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Propagation of an ultrashort pulse of light through strongly scattering media generates an intricate spatio-spectral speckle that can be described by means of the multi-spectral transmission matrix (MSTM). In conjunction with a spatial…
The mathematical theory of compressed sensing (CS) asserts that one can acquire signals from measurements whose rate is much lower than the total bandwidth. Whereas the CS theory is now well developed, challenges concerning hardware…
The movement of molecules inside living cells is a fundamental feature of biological processes. The ability to both observe and analyse the details of molecular diffusion in vivo at the single molecule and single cell level can add…
To reach its optimal performance, Fizeau interferometry requires that we work to resolve instrumental biases through calibration. One common technique used in high contrast imaging is angular differential imaging, which calibrates the point…
Transmission matrices are valuable tools to describe and control light transport through scattering media. There are only a few cases where the transmission matrix can be compared to microscopic theories. Here we measure the…
We prove the flat space analogue of the Flato-Fronsdal theorem. It features the flat space singleton representation suggested recently. We do that by deriving a kernel that intertwines a pair of singleton representations with massless…
Fractional equations have become the model of choice in several applications where heterogeneities at the microstructure result in anomalous diffusive behavior at the macroscale. In this work we introduce a new fractional operator…
Single-pixel imaging has emerged as a key technique in fluorescence microscopy, where fast acquisition and reconstruction are crucial. In this context, images are reconstructed from linearly compressed measurements. In practice, total…
We study finitely cyclic self-adjoint operators in a Hilbert space, i.e. self-adjoint operators that posses such a finite subset in the domain that the orbits of all its elements with respect to the operator are linearly dense in the space.…
The point spread function (PSF) is fundamental to any type of microscopy, most importantly so for single-molecule localization techniques, where the exact PSF shape is crucial for precise molecule localization at the nanoscale. However,…
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…
The use of cross-diffusion systems as mathematical models of different image processes is investigated. The present paper is concerned with linear filtering. First, those systems satisfying the most important scale-space properties are…
A wavelet is a special case of a vector in a separable Hilbert space that generates a basis under the action of a collection, or system, of unitary operators. We will describe the operator-interpolation approach to wavelet theory using the…
Wavefront-shaping is a promising approach for imaging fluorescent targets deep inside scattering tissue despite strong aberrations. It enables focusing an incoming illumination into a single spot inside tissue, as well as correcting the…
Extraordinary optical transmission and good focusing properties of a two-dimensional scattering structure is presented. The structure is made of Fresnel zone plates periodically arranged along two orthogonal directions. Each plate consists…
We demonstrate the first planar Airy light-sheet microscope. Fluorescence light-sheet microscopy has become the method of choice to study large biological samples with cellular or sub-cellular resolution. The propagation-invariant Airy beam…
We consider the application of a subspace migration (SM) algorithm to quickly identify small objects in microwave imaging. In various problems, it is easy to measure the diagonal elements of the scattering matrix if the location of the…
Scanning probe microscopy (SPM) images of regularly arranged spatially periodic objects can be processed crystallographically. The resulting information may be used to remove from the SPM image distortions that are due to a less than…
We theoretically study the problem of detecting dipole radiation in an optical system of high numerical aperture in which the detector is sensitive to \textit{field amplitude}. In particular, we model the phase sensitive detector as a…
An improved formulation of the one-step model of photoemission from crystal surfaces is proposed which overcomes different limitations of the original theory. Considering the results of an electronic-structure calculation, the electronic…