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Figure 3. Schematic of the mechanism of expanding the Fourier frequency of collecting the spatial distribution of the signals for imaging.( a) Wave vector in the Fourier space of signal collection using an objective lens from a diffraction limited spot,( b) Fourier space augmented by the projected structured line with wave vector( k s),( c) combined wave vector of the objective and the structured light in one direction, and( d) The combined Fourier space addressed using the microscope.
heterodyne detection of spatial frequencies x object of the object under test. The structured illumination provides a local oscillator spatial frequency c k s anditisshifting( or folding) spatial frequency components of the object image within the range of x s � x 0 and x s + x 0( Fig. 3).
3.1.1 Linear SIM
SIM has been introduced by Gustafsson [ 15 ] andhasshown to provide images of fluorescent objects with an up to twofold resolution enhancement compared to wide-field microscopy. The reason for this limitation is because the structured illumination used is typically provided by an interference pattern, which is illuminating the object via the illumination optics of the microscope. Therefore, the local oscillator frequency is limited by the bandwidth of the illumination optics x 0, ill. which usually is smaller or equal to the bandwidth of the imaging optics:
x s x 0; ill: x 0:
SIM can be easily applied also for non-fluorescent objects, i. e. it can be adapted for label-free SRM as well. The structured illumination can also be achieved by spatio-temporal fast scanning of a small light spot, e. g. a focussed laser beam [ 30 ]. In principle, this opens the option to achieve higher local oscillator frequencies x s > x 0 if a sub-diffraction light spot can be created and quickly scanned over the object. In this direction recently we investigated options to create such small controllable light spot e. g. by using novel plasmonic lens concepts [ 31 ] or by fast scanning photonic nano-jets [ 32 ].
3.1.2 Non-linear SIM
To extend the spatial frequency of the local oscillator, nonlinear interactions such as saturation or multi-photon processes can be used. In saturated structured illumination microscopy( SSIM) [ 16 ] the non-linearity results from the saturation of excitation states, which generate higher order of harmonics in the detection( typically fluorescence) signal, which can be used as local oscillators with higher spatial frequencies well above the cut-off frequency x s >> x 0.
The high order harmonics can expand the optical bandwidth, resulting in a better resolution than conventional SIM. Although the SSIM resolution is theoretically unlimited, the signal-to-noise ratio practically limits the resolution. Gustafsson et al showed a resolution in the order of 50 nm on a fluorescence sample using this technique [ 16, 17 ].
The SIM technique can be applied for other nonlinear light-matter interactions, such as Raman scattering microscopy, coherent anti-Stokes Raman scattering( CARS) microscopy as well as second harmonic generation( SHG) and third harmonic generation( THG) microscopy. SHG and THG microscopies have emerged as powerful imaging modalities to examine the structural properties of label-free samples [ 33 ]. However, the SHG process requires the environment to be non-centrosymmetric at the excitation wavelength scale, whereas the THG process requires a medium with intrinsic inhomogeneities due to a refractive index mismatch [ 34, 35 ]. Typical lateral resolution in SHG and THG is limited to the longer excitation wavelength and lower numerical aperture [ 35 ]. Therefore, the resolution improvement with these techniques is a challenge. Huttunen et al. [ 36 ] proposed a coherent nonlinear SIM scheme based on spatially modulating the phase of the incident field and using interferometric detection for extracting the emitted complex-valued field. With this method, lateral resolution can be improved four- and six-fold for SHG and THG processes, respectively.
In the context of SIM for inelastic scattering such as Raman scattering, the spatial distribution of Raman scatterer is excited with structured excitation light intensity. Since the light emitted from a point is proportional to the product of the amount of Raman scatterer and the local excitation light intensity, a beat pattern, known as Moiré fringes, will appear in the observed image. The spatial resolution obtained in such a configuration is( see Fig. 3):
1 d s ¼ ðk 0 þ k s Þ:
Since the highest spatial frequency that can be imposed by the same objective can be k 0, the maximum resolution obtainable in this scheme is: