Sparsity-based super-resolution microscopy from correlation information: erratum.

Two references on sparse deconvolution of high-density fluorescence microscopy images are added to [Opt. Express26(14), 18238 (2018)].

Sparsity-based super-resolution microscopy from correlation information.

For more than a century, the wavelength of light was considered to be a fundamental limit on the spatial resolution of optical imaging. Particularly in light microscopy, this limit, known as Abbe's diffraction limit, places a fundamental constraint on the ability to image sub-cellular organelles with high resolution. However, modern microscopy techniques such as STED, PALM, and STORM, manage to recover sub-wavelength information, by relying on fluorescence imaging. Specifically, PALM/STORM acquire large sequences of fluorescence images from molecules attached to the organelles within the imaged specimen, such that in each frame only a small set of fluorophores are active. The position of each fluorophore can be found accurately in each frame, and the image is recovered by superimposing the points from all frames. The resulting grainy image is subsequently smoothed to produce the final super-resolved image with a resolution of tens of nano-meters. However, because PALM/STORM rely on many (>10,000) exposures, they suffer from poor temporal resolution. To address that, super-resolution optical fluctuation imaging (SOFI) was shown to produce sub-diffraction images with increased temporal resolution, by allowing for higher fluorophore density and exploiting the temporal statistics of the emissions. However, the improved temporal resolution of SOFI comes at the expense of its spatial resolution, which is not as high as that of PALM/STORM. Here, we present a new method called SPARCOM: sparsity-based super-resolution correlation microscopy, which combines a shorter integration time than previously reported with spatial resolution comparable to PALM and STORM. SPARCOM relies on sparsity in the correlation domain, exploiting the sparse distribution of fluorescent molecules and the lack of correlation between different emitters. We demonstrate our technique in simulations and in experiments and provide comparisons to state-of-the-art high density methods.

Non-diffracting multi-electron vortex beams balancing their electron-electron interactions.

The wave-like nature of electrons has been known for almost a century, but only in recent years has the ability to shape the wavefunction of EBeams (Electron-Beams) become experimentally accessible. Various EBeam wavefunctions have been demonstrated, such as vortex, self-accelerating, Bessel EBeams etc. However, none has attempted to manipulate multi-electron beams, because the repulsion between electrons rapidly alters the beam shape. Here, we show how interference effects of the quantum wavefunction describing multiple electrons can be used to exactly balance both the repulsion and diffraction-broadening. We propose non-diffracting wavepackets of multiple electrons, which can also carry orbital angular momentum. Such wavefunction shaping facilitates the use of multi-electron beams in electron microscopy with higher current without compromising on spatial resolution. Simulating the quantum evolution in three-dimensions and time, we show that imprinting such wavefunctions on electron pulses leads to shape-preserving multi-electrons ultrashort pulses. Our scheme applies to any beams of charged particles, such as protons and ion beams.Vortex electron beams are generated using single electrons but their low beam-density is a limitation in electron microscopy. Here the authors propose a scheme for the realization of non-diffracting electron beams by shaping wavepackets of multiple electrons and including electron-electron interactions.

Sparsity-based Ankylography for Recovering 3D molecular structures from single-shot 2D scattered light intensity.

Deciphering the three-dimensional (3D) structure of complex molecules is of major importance, typically accomplished with X-ray crystallography. Unfortunately, many important molecules cannot be crystallized, hence their 3D structure is unknown. Ankylography presents an alternative, relying on scattering an ultrashort X-ray pulse off a single molecule before it disintegrates, measuring the far-field intensity on a two-dimensional surface, followed by computation. However, significant information is absent due to lower dimensionality of the measurements and the inability to measure the phase. Recent Ankylography experiments attracted much interest, but it was counter-argued that Ankylography is valid only for objects containing a small number of volume pixels. Here, we propose a sparsity-based approach to reconstruct the 3D structure of molecules. Sparsity is natural for Ankylography, because molecules can be represented compactly in stoichiometric basis. Utilizing sparsity, we surpass current limits on recoverable information by orders of magnitude, paving the way for deciphering the 3D structure of macromolecules.