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

Mechanically scanned interference pattern structured illumination imaging

We present a fully lensless single pixel imaging technique using mechanically scanned interference patterns. The method uses only simple, flat optics; no lenses, curved mirrors, or acousto-optics are used in pattern formation or detection. The resolution is limited by the numerical aperture of the angular access to the object, with a fundamental limit of a quarter wavelength and no fundamental limit on working distance. While it is slower than some similar techniques, the lack of a lens objective and simplification of the required optics could make it more applicable in difficult wavelength regimes such as UV or X-ray.

Improving techniques for diagnostics of laser pulses by compact representations

We propose and demonstrate, numerically and experimentally, use of sparsity as prior information for extending the capabilities and performance of techniques and devices for laser pulse diagnostics. We apply the concept of sparsity in three different applications. First, we improve a photodiode-oscilloscope system's resolution for measuring the intensity structure of laser pulses. Second, we demonstrate the intensity profile reconstruction of ultrashort laser pulses from intensity autocorrelation measurements. Finally, we use a sparse representation of pulses (amplitudes and phases) to retrieve measured pulses from incomplete spectrograms of cross-correlation frequency-resolved optical gating traces.

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.

Single-shot 3D coherent diffractive imaging of core-shell nanoparticles with elemental specificity

We report 3D coherent diffractive imaging (CDI) of Au/Pd core-shell nanoparticles with 6.1 nm spatial resolution with elemental specificity. We measured single-shot diffraction patterns of the nanoparticles using intense x-ray free electron laser pulses. By exploiting the curvature of the Ewald sphere and the symmetry of the nanoparticle, we reconstructed the 3D electron density of 34 core-shell structures from these diffraction patterns. To extract 3D structural information beyond the diffraction signal, we implemented a super-resolution technique by taking advantage of CDI’s quantitative reconstruction capabilities. We used high-resolution model fitting to determine the Au core size and the Pd shell thickness to be 65.0 ± 1.0 nm and 4.0 ± 0.5 nm, respectively. We also identified the 3D elemental distribution inside the nanoparticles with an accuracy of 3%. To further examine the model fitting procedure, we simulated noisy diffraction patterns from a Au/Pd core-shell model and a solid Au model and confirmed the validity of the method. We anticipate this super-resolution CDI method can be generally used for quantitative 3D imaging of symmetrical nanostructures with elemental specificity.

Sparsity-Based Super Resolution for SEM Images

The scanning electron microscope (SEM) is an electron microscope that produces an image of a sample by scanning it with a focused beam of electrons. The electrons interact with the atoms in the sample, which emit secondary electrons that contain information about the surface topography and composition. The sample is scanned by the electron beam point by point, until an image of the surface is formed. Since its invention in 1942, the capabilities of SEMs have become paramount in the discovery and understanding of the nanometer world, and today it is extensively used for both research and in industry. In principle, SEMs can achieve resolution better than one nanometer. However, for many applications, working at subnanometer resolution implies an exceedingly large number of scanning points. For exactly this reason, the SEM diagnostics of microelectronic chips is performed either at high resolution (HR) over a small area or at low resolution (LR) while capturing a larger portion of the chip. Here, we employ sparse coding and dictionary learning to algorithmically enhance low-resolution SEM images of microelectronic chips-up to the level of the HR images acquired by slow SEM scans, while considerably reducing the noise. Our methodology consists of two steps: an offline stage of learning a joint dictionary from a sequence of LR and HR images of the same region in the chip, followed by a fast-online super-resolution step where the resolution of a new LR image is enhanced. We provide several examples with typical chips used in the microelectronics industry, as well as a statistical study on arbitrary images with characteristic structural features. Conceptually, our method works well when the images have similar characteristics, as microelectronics chips do. This work demonstrates that employing sparsity concepts can greatly improve the performance of SEM, thereby considerably increasing the scanning throughput without compromising on analysis quality and resolution.

Frontier methods in coherent X-ray diffraction for high-resolution structure determination

In 1912, Max von Laue and collaborators first observed diffraction spots from a millimeter-sized crystal of copper sulfate using an X-ray tube. Crystallography was born of this experiment, and since then, diffraction by both X-rays and electrons has revealed a myriad of inorganic and organic structures, including structures of complex protein assemblies. Advancements in X-ray sources have spurred a revolution in structure determination, facilitated by the development of new methods. This review explores some of the frontier methods that are shaping the future of X-ray diffraction, including coherent diffractive imaging, serial femtosecond X-ray crystallography and small-angle X-ray scattering. Collectively, these methods expand the current limits of structure determination in biological systems across multiple length and time scales.

Single-shot and single-sensor high/super-resolution microwave imaging based on metasurface

Real-time high-resolution (including super-resolution) imaging with low-cost hardware is a long sought-after goal in various imaging applications. Here, we propose broadband single-shot and single-sensor high-/super-resolution imaging by using a spatio-temporal dispersive metasurface and an imaging reconstruction algorithm. The metasurface with spatio-temporal dispersive property ensures the feasibility of the single-shot and single-sensor imager for super- and high-resolution imaging, since it can convert efficiently the detailed spatial information of the probed object into one-dimensional time- or frequency-dependent signal acquired by a single sensor fixed in the far-field region. The imaging quality can be improved by applying a feature-enhanced reconstruction algorithm in post-processing, and the desired imaging resolution is related to the distance between the object and metasurface. When the object is placed in the vicinity of the metasurface, the super-resolution imaging can be realized. The proposed imaging methodology provides a unique means to perform real-time data acquisition, high-/super-resolution images without employing expensive hardware (e.g. mechanical scanner, antenna array, etc.). We expect that this methodology could make potential breakthroughs in the areas of microwave, terahertz, optical, and even ultrasound imaging.

Sparsity-based super-resolved coherent diffraction imaging of one-dimensional objects

Phase-retrieval problems of one-dimensional (1D) signals are known to suffer from ambiguity that hampers their recovery from measurements of their Fourier magnitude, even when their support (a region that confines the signal) is known. Here we demonstrate sparsity-based coherent diffraction imaging of 1D objects using extreme-ultraviolet radiation produced from high harmonic generation. Using sparsity as prior information removes the ambiguity in many cases and enhances the resolution beyond the physical limit of the microscope. Our approach may be used in a variety of problems, such as diagnostics of defects in microelectronic chips. Importantly, this is the first demonstration of sparsity-based 1D phase retrieval from actual experiments, hence it paves the way for greatly improving the performance of Fourier-based measurement systems where 1D signals are inherent, such as diagnostics of ultrashort laser pulses, deciphering the complex time-dependent response functions (for example, time-dependent permittivity and permeability) from spectral measurements and vice versa.

In measurements that employ phase retrieval algorithms, such as coherent diffraction imaging, reconstruction of one-dimensional signals is challenging due to ambiguity issues. Here, the authors demonstrate super-resolution coherent imaging of one-dimensional objects by utilizing sparsity prior information.