Nonlinear scanning structured illumination microscopy based on nonsinusoidal modulation

Structured illumination microscopy (SIM) is an essential super-resolution microscopy technique that enhances resolution. Several images are required to reconstruct a super-resolution image. However, linear SIM resolution enhancement can only increase the spatial resolution of microscopy by a factor of two at most because the frequency of the structured illumination pattern is limited by the cutoff frequency of the excitation point spread function. The frequency of the pattern generated by the nonlinear response in samples is not limited; therefore, nonlinear SIM (NL-SIM), in theory, has no inherent limit to the resolution. In the present study, we describe a two-photon nonlinear SIM (2P-SIM) technique using a multiple harmonics scanning pattern that employs a composite structured illumination pattern, which can produce a higher order harmonic pattern based on the fluorescence nonlinear response in a 2P process. The theoretical models of super-resolution imaging were established through our simulation, which describes the working mechanism of the multi-frequency structure of the nonsinusoidal function to improve the resolution. The simulation results predict that a 5-fold improvement in resolution in the 2P-SIM is possible.