Related papers: Basis-neutral Hilbert-space analyzers
Optical long baseline interferometry was recently established as a technique capable of resolving stars and their circumstellar environments at the milliarcsecond (mas) resolution level. This high-resolution opens an entire new window to…
Gravitational lensing time delays depend upon the Hubble constant and the density distribution of the lensing galaxies. This allows one to either model the lens and estimate the Hubble constant, or to use a prior on the Hubble constant from…
In this paper we investigate a new notion of bases in Hilbert spaces and similar to fusion frame theory we introduce fusion bases theory in Hilbert spaces. We also introduce a new definition of fusion dual sequence associated with a fusion…
Increasingly large parameter spaces, used to more accurately model precision observables in physics, can paradoxically lead to large deviations in the inferred parameters of interest -- a bias known as volume projection effects -- when…
This thesis presents a collection of different researches on non-standard optics in view of enhancing the performances of the Advanced Gravitational waves interferometric detectors, where the thermal noise of the test masses is expected to…
Binary decision theory has been applied to the general interferometric problem. Optimal detection scheme-according to the Neyman-Pearson criterion-has been considered for different phase-enhanced states of radiation field, and the…
In the context of the Laser Interferometer Space Antenna (LISA), the laser subsystems exhibit frequency fluctuations that introduce significant levels of noise into the measurements, surpassing the gravitational wave signal by several…
Arguments based on general principles of quantum mechanics suggest that a minimum length or time associated with Planck-scale unification may entail a new kind of observable uncertainty in the transverse position of macroscopically…
Aperture synthesis instruments providing a generally highly uniform sampling of the visibility function often leave an unsampled hole near the origin of the (u,v)-plane. In this paper, originally published in 1979, we first describe the…
Energy consumption and hardware cost of signal digitization together with the management of the resulting data volume form serious issues for high-rate measurement systems with multiple sensors. Switching to binary sensing front-ends…
Measurement technology employing optical interference phenomena such as a fringe pattern or frequency shift has been evolving for more than a century. The systems are being designed better, and their components are being built better. But…
Nonlinear systems of affine control inputs overarch many sensor fusion instances. Analyzing whether a state variable in such a nonlinear system can be estimated (i.e., observability) informs better estimator design. Among the research on…
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…
We use the spatial degree of freedom of light modes to construct optical analogues of generalized quantum coherent states for Hermite- and Laguerre-Gauss modes. Our optical analogues preserve the statistical properties of their quantum…
Given a countable metric space, we can consider its end. Then a basis of a Hilbert space indexed by the metric space defines an end of the Hilbert space, which is a new notion and different from an end as a metric space. Such an indexed…
We propose an interferometric scheme where each photon returns one bit of the binary expansion of an unknown phase. It sets up a method for estimating the phase value at arbitrary uncertainty. This strategy is global, since it requires no…
Current attempts to probe general relativistic effects in quantum mechanics focus on precision measurements of phase shifts in matter-wave interferometry. Yet, phase shifts can always be explained as arising due to an Aharonov-Bohm effect,…
We develope a local theory for frames on finite dimensional Hilbert spaces. In particular, a bounded frame on a finite dimensional Hilbert space contains a subset which is a good Riesz basis for a percentage (arbitrarily close to one) of…
In theory of optical aberrations, an aberrated wavefront is represented by its coefficients in some orthogonal basis, for instance by Zernike polynomials. However, many wavefront measurement techniques implicitly approximate the gradient of…
The modal dispersion of waveguides often limits integrated photonic devices to operation with a single polarization state. This presents a challenge for sensing and spectroscopy applications, which often require polarization diversity over…