Related papers: The Cone of Mueller Matrices
Based on the convex hull construction algorithm, a new geometrical model of ice crystals is proposed to investigate the scattering properties of cirrus clouds particles. Light scattering matrices involving complete polarization information…
Momentum space polarization singularities of light appear as vectorial twists in the scattered and radiated far field patterns of exotic photonic structures. They relate to important concepts such as bound states in the continuum,…
The centralizer algebra of a matrix consists of those matrices that commute with it. We investigate the basic representation-theoretic invariants of centralizer algebras, namely their radicals, projective indecomposable modules, injective…
We study the tropicalization of the image of the cone of positive definite matrices under the principal minors map. It is a polyhedral subset of the set of $M$-concave functions on the discrete $n$-dimensional cube. We show it coincides…
A large number matrix optimization problems are described by orthogonally invariant norms. This paper is devoted to the study of variational analysis of the orthogonally invariant norm cone of symmetric matrices. For a general orthogonally…
We show that it is possible to measure polarization with a polarimeter that gets rid of the seeing while still measuring at a frequency well below that of the seeing. We study a standard polarimeter made of two retarders and a beamsplitter.…
A method for the determination of the projection geometry of highly magnifying cone beam micro computed tomography systems based on few rotating fiducial markers of unknown position within the field of view is derived. By employing the…
This study is concerned with the design of a Mueller imaging polarimeter for the visualization of spatially-varying Mueller matrix fields. A simplified calibration procedure is advocated, where all the optical elements are calibrated…
In recent work with Lins and Nussbaum the first author gave an algorithm that can detect the existence of a positive eigenvector for order-preserving homogeneous maps on the standard positive cone. The main goal of this paper is to…
Linear polarized light has been used to view the solar corona for over 150 years. While the familiar Stokes representation for polarimetry is complete, it is best matched to a laboratory setting and therefore is not the most convenient…
This paper presents a definition for local linearizations of rational matrices and studies their properties. This definition allows us to introduce matrix pencils associated to a rational matrix that preserve its structure of zeros and…
Magnetic fields in cool stars are ubiquitous but can still be challenging to characterize due to their complexity and relatively low strength. The polarization signature amplitudes are proportional to the field strength, and current studies…
Profile comparison of the Stokes parameters $V$ and $I$ is a powerful tool for maser data analysis, providing the first direct methods for unambiguous determination of (1) the maser saturation stage, (2) the amplification optical depth and…
We employ the magnetic and velocity fields from turbulent dynamo simulations to synthesize the polarization of a typical photospheric line. The synthetic Stokes profiles have properties in common with those observed in the quiet Sun. The…
It was generally assumed that the Stokes parameters are complete characterization for the state of polarization of a plane light wave so that their counterparts in quantum optics, called the Stokes operators, represent the polarization of…
We analyze an experimental setup in which a quasi-monochromatic spatially coherent beam of light is used to probe a paraxial optical scatterer. We discuss the effect of the spatial coherence of the probe beam on the Mueller matrix…
We give a general formula for generators of the NL-cone, the cone of effective linear combinations of irreducible components of Noether-Lefschetz divisors, on an orthogonal modular variety. We then fully describe the NL-cone and its…
Matrices are two-dimensional data structures allowing one to conceptually organize information. For example, adjacency matrices are useful to store the links of a network; correlation matrices are simple ways to arrange gene co-expression…
Most cosmic microwave background experiments observe the sky along circular or near-circular scans on the celestial sphere. For such experiments, we show that simple linear systems connect the Fourier spectra of temperature and polarization…
This paper introduces Modular Linear Tokenization (MLT), a reversible and deterministic technique for encoding high-cardinality categorical identifiers into compact numerical vectors. Unlike traditional hashing or one-hot encodings, MLT…