Fig. 4.

Resolution extension by nonlinear structured illumination. (a) The region of frequency space that is observable by conventional microscopy (compare with Fig. 2a). (b) An example of a sinusoidal illumination pattern. (c) That illumination pattern has three frequency components: one at the origin (black), representing the average intensity, and two at ±k₁, representing the modulation (dark gray). These are also the frequency components of the effective excitation under linear (i.e., nonsaturating) structured illumination. Under conditions of saturation, or other nonlinear effects, a theoretically infinite number of additional components appear in the effective excitation; the three lowest harmonics are shown here (light gray). (d) Observable regions for conventional microscopy (black), linear structured illumination (dark gray), and nonlinear structured-illumination microscopy (light gray) based on those three lowest harmonics. (e) Corresponding observable regions if the procedure is repeated with other pattern orientations. The much larger region of observable spatial frequencies (e) compared with that shown in a makes it possible to reconstruct the sample with correspondingly increased spatial resolution.