In the top curve, the higher pulse energy causes fluorescence to saturate near the peaks of the pattern, leading to an asymmetric curve form with broad peaks and sharp valleys. The bottom curve approximately follows the sinusoidal illumination pattern, because the peak energy density is below the saturation regime. ( a) Profiles through images of a thin fluorescent layer illuminated by a Gaussian laser beam modulated by sinusoidal stripes with a period of 2.5 μm, with a peak energy density per pulse of 0.58 mJ/cm 2 (bottom curve) and 37 mJ/cm 2 (top curve). Verification of harmonic production through saturation. 5 b, bottom trace), indicating that the fluorescent response is noticeably nonlinear because of saturation effects already at that energy density.įig. The lowest harmonic is seen also at the lower pulse energy ( Fig. Fourier analysis of this pattern revealed five detectable harmonics at higher spatial frequencies than that of the illumination ( Fig. This behavior is in good qualitative agreement with expectations ( Fig. 5 a, top trace) as fluorescence saturated in the high-intensity regions. At a higher peak energy density of 37 mJ/cm 2, however, the emission pattern changed drastically, taking on broad, flat peaks and sharp, narrow valleys ( Fig. 5 a, bottom trace), not deviating far from the illumination intensity pattern. At a relatively low peak energy density per pulse of 0.58 mJ/cm 2, the observed pattern of emission was approximately sinusoidal ( Fig. Images were exposed for 0.1 s, corresponding to ≈600 excitation pulses. The fluorescent layer sample was illuminated by the line-pattern-modulated Gaussian beam described above. 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. ( e) Corresponding observable regions if the procedure is repeated with other pattern orientations. ( 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. 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). These are also the frequency components of the effective excitation under linear (i.e., nonsaturating) structured illumination. ( c) That illumination pattern has three frequency components: one at the origin (black), representing the average intensity, and two at ± k 1, representing the modulation (dark gray). ( b) An example of a sinusoidal illumination pattern. ( a) The region of frequency space that is observable by conventional microscopy (compare with Fig. Resolution extension by nonlinear structured illumination. Hence, normal, linear, structured-illumination microscopy (and confocal microscopy, which is a particular case of structured illumination) can extend resolution only by a factor of ≈2.įig. Thus, k 1 cannot be made larger than 2 NA/λ exc ≈ k 0, so the new resolution limit k 0 + k 1 can be at most ≈2 k 0. Unfortunately, the set of spatial frequencies that can be generated in a light field is limited by diffraction in the same way as the set of frequencies that can be observed. Thus, to maximize the resolution, it is desirable for the illumination to contain as high spatial frequencies k 1 as possible. The new information increases the highest observable spatial frequency (the resolution) from k 0 to k 0+ k 1. Thus, the information within that circle has been made indirectly observable it can be extracted by using a phase-shift method ( 17). Those fringes will be observable in the microscope if | k – k 1| < k 0, that is, if k lies within a circle of radius k 0 around k 1 ( Fig. If the illumination contains a spatial frequency k 1, then each sample frequency k gives rise to moiré fringes at the difference frequency k – k 1.
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