Applying structured illumination microscopy to coherent imaging modalities such as scattering does not yield any additional information beyond that provided by oblique illumination. It thus yields no resolution enhancement over the Abbe diffraction limit, which was derived precisely for that case.
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Rainer Heintzmann holds a patent (patent no. WO2000052512A1) on nonlinear structured illumination microscopy. Kai Wicker currently works for a company that has an associated enterprise with a structured illumination microscope in their sales portfolio.
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Wicker, K., Heintzmann, R. Resolving a misconception about structured illumination. Nature Photon 8, 342–344 (2014). https://doi.org/10.1038/nphoton.2014.88
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DOI: https://doi.org/10.1038/nphoton.2014.88
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