The basis of structured illumination. (Left) Moiré fringes (dark bands) form between two periodic patterns. (Right) The blue circle (I) indicates the “observable region” of spatial frequencies in a conventional microscope. The three Fourier components of a sinusoidally striped illumination pattern (blue dots) must fall within this circle to be observable within the diffraction limit. (II) Illuminating the sample with structured light extends the observable region in (I) to contain the spatial frequencies within two offset regions (violet). (III) Moving and rotating the structured illumination can extend the frequency space by as much as a factor of 2.