Super-resolution fluorescence microscopy is an important tool in biomedical research for its ability to discern features smaller than the diffraction limit. However, due to its difficult implementation and high cost, the universal application of super-resolution microscopy is not feasible. In this paper, we propose and demonstrate a new kind of super-resolution fluorescence microscopy that can be easily implemented and requires neither additional hardware nor complex post-processing. The microscopy is based on the principle of stepwise optical saturation (SOS), where $M$ steps of raw fluorescence images are linearly combined to generate an image with a $sqrt{M}$-fold increase in resolution compared with conventional diffraction-limited images. For example, linearly combining (scaling and subtracting) two images obtained at regular powers extends resolution by a factor of $1.4$ beyond the diffraction limit. The resolution improvement in SOS microscopy is theoretically infinite but practically is limited by the signal-to-noise ratio. We perform simulations and experimentally demonstrate super-resolution microscopy with both one-photon (confocal) and multiphoton excitation fluorescence. We show that with the multiphoton modality, the SOS microscopy can provide super-resolution imaging deep in scattering samples.
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