The majority of optical super-resolution imaging methods have been developed for thin or transparent biological samples, where the effects of scattering are minimized. Moreover, most of these techniques are based on the manipulation of fluorescent probes, or other molecular real-energy states. Multiphoton spatial frequency modulated imaging (MP-SPIFI) provides a pathway for super-resolving fine structures through multiple scattering lengths by making use of a modulated line focus and nonlinear excitation, and is applicable to both fluorescence and harmonic generation imaging. The technique works by projecting a set of 1D spatial frequencies onto the object, and utilizing the multiphoton interaction to drive harmonics of the spatial frequencies. The result is that an n-photon interaction yields frequency support of nearly 2n beyond the lens NA in the lateral x-dimension, along the line focus. However, the axial resolution of the object is limited in the conventional way by how tightly the line is focused. Here, we improve axial resolution by employing a limited-angle diffraction tomography, where the illumination is rotated in the x-z plane relative to the sample. The set of angular measurements are coherently combined in spatial-frequency space. Using a priori information about the location of each measurement in this kx-kz space greatly enhances the signal-to-noise ratio of the reconstructed object. We expect the method to be a useful way to improve resolution in deep-tissue imaging, or with any sample that exhibits strong scattering.
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