Related papers: Basis-neutral Hilbert-space analyzers
Time delay cosmography uses the arrival time delays between images in strong gravitational lenses to measure cosmological parameters, in particular the Hubble constant $H_0$. The lens models used in time delay cosmography omit dark matter…
This paper provides a comprehensive framework for designing functional observers for linear systems subject to delayed output measurements. Moving beyond traditional methodologies, the proposed observer generates an estimate $\hat{z}(t)$…
A typical application for laser interferometers is a precision measurement of length changes that result in interferometric phase shifts. Such phase changes are typically predicted numerically, due to the com- plexity of the overlap…
The Fresnel Interferometric Imager is a space-based astronomical telescope project yielding milli-arc second angular resolution and high contrast images with loose manufacturing constraints. This optical concept involves diffractive…
It is shown here that precision is gained by analyzing the interferometric spectra directly from the interferograms, with no previous Fourier transformation to put them in the standard frequency domain. The method is based on the…
An optical field will undergo coherent diffusion when it is mapped into thermal-motioned atoms, e.g., in a slow or storage light process. As was demonstrated before, such diffusion effect is equivalent to a spatial low-pass filter…
Atom interferometers are sensitive to a wide range of forces by encoding their signals in interference patterns of matter waves. To estimate the magnitude of these forces, the underlying phase shifts they imprint on the atoms must be…
Phase-sensitive coherent imaging exploits changes in the phases of backscattered light to observe tiny alterations of scattering structures or variations of the refractive index. But moving scatterers or a fluctuating refractive index…
We construct frames adapted to a given cover of the time-frequency or time-scale plane. The main feature is that we allow for quite general and possibly irregular covers. The frame members are obtained by maximizing their concentration in…
The Wide-Field Imaging Interferometry Testbed (WIIT) will provide valuable information for the development of space-based interferometers. This laboratory instrument operates at optical wavelengths and provides the ability to test…
If $\mu $ is a positive Borel measure on the interval $[0, 1)$ we let $\mathcal H_\mu $ be the Hankel matrix $\mathcal H_\mu =(\mu_{n, k})_{n,k\ge 0}$ with entries $\mu_{n, k}=\mu_{n+k}$, where, for $n\,=\,0, 1, 2, \dots $, $\mu_n$ denotes…
Refraction at the interface between two materials is fundamental to the interaction of light with photonic devices and to the propagation of light through the atmosphere at large. Underpinning the traditional rules for the refraction of an…
Here we introduce interferometric devices by combining optical feedback (cavities) with unbiased multiports, which unlike traditional beam dividers, allow light to reflect back out of the port from which it originated. By replacing the…
This paper presents an overview of close parallels that exist between the theory of positive operator-valued measures (POVMs) associated with a separable Hilbert space and the theory of frames on that space, including its most important…
Optical levitation of nanoscale particles has emerged as a platform for precision measurement. Extremely low damping, together with optical interferometric position detection, makes possible exquisite force measurement and promises…
We present a technique for the approximation of a class of Hilbert space-valued maps which arise within the framework of Model Order Reduction for parametric partial differential equations, whose solution map has a meromorphic structure.…
Interferometry can measure the shape or the material density of a system that could not be measured otherwise by recording the difference between the phase change of a signal and a reference phase. This difference is always between $-\pi$…
We describe how weak phase modulations applied to classical coherent light in specially modified linear interferometers can be used to perform primitive computational tasks. Instead of encoding operations within a fixed unitary state, the…
In this paper, we propose a new paradigm for atom interferometry and demonstrate that there exists a universal set of atom optic components for inertial sensing. These components constitute gates with which we carry out quantum operations…
This note deals with a problem of the probabilistic Ramsey theory in functional analysis. Given a linear operator $T$ on a Hilbert space with an orthogonal basis, we define the isomorphic structure $\Sigma(T)$ as the family of all subsets…