Numerical analysis of structured illumination microscopy: Influence of illumination pattern geometry and fringe thickness on resolution enhancement

Structured illumination microscopy (SIM) enables optical imaging beyond the diffraction limit by heterodyning high spatial frequencies into the observable passband of a conventional microscope. In this work, a complete numerical framework is developed to investigate how illumination pattern geometry and structural parameters influence image formation and resolution enhancement in two-dimensional SIM. Synthetic samples representing periodic arrays of polymer nanotubes are modeled under multiple illumination families, including sinusoidal, Ronchi, sawtooth, and triangular configurations. Each simulation incorporates realistic photon shot noise, detector readout noise, and the optical transfer function (OTF) of a high-numerical-aperture system. Quantitative metrics such as full width at half maximum (FWHM), intensity dip metric, modulation contrast, edge sharpness, contrast-to-noise ratio (CNR), and high-frequency spectral energy are extracted to evaluate performance as a function of fringe thickness. The results demonstrate that structured illumination significantly narrows the effective point-spread function (PSF), enhances image contrast, and recovers otherwise inaccessible high-frequency details. Non-sinusoidal patterns yield improved resolution due to their richer harmonic content, though with minor side-lobe artifacts. Generally, the proposed simulation framework provides both physical insight and practical guidance for optimizing illumination design and achieving higher fidelity in super-resolution SIM imaging.