Related papers: On problem of polarization tomography, I
We give uniqueness theorem and reconstruction algorithm for the nonlinearized problem of finding the dielectric anisotropy f of the medium from non-overdetermined polarization tomography data. We assume that the medium has uniform…
The thesis concentrates on two problems in discrete geometry, whose solutions are obtained by analytic, probabilistic and combinatoric tools. The first chapter deals with the strong polarization problem. This states that for any sequence…
For $\pi^0\eta$-photoproduction on the nucleon formal expressions are developed for the five-fold differential cross section and the recoil polarization including beam and target polarizations. The polarization observables are described by…
Polarization is a basic property of light and is fundamentally linked to the internal geometry of a source of radiation. Polarimetry complements photometric, spectroscopic, and imaging analyses of sources of radiation and has made possible…
Polarimetric imaging can provide valuable information about biological samples in a wide range of applications. Detrimental scattering however currently limits the imaging depth of in-vivo imaging to approximately 1 transport mean free…
We consider the problem of determination of a magnetic field from three dimensional polarimetric neutron tomography data. We see that this is an example of a non-Abelian ray transform and that the problem has a globally unique solution for…
An optical waveplate rotating light polarization can be modeled as a single-qubit unitary operator, whose action can be experimentally determined via quantum process tomography. Standard approaches to tomographic problems rely on the…
We introduce a tomography approach to describe the optical response of a cavity quantum electrodynamics device, beyond the semiclassical image of polarization rotation, by analyzing the polarization density matrix of the reflected photons…
In this paper, we consider linear ill-posed problems in Hilbert spaces and their regularization via frame decompositions, which are generalizations of the singular-value decomposition. In particular, we prove convergence for a general class…
This paper concerns the inverse problem of determining a planar conductivity inclusion. Our aim is to analytically recover from the generalized polarization tensors (GPTs), which can be obtained from exterior measurements, a homogeneous…
The problem of imaging materials with circular polarization properties is discussed within the framework of vectorial ptychography. We demonstrate, both theoretically and numerically, that using linear polarizations to investigate such…
This is a short review of some recent results obtained by the author. These results are related the problem of obtaining polynomial identities (computational formulas) for some matrix functions by means of the known polarization theorem,…
The creation and detection of atomic polarization is examined theoretically, through the study of basic optical-pumping mechanisms and absorption and fluorescence measurements, and the dependence of these processes on the size of ground-…
A generalized variant of the Calder\'on problem from electrical impedance tomography with partial data for anisotropic Lipschitz conductivities is considered in an arbitrary space dimension $n \geq 2$. The following two results are shown:…
We formulate and investigate a statistical inverse problem of a random tomographic nature, where a probability density function on $\mathbb{R}^3$ is to be recovered from observation of finitely many of its two-dimensional projections in…
Polarization of light rotates in a gravitational field. The accrued phase is operationally meaningful only with respect to a local polarization basis. In stationary space-times, we construct local reference frames that allow us to isolate…
We present a method for imaging small scatterers in a homogeneous medium from polarization measurements of the electric field at an array. The electric field comes from illuminating the scatterers with a point source with known location and…
The vectorial evolution of polarized light interaction with a medium can reveal its microstructure and anisotropy beyond what can be obtained from scalar light interaction. Anisotropic properties (diattenuation, retardance, and…
In this paper, we consider an inverse conductivity problem on a bounded domain $\Omega\subset\mathbb{R}^n$, $n\geq2$, also known as Electrical Impedance Tomography (EIT), for the case where unknown impenetrable obstacles are embedded into…
The vast majority of Shape-from-Polarization (SfP) methods work under the oversimplified assumption of using orthographic cameras. Indeed, it is still not well understood how to project the Stokes vectors when the incoming rays are not…