Super-Resolution in Phase Space

This work considers the problem of super-resolution. The goal is to resolve a Dirac distribution from knowledge of its discrete, low-pass, Fourier measurements. Classically, such problems have been dealt with parameter estimation methods. Recently, it has been shown that convex-optimization based formulations facilitate a continuous time solution to the super-resolution problem. Here we treat super-resolution from low-pass measurements in Phase Space. The Phase Space transformation parametrically generalizes a number of well known unitary mappings such as the Fractional Fourier, Fresnel, Laplace and Fourier transforms. Consequently, our work provides a general super- resolution strategy which is backward compatible with the usual Fourier domain result. We consider low-pass measurements of Dirac distributions in Phase Space and show that the super-resolution problem can be cast as Total Variation minimization. Remarkably, even though are setting is quite general, the bounds on the minimum separation distance of Dirac distributions is comparable to existing methods.Comment: 10 Pages, short paper in part accepted to ICASSP 201

Arbitrarily High Super-Resolving Phase Measurements at Telecommunication Wavelengths

We present two experiments that achieve phase super-resolution at telecommunication wavelengths. One of the experiments is realized in the space domain and the other in the time domain. Both experiments show high visibilities and are performed with standard lasers and single-photon detectors. The first experiment uses six-photon coincidences, whereas the latter needs no coincidence measurements, is easy to perform, and achieves, in principle, arbitrarily high phase super-resolution. Here, we demonstrate a 30-fold increase of the resolution. We stress that neither entanglement nor joint detection is needed in these experiments, demonstrating that neither is necessary to achieve phase super-resolution.Comment: 5 pages, 7 figure

Fourier Magnetic Imaging with Nanoscale Resolution and Compressed Sensing Speed-up using Electronic Spins in Diamond

Optically-detected magnetic resonance using Nitrogen Vacancy (NV) color centres in diamond is a leading modality for nanoscale magnetic field imaging, as it provides single electron spin sensitivity, three-dimensional resolution better than 1 nm, and applicability to a wide range of physical and biological samples under ambient conditions. To date, however, NV-diamond magnetic imaging has been performed using real space techniques, which are either limited by optical diffraction to 250 nm resolution or require slow, point-by-point scanning for nanoscale resolution, e.g., using an atomic force microscope, magnetic tip, or super-resolution optical imaging. Here we introduce an alternative technique of Fourier magnetic imaging using NV-diamond. In analogy with conventional magnetic resonance imaging (MRI), we employ pulsed magnetic field gradients to phase-encode spatial information on NV electronic spins in wavenumber or k-space followed by a fast Fourier transform to yield real-space images with nanoscale resolution, wide field-of-view (FOV), and compressed sensing speed-up.Comment: 31 pages, 10 figure

Field-portable pixel super-resolution colour microscope.

Based on partially-coherent digital in-line holography, we report a field-portable microscope that can render lensfree colour images over a wide field-of-view of e.g., >20 mm(2). This computational holographic microscope weighs less than 145 grams with dimensions smaller than 17×6×5 cm, making it especially suitable for field settings and point-of-care use. In this lensfree imaging design, we merged a colorization algorithm with a source shifting based multi-height pixel super-resolution technique to mitigate 'rainbow' like colour artefacts that are typical in holographic imaging. This image processing scheme is based on transforming the colour components of an RGB image into YUV colour space, which separates colour information from brightness component of an image. The resolution of our super-resolution colour microscope was characterized using a USAF test chart to confirm sub-micron spatial resolution, even for reconstructions that employ multi-height phase recovery to handle dense and connected objects. To further demonstrate the performance of this colour microscope Papanicolaou (Pap) smears were also successfully imaged. This field-portable and wide-field computational colour microscope could be useful for tele-medicine applications in resource poor settings

Optical Vortices during a Super-Resolution Process in a Metamaterial

We show that a super-resolution process with 100% visibility is characterized by the formation of a point of phase singularity in free space outside the lens in the form of a saddle with topological charge equal to -1. The saddle point is connected to two vortices at the end boundary of the lens, and the two vortices are in turn connected to another saddle point inside the lens. The structure saddle-vortices-saddle is topologically stable. The formation of the saddle point in free space explains also the negative flux of energy present in a certain region of space outside the lens. The circulation strength of the power flow can be controlled by varying the position of the object plane with respect to the lens

Interferometric localization microscopy

pre-printInterference of signal in Fourier space, emitted from single probes, is used to localize it by recording and computing the phase of the fringes. Such system has applications in super resolution localization microscopy

Super-resolution x-ray phase-contrast and dark-field imaging with a single 2D grating and electromagnetic source stepping

Here we report a method for increased resolution of single exposure three modality x-ray images using super-resolution. The three x-ray image modalities are absorption-, differential phase-contrast-, and dark-field-images. To create super-resolution, a non-mechanically movable micro-focus x-ray source is used. A series of almost identical x-ray projection images is obtained while the point source is translated in a two-dimensional grid pattern. The three image modalities are extracted from fourier space using spatial harmonic analysis, also known as the single-shot method. Using super-resolution on the low-resolution series of the three modalities separately results in high-resolution images for the modalities. This approach allows to compensate for the inherent loss in resolution caused by the single-shot method without increasing the need for stability or algorithms accounting for possible motion