Related papers: Basis-neutral Hilbert-space analyzers
This paper summarizes and generalizes a recently proposed mathematical framework that unifies the standard formalisms of special relativity and quantum mechanics. The framework is based on Hilbert spaces H of functions of four space-time…
The current status of the high spatial resolution imaging interferometry in optical astronomy is reviewed in the light of theoretical explanation, as well as of experimental constraints that exist in the present day technology. The basic…
Weaving Hilbert space frames have been introduced recently by Bemrose et al. to deal with some problems in distributed signal processing. In this paper, we survey this topic from the viewpoint of the duality principle, so we obtain new…
The time delay between the arrival of photons of multiple images of time variable sources can be used to constrain absolute distances in the Universe (Refsdal 1964), and in turn obtain a direct estimate of the Hubble constant and other…
All-reflective interferometer configurations have been proposed for the next generation of gravitational wave detectors, with diffractive elements replacing transmissive optics. However, an additional phase noise creates more stringent…
We have developed an algorithm that constructs a model of a reconfigurable optical interferometer, independent of specific architectural constraints. The programming of unitary transformations on the interferometer's optical modes relies on…
The Hermite-Birkhoff interpolation problem of a function given on arbitrarily distributed points on the sphere and other manifolds is considered. Each proposed interpolant is expressed as a linear combination of basis functions, the…
In long-baseline interferometry, bandwidth smearing of an extended source occurs at finite bandwidth when its different components produce interference packets that only partially overlap. In this case, traditional model fitting or image…
We introduce a convenient formalism to evaluate the frequency-shift affecting a light signal propagating on a general curved background. Our formulation, which is based on the laws of geometric optics in a general relativistic setting,…
Interferometry provides one of the possible routes to ultra-high angular resolution for X-ray and gamma-ray astronomy. Sub-micro-arc-second angular resolution, necessary to achieve objectives such as imaging the regions around the event…
We investigate interferometric techniques to estimate the deflection angle of an optical beam and compare them to the direct detection of the beam deflection. We show that quantum metrology methods lead to a unifying treatment for both…
I derive in this paper theoretical expressions for biases on fringe contrast and fringe visibility phase for optical interferometers whose polarizing properties can be described by beam rotation, retardance, and diattenuation. The nature of…
We treat the problem of a Michelson interferometer in the field of a plane gravitational wave in the framework of general relativity. The arms of the interferometer are regarded as the world lines of the light beams, whose motion is…
Nonlinear interferometers are promising tools for quantum metrology, as they are characterized by an improved phase sensitivity scaling compared to linear interferometers operating with classical light. However, the multimodeness of the…
We present Hilbert space representation for a relatively broad class of minimum-length deformed quantum mechanical models obtained by incorporating a space-time uncertainty relation into quantum mechanics. The correspondingly modified field…
Coherent states in a projected Hilbert space have many useful properties. When there are conserved quantities, a representation of the entire Hilbert space is not necessary. The same issue arises when conditional observations are made with…
Kernel-phase is a data analysis method based on a generalization of the notion of closure-phase invented in the context of interferometry, but that applies to well corrected diffraction dominated images produced by an arbitrary aperture.…
We consider an alternative formula for time delay in gravitational lensing. Imposing a smoothness condition on the gravitationally deformed paths followed by the photons from the source to the observer, we show that our formula displays the…
The generalization of the Koopman operator to systems with control input and the derivation of a nonlinear fundamental lemma are two open problems that play a key role in the development of data-driven control methods for nonlinear systems.…
Space borne nulling interferometry in the mid-infrared waveband is one of the most promising techniques for characterizing the atmospheres of extra-solar planets orbiting in the habitable zone of their parent star, and possibly discovering…