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We establish a regular sampling theory in the range of the analysis operator of a continuous frame having a unitary structure. The unitary structure is related with a unitary representation of a locally compact abelian group on a separable…
Role of the normal polarization in the far-field subwavelength imaging granted by a dielectric microsphere or microcylinder is discussed and the hypotheses explaining this experimental fact are suggested. One of these hypotheses is…
We formulate an S-matrix theory in which localisation effects of the particle interactions involved in a scattering process are consistently taken into account. In the limit of an infinite spread of all interactions, the S-matrix assumes…
We study the spectral and scattering theory of light transmission in a system consisting of two asymptotically periodic waveguides, also known as one-dimensional photonic crystals, coupled by a junction. Using analyticity techniques and…
The dynamics of a collection of resonant atoms embedded inside an inhomogeneous nondispersive and lossless dielectric is described with a dipole Hamiltonian that is based on a canonical quantization theory. The dielectric is described…
Based on diffraction theory and the propagation of the light, Fourier optics is a powerful tool allowing the estimation of a visible-range imaging system to transfer the spatial frequency components of an object. The analyses of the imaging…
Let $H_0$ and $H$ be self-adjoint operators in a Hilbert space. In the scattering theory framework, we describe the essential spectrum of the difference $\varphi(H)-\varphi(H_0)$ for piecewise continuous functions $\varphi$. This…
Luminescence imaging is invaluable for studying biological and material systems, particularly when advanced protocols that exploit temporal dynamics are employed. However, implementing such protocols often requires custom instrumentation,…
A solid-state active beamformer based on the annular-ring diffraction pattern is proposed for an integrated photonic platform. Such a circularly symmetric annular-ring aperture achieves radiating element limited FOV. Furthermore, it is…
Fluorescence lifetime imaging microscopy (FLIM) is an important technique to understand the chemical micro-environment in cells and tissues since it provides additional contrast compared to conventional fluorescence imaging. When two…
The purpose of this paper is to give an overview of the operator structure of frames, where the operator belongs to certain classes of linear operators and the element belongs to $H$. We discuss the size of the set of such elements. Also,…
I present a somewhat selective review of microlensing theory, covering five major areas: 1) the derivation of the basic formulae, 2) the relation between the observables and the fundamental physical parameters, 3) binaries, 4) astrometric…
Spontaneous emission spectra of two initially excited closely spaced identical atoms are very sensitive to the strength and the direction of the applied magnetic field. The relevant schemes are considered that ensure the determination of…
We prove that it is impossible to distinguish two spatially coinciding fluorescent molecules from a single rotating molecule using polarization-sensitive imaging, even if one modulates the polarization of the illumination or the detection…
Fusion frames are a very active area of research today because of their myriad of applications in pure mathematics, applied mathematics, engineering, medicine, signal and image processing and much more. They provide a great flexibility for…
Optical fluorescence imaging is capable of measuring both the spatial and rotational dynamics of single molecules. However, unavoidable measurement noise will result in inaccurate estimates of rotational dynamics, causing a molecule to…
Interferometric scattering microscopy is a powerful technique that enables various applications, such as mass photometry and particle tracking. Here we present a numerical toolbox to simulate images obtained in interferometric scattering,…
We develop a formalism for the calculation of the macroscopic dielectric response of composite systems made of particles of one material embedded periodically within a matrix of another material, each of which is characterized by a well…
Fluorescence fluctuation spectroscopy is applied to study molecules, passing through a small observation volume, usually subjected to diffusive or convective motion in liquid phase. We suggest that such a technique could be used to measure…
We show that structural information can be extracted from single molecule localization microscopy (SMLM) data. More precisely, we reinterpret SMLM data as the measures of a phaseless optical diffraction tomography system for which the…