Single-shot layered reflectance separation using a polarized light field camera

We present a novel computational photography technique for single shot separation of diffuse/specular reflectance as well as novel angular domain separation of layered reflectance. Our solution consists of a two-way polarized light field (TPLF) camera which simultaneously captures two orthogonal states of polarization. A single photograph of a subject acquired with the TPLF camera under polarized illumination then enables standard separation of diffuse (depolarizing) and polarization preserving specular reflectance using light field sampling. We further demonstrate that the acquired data also enables novel angular separation of layered reflectance including separation of specular reflectance and single scattering in the polarization preserving component, and separation of shallow scattering from deep scattering in the depolarizing component. We apply our approach for efficient acquisition of facial reflectance including diffuse and specular normal maps, and novel separation of photometric normals into layered reflectance normals for layered facial renderings. We demonstrate our proposed single shot layered reflectance separation to be comparable to an existing multi-shot technique that relies on structured lighting while achieving separation results under a variety of illumination conditions

Maximum Angular Separation Epochs for Exoplanet Imaging Observations

Direct imaging of exoplanets presents both significant challenges and significant gains. The advantages primarily lie in receiving emitted and, with future instruments, reflected photons at phase angles not accessible by other techniques, enabling the potential for atmospheric studies and the detection of rotation and surface features. The challenges are numerous and include coronagraph development and achieving the necessary contrast ratio. Here, we address the specific challenge of determining epochs of maximum angular separation for the star and planet. We compute orbital ephemerides for known transiting and radial velocity planets, taking Keplerian orbital elements into account. We provide analytical expressions for angular star--planet separation as a function of the true anomaly, including the locations of minimum and maximum. These expressions are used to calculate uncertainties for maximum angular separation as a function of time for the known exoplanets, and we provide strategies for improving ephemerides with application to proposed and planned imaging missions.Comment: 7 pages, 3 figures, 1 table, accepted for publication in the Astronomical Journa

Weak measurement of elliptical dipole moments by C point splitting

We investigate points of circular polarization in the far field of elliptically polarized dipoles and establish a relation between the angular position and helicity of these C points and the dipole moment. In the case of highly eccentric dipoles, the C points of opposite handedness exhibit only a small angular separation and occur in the low intensity region of the emission pattern. In this regard, we introduce an optical weak measurement approach that utilizes the transverse electric (azimuthal) and transverse magnetic (radial) far-field polarization basis. Projecting the far field onto a spatially varying post-selected polarization state reveals the angular separation and the helicity of the C points. We demonstrate the applicability of this approach and determine the elliptical dipole moment of a particle sitting on an interface by measuring the C points in its far field.Comment: 5 pages, 4 figure

Measurement of BB angular correlations based on secondary vertex reconstruction at √s = 7 TeV

A measurement of the angular correlations between beauty and anti-beauty hadrons (BB) produced in pp collisions at a centre-of-mass energy of 7 TeV at the CERN LHC is presented, probing for the first time the region of small angular separation. The B hadrons are identified by the presence of displaced secondary vertices from their decays. The B hadron angular separation is reconstructed from the decay vertices and the primary-interaction vertex. The differential BB production cross section, measured from a data sample collected by CMS and corresponding to an integrated luminosity of 3.1 pb^(−1), shows that a sizable fraction of the BB pairs are produced with small opening angles. These studies provide a test of QCD and further insight into the dynamics of bb production

On the spectroastrometric separation of binary point-source fluxes

Spectroastrometry is a technique which has the potential to resolve flux distributions on scales of milliarcseconds. In this study, we examine the application of spectroastrometry to binary point sources which are spatially unresolved due to the observational point spread function convolution. The technique uses measurements with sub-pixel accuracy of the position centroid of high signal-to-noise long-slit spectrum observations. With the objects in the binary contributing fractionally more or less at different wavelengths (particularly across spectral lines), the variation of the position centroid with wavelength provides some information on the spatial distribution of the flux. We examine the width of the flux distribution in the spatial direction, and present its relation to the ratio of the fluxes of the two components of the binary. Measurement of three observables (total flux, position centroid and flux distribution width) at each wavelength allows a unique separation of the total flux into its component parts even though the angular separation of the binary is smaller than the observations' point-spread function. This is because we have three relevant observables for three unknowns (the two fluxes, and the angular separation of the binary), which therefore generates a closed problem. This is a wholly different technique than conventional deconvolution methods, which produce information on angular sizes of the sampling scale. Spectroastrometry can produce information on smaller scales than conventional deconvolution, and is successful in separating fluxes in a binary object with a separation of less than one pixel. We present an analysis of the errors involved in making binary object spectroastrometric measurements and the separation method, and highlight necessary observing methodology.Comment: 11 pages, 8 figures, accepted for publication in Astronomy and Astrophysic

Solving the Darwin problem in the first post-Newtonian approximation of general relativity

We analytically calculate the equilibrium sequence of the corotating binary stars of incompressible fluid in the first post-Newtonian(PN) approximation of general relativity. By calculating the total energy and total angular momentum of the system as a function of the orbital separation, we investigate the innermost stable circular orbit for corotating binary(we call it ISCCO). It is found that by the first PN effect, the orbital separation of the binary at the ISCCO becomes small with increase of the compactness of each star, and as a result, the orbital angular velocity at the ISCCO increases. These behaviors agree with previous numerical works.Comment: 33 pages, revtex, 4 figures(eps), accepted for publication in Phys. Rev.

The Dirac Equation Is Separable On The Dyon Black Hole Metric

Using the tetrad formalism, we carry out the separation of variables for the massive complex Dirac equation in the gravitational and electromagnetic field of a four-parameter (mass, angular momentum, electric and magnetic charges) black hole.Comment: 13 page

The Yamabe invariant for axially symmetric two Kerr black holes initial data

An explicit 3-dimensional Riemannian metric is constructed which can be interpreted as the (conformal) sum of two Kerr black holes with aligned angular momentum. When the separation distance between them is large we prove that this metric has positive Ricci scalar and hence positive Yamabe invariant. This metric can be used to construct axially symmetric initial data for two Kerr black holes with large angular momentum.Comment: 14 pages, 2 figure