Combining Undersampled Dithered Images

Undersampled images, such as those produced by the HST WFPC-2, misrepresent fine-scale structure intrinsic to the astronomical sources being imaged. Analyzing such images is difficult on scales close to their resolution limits and may produce erroneous results. A set of ``dithered'' images of an astronomical source generally contains more information about its structure than any single undersampled image, however, and may permit reconstruction of a ``superimage'' with Nyquist sampling. I present a tutorial on a method of image reconstruction that builds a superimage from a complex linear combination of the Fourier transforms of a set of undersampled dithered images. This method works by algebraically eliminating the high order satellites in the periodic transforms of the aliased images. The reconstructed image is an exact representation of the data-set with no loss of resolution at the Nyquist scale. The algorithm is directly derived from the theoretical properties of aliased images and involves no arbitrary parameters, requiring only that the dithers are purely translational and constant in pixel-space over the domain of the object of interest. I show examples of its application to WFC and PC images. I argue for its use when the best recovery of point sources or morphological information at the HST diffraction limit is of interest.Comment: 22 pages, 9 EPS figures, submitted to PAS

The Te-d1 mode reflection coefficient of a ground-plane mounted parallel-plate waveguide illuminating a reflecting sheet

Symmetric parallel plate waveguide reflection coefficient analyze

Atmospheric Chemistry for Astrophysicists: A Self-consistent Formalism and Analytical Solutions for Arbitrary C/O

We present a self-consistent formalism for computing and understanding the atmospheric chemistry of exoplanets from the viewpoint of an astrophysicist. Starting from the first law of thermodynamics, we demonstrate that the van't Hoff equation (which describes the equilibrium constant), Arrhenius equation (which describes the rate coefficients) and procedures associated with the Gibbs free energy (minimisation, rescaling) have a common physical and mathematical origin. We address an ambiguity associated with the equilibrium constant, which is used to relate the forward and reverse rate coefficients, and restate its two definitions. By necessity, one of the equilibrium constants must be dimensionless and equate to an exponential function involving the Gibbs free energy, while the other is a ratio of rate coefficients and must therefore possess physical units. We demonstrate that the Arrhenius equation takes on a functional form that is more general than previously stated without recourse to tagging on ad hoc functional forms. Finally, we derive analytical models of chemical systems, in equilibrium, with carbon, hydrogen and oxygen. We include acetylene and are able to reproduce several key trends, versus temperature and carbon-to-oxygen ratio, published in the literature. The rich variety of behavior that mixing ratios exhibit as a function of the carbon-to-oxygen ratio is merely the outcome of stoichiometric book-keeping and not the direct consequence of temperature or pressure variations.Comment: Accepted by ApJ. 9 pages, 4 figure

Aperture reflection coefficient of a parallel- plate waveguide by wedge diffraction analysis

Aperture reflection coefficient of parallel plate waveguide by wedge diffraction analysi

Electroweak Baryogenesis in R-symmetric Supersymmetry

We demonstrate that electroweak baryogenesis can occur in a supersymmetric model with an exact R-symmetry. The minimal R-symmetric supersymmetric model contains chiral superfields in the adjoint representation, giving Dirac gaugino masses, and an additional set of "R-partner" Higgs superfields, giving R-symmetric \mu-terms. New superpotential couplings between the adjoints and the Higgs fields can simultaneously increase the strength of the electroweak phase transition and provide additional tree-level contributions to the lightest Higgs mass. Notably, no light stop is present in this framework, and in fact, we require both stops to be above a few TeV to provide sufficient radiative corrections to the lightest Higgs mass to bring it up to 125 GeV. Large CP-violating phases in the gaugino/higgsino sector allow us to match the baryon asymmetry of the Universe with no constraints from electric dipole moments due to R-symmetry. We briefly discuss some of the more interesting phenomenology, particularly of the of the lightest CP-odd scalar.Comment: 17 pages, 8 figure

Superconductivity in Inhomogeneous Hubbard Models

We present a controlled perturbative approach to the low temperature phase diagram of highly inhomogeneous Hubbard models in the limit of small coupling, $t'$, between clusters. We apply this to the dimerized and checkerboard models. The dimerized model is found to behave like a doped semiconductor, with a Fermi-liquid groundstate with parameters ({\it e.g.} the effective mass) which are smooth functions of the Hubbard interaction, $U$. By contrast, the checkerboard model has a nodeless d-wave superconducting state (preformed pair condensate, $d$-BEC) for $0 < U < U_c$, which smoothly crosses over to an intermediate BCS-like superconducting phase ($d$-BCS), also with no nodal quasi-particles, for $|U - U_c| < {\cal O}(t^\prime)$, which gives way to a Fermi liquid phase at large $U > U_c = 4.58$.Comment: 7 pages, a sign error in Eq.(3) has been corrected and its consequence has been discussed with updated figure

Reconciliation of generalized refraction with diffraction theory

When an electromagnetic wave is obliquely incident on the interface between two homogeneous media with different refractive indices, the requirement of phase continuity across the interface generally leads to a shift in the trajectory of the wave. When a linearly position dependent phase shift is imposed at the interface, the resulting refraction may be described using a generalized version of Snell's law. In this Letter, we establish a formal equivalence between generalized refraction and blazed diffraction gratings, further discussing the relative merits of the two approaches.Comment: Submitted to Optics Letter