
buried by the noise, hampering the fidelity of the reconstructed images. In
this work, we systematically study the impact of the noise on the quality and
resolution of chiral domain images obtained by chiral SIM. We analytically
describe the signal-to-noise ratio of the reconstructed chiral SIM image in the
Fourier domain and verify our theoretical calculations with numerical
demonstrations. Accordingly, we discuss the feasibility of chiral SIM in
different experimental scenarios and propose possible strategies to enhance the
signal-to-noise ratio for samples with weak circular dichroism.
