Linear super-resolution microscopy via synthesis aperture approach permits fast acquisition because of its wide-field implementations, however, it has been limited in resolution because a missing spatial-frequency band occurs when trying to use a shift magnitude surpassing the cutoff frequency of the detection system beyond a factor of two, which causes ghosting to appear. Here, we propose a method of chip-based 3D nanoscopy through large and tunable spatial-frequency-shift effect, capable of covering full extent of the spatial-frequency component within a wide passband. The missing of spatial-frequency can be effectively solved by developing a spatial-frequency-shift actively tuning approach through wave vector manipulation and operation of optical modes propagating along multiple azimuthal directions on a waveguide chip to interfere. In addition, the method includes a chip-based sectioning capability, which is enabled by saturated absorption of fluorophores. By introducing ultra-large propagation effective refractive index, nanoscale resolution is possible, without sacrificing the temporal resolution and the field-of-view. Imaging on GaP waveguide material demonstrates a lateral resolution of lamda/10, which is 5.4 folds above Abbe diffraction limit, and an axial resolution of lamda/19 using 0.9 NA detection objective. Simulation with an assumed propagation effective refractive index of 10 demonstrates a lateral resolution of lamda/22, in which the huge gap between the directly shifted and the zero-order components is completely filled to ensure the deep-subwavelength resolvability. It means that, a fast wide-field 3D deep-subdiffraction visualization could be realized using a standard microscope by adding a mass-producible and cost-effective spatial-frequency-shift illumination chip.
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