Superresoltuion (SR) microscopy is a valuable tool for biological studies. While the ability to resolve features to 20 nm and below is now routine in transparent specimens, such as cell cultures and cleared specimens, many areas of biological study have not been probed with SR imaging. Further, SR microscopy has thus far been limited primarily to contrast mechanisms that rely on real energy states of a target molecule, with fluorescence being the dominant modality. We recently demonstrated that spatial-frequency modulated imaging (SPIFI) enables superresolved imaging for both multiphoton fluorescence and nonlinear coherent scattering with single-pixel detection. The technique operates by projecting a set of spatial frequencies in one dimension along a spatiotemporally modulated line-focus that illuminates the specimen. Harmonics of the spatial frequencies projected onto the specimen encode spatial information beyond the diffraction limit of the illumination light. This additional information scales with the order of the nonlinearity, but is limited to the single dimension in which the grating sequence is projected. Consequently, 2D images collected with SR SPIFI are diffraction limited in the dimension perpendicular to the line focus. In this work, we extend our technique to a two-dimensional resolution enhancement with an inverse-domain lateral computed tomography. By enabling 2D SR SPIFI while maintaining single-pixel detection, we anticipate more widespread use of this method for imaging in turbid media.
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