A method includes: (a) providing spatially-patterned activation radiation to a sample that includes phototransformable labels, where an optical parameter of the spatially-patterned activation radiation varies periodically in space; (b) providing spatially-patterned excitation radiation to the sample, where an optical parameter of the spatially-patterned excitation radiation varies periodically in space, where (a) and (b) create a non-linear fluorescence emission pattern within the sample, the pattern including H modulation harmonics, with H>1. The method includes (c) detecting radiation emitted from the activated and excited labels, (d) storing detected radiation data, and (e) spatially shifting one or both of the spatially-patterned excitation radiation and the spatially-patterned activation radiation with respect to the sample to spatially shift the non-linear fluorescence emission pattern within the sample, and (f) repeating (a)-(e) at least N times, with N>2. Then, a sub-diffraction-limited final image of the sample is generated based on the stored data for the N positions of the non-linear fluorescence emission pattern within the sample.