[Download Saints Row The Third Highly Compressed
Ainoha Sistek
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Nonlinear structured illumination microscopy (nSIM) is an effective approach for super-resolution wide-field fluorescence microscopy with a theoretically unlimited resolution. In nSIM, carefully designed, highly-contrasted illumination patterns are combined with the saturation of an optical transition to enable sub-diffraction imaging. While the technique proved useful for two-dimensional imaging, extending it to three-dimensions is challenging due to the fading of organic fluorophores under intense cycling conditions. Here, we present a compressed sensing approach that allows 3D sub-diffraction nSIM of cultured cells by saturating fluorescence excitation. Exploiting the natural orthogonality of speckles at different axial planes, 3D probing of the sample is achieved by a single two-dimensional scan. Fluorescence contrast under saturated excitation is ensured by the inherent high density of intensity minima associated with optical vortices in polarized speckle patterns. Compressed speckle microscopy is thus a simple approach that enables 3D super-resolved nSIM imaging with potentially considerably reduced acquisition time and photobleaching.
Super-resolution fluorescence microscopy has proven to be a fundamental tool in biology to unveil processes occurring at the nano-scale1. Subdiffraction imaging can be obtained by exciting the fluorescent probes in a nonlinear regime, either inducing binary stochastic responses2,3 or under saturated conditions4,5. The saturated optical transition can be absorption5,6, stimulated emission4,7, ground state depletion8 or fluorescence photo-switching, generalized as REversible Saturable Optical Linear Fluorescence Transitions (RESOLFT) techniques9,10. Illumination with patterned light excitation then appears as an essential scheme11,12.
In the linear excitation regime, structured illumination microscopy (SIM) with fringes13, grids14, or speckles15,16,17 can provide up to a twofold improvement in resolution as compared to widefield imaging, especially in three dimensions (3D)18. Imaging in 3D is then obtained by acquiring every single transverse plane. In this configuration, fluorescence arising from out-of-focus planes is thus induced to be wasted since suppressed by numerical sectioning19. Fluorescence-signal-wasting is all the more detrimental under optical-saturation conditions, required to allow breaking the diffraction limit up to theoretically unlimited resolutions, in which case nonlinear photo-bleaching may occur5,20. Typically, the fragility of dyes has never allowed recording several transverse planes in saturated-excitation structured-illumination microscopy. 3D fluorescence nanoscopy requirements thus call for compressed sensing approaches21.
Random wavefields feature two main interesting properties that make them suitable for 3D super-resolution microscopy. First, speckle patterns lying in different transverse planes are orthogonal relatively to the cross-correlation product (Supplementary Note 2), thus allowing axial discrimination of two-dimensional objects22,23. This property exactly provides the random-projection-measurement configuration ideally suited for compressed imaging reconstruction24,25, in particular for 3D imaging26. Second, speckles exhibit strong intensity contrasts since naturally containing a high density of optical vortices of topological charge one27, such as typically used in STimulated Emission Depletion (STED) microscopy28. Optical vortices in speckles are associated with nodal lines of intensity (in 3D) that can confine fluorescence to subdiffraction dimensions29, despite the contribution of the axial field. Indeed, in tightly focused beams, the vectorial nature of light cannot be neglected, especially under saturated conditions, in which case the axial field may destroy most of intensity zeros. Whether it is possible to break the diffraction barrier with saturated speckle patterns has remained an open theoretical question30.
Here, we demonstrate the possibility to achieve 3D super-resolution imaging by a single 2D raster scan under saturated fluorescence excitation with tightly focused speckle patterns. Using a custom-built speckle scanning microscope, we can image with a factor 3.3 beyond the diffraction barrier. Super-resolution imaging capabilities are characterized using fluorescent nano-beads, and applied for imaging stained lysosomes in fixed cultured cells.
The scanning speckle microscope is sketched in Fig. 1a. A spatial light modulator (SLM), conjugated to the back focal plane of the objective lens, is used to generate a 3D fully developed speckle pattern (See Methods and Supplementary Fig. 1 for a more complete description). A regular diffuser could replace the SLM but the latter allows a dynamic control of the size of the illuminating speckle pattern and thus of the intensity at the sample plane. The random wave entering the objective is circularly polarized in order to minimize the axial field at isotropic vortices of same handedness and so, to provide isotropic super-resolution in transverse planes under saturated excitation conditions (see Supplementary Note 8).
The intensity profile of a 3D speckle pattern (Fig. 1c) in a transverse xy-plane (Fig. 1d, e) and in an axial xz-plane (Fig. 1f, g) is shown both under nonsaturated (Fig. 1d, f) and saturated (Fig. 1e, g) excitation conditions. Speckle point spread functions (SPSF) were obtained by scanning isolated fluorescent nano-beads. Under saturated illumination conditions, dark round-shaped points remain both in the xy and in the xz sections (highlighted by dashed ellipses in Fig. 1e, g), which can be attributed to the crossing of these planes by nodal vortex lines. These dark points ensure contrast conservation under saturated excitation, so enlarging the power spectrum of the SPSF (Fig. 1h, i) and demonstrating the larger accessible spectral support of the optical transfer function for imaging applications. Contrast conservation under saturated conditions is at the basis of RESOLFT microscopy, in which resolution typically scales as32:
Imaging with random structures raises the specific challenge of object reconstruction. Techniques have been developed to reconstruct images even when the speckles are unknown15,17 especially through scattering samples33,34,35,36. Adding sparsity constraints to the rebuilt object is particularly helpful, especially to retrieve 3D information from 2D images26. Adding sparsity priors about the object in compressive sensing approaches may even provide details smaller than the resolution of the instrument36. Conversely, in our case, super-resolution information is experimentally extracted from the sample thanks to the power spectrum enlargement of the optical transfer function under saturated fluorescence excitation. In order to demonstrate so, we first perform plane-by-plane Wiener deconvolution37,38. Interestingly, Wiener deconvolution being just a cross-correlation product with a spectral renormalization, speckles satisfy the same orthogonality properties (see Supplementary Note 3). A single parameter must be adjusted: the mean power spectral density of the noise of images. In our results, we tuned this parameter by visual image optimization.
Reconstruction by plane-by-plane Wiener deconvolution of the 2D speckle image exploits the statistical orthogonality of speckles lying in different axial planes. However, since speckles are only orthogonal in a statistical sense, out-of-focus point-sources contribute to a background noise whose amplitude is inversely proportional to the number of speckle grains (see Supplementary Note 4). In a worst-case scenario, a bright out-of-focus point-source may even theoretically blind a fainter one because of the out-of-focus reconstruction background. In Supplementary Note 4, we demonstrate that for a scanning speckle pattern containing N speckle grains in each axial plane, the sample should not exhibit more than \(\simeq \sqrt N\) point-sources to maintain a signal to noise ratio higher than 1 after cross-correlation projection. Wiener reconstruction is expected to require similar conditions. Moreover, even for an isolated point source, reconstruction by Wiener deconvolution yields a peak surrounded by noise. For these reasons, although vesicles can be distinguished, a significant background is observed in Wiener-reconstructed images in Fig. 3b.
Such reconstruction noise artifacts can be suppressed using compressed sensing algorithms. In this regard, our speckle scanning techniques probing the sample with random point spread functions, is ideally suited21,24. Here, a fast iterative shrinkage-thresholding algorithm (FISTA) was used43,44. This algorithm iteratively solves such linear inverse problem as ours, by additionally taking the sample sparsity into account. FISTA converges toward a Lagrangian minimization:
The presented results were obtained with a very simple and inexpensive system, where the microscope objective could be easily changed for any high NA optics (like a condenser), whose optical properties are poor but which can efficiently collect the fluorescence signal. In our experiments, we observed that photo-bleaching (Supplementary Fig. 8) was less critical than background signal originating from the optics and the immersion oil (Supplementary Fig. 7). Here, background signal was important because fluorescence excitation was saturated, but 3D super-resolution speckle imaging could also be performed saturating other optical transitions such as stimulated emission, which makes use of red-shifted light as an intense laser beam and thus both reduces background signal and photo-bleaching. In this case, speckle patterns having inverted intensity contrast47 could be used for the excitation and the de-excitation speckle patterns. Speckles with tailored statistical properties could also be used48, such as non-Rayleigh speckles49, potentially improving statistical orthogonality. Nondiffracting speckle beams50 could also allow tuning the depth of field.
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