Polynomial fitting and interpolation on circular sections

We construct Weakly Admissible polynomial Meshes (WAMs) on circular sections, such as symmetric and asymmetric circular sectors, circular segments, zones, lenses and lunes. The construction resorts to recent results on subperiodic trigonometric interpolation. The paper is accompanied by a software package to perform polynomial fitting and interpolation at discrete extremal sets on such regions

Polynomial Meshes: Computation and Approximation

We present the software package WAM, written in Matlab, that generates Weakly Admissible Meshes and Discrete Extremal Sets of Fekete and Leja type, for 2d and 3d polynomial least squares and interpolation on compact sets with various geometries. Possible applications range from data fitting to high-order methods for PDEs

An elementary approach to polynomial optimization on polynomial meshes

A polynomial mesh on a multivariate compact set or manifold is a sequence of finite norming sets for polynomials whose norming constant is independent of degree. We apply the recently developed theory of polynomial meshes to an elementary discrete approach for polynomial optimization on nonstandard domains, providing a rigorous (over)estimate of the convergence rate. Examples include surface/solid subregions of sphere or torus, such as caps, lenses, lunes, and slices

Subperiodic Dubiner distance, norming meshes and trigonometric polynomial optimization

We extend the notion of Dubiner distance from algebraic to trigonometric polynomials on subintervals of the period, and we obtain its explicit form by the Szego variant of Videnskii inequality. This allows to improve previous estimates for Chebyshev-like trigonometric norming meshes, and suggests a possible use of such meshes in the framework of multivariate polynomial optimization on regions defined by circular arcs

Circular polarization measurement in millimeter-wavelength spectral-line VLBI observations

This paper considers the problem of accurate measurement of circular polarization in imaging spectral-line VLBI observations in the lambda=7 mm and lambda=3 mm wavelength bands. This capability is especially valuable for the full observational study of compact, polarized SiO maser components in the near-circumstellar environment of late-type, evolved stars. Circular VLBI polarimetry provides important constraints on SiO maser astrophysics, including the theory of polarized maser emission transport, and on the strength and distribution of the stellar magnetic field and its dynamical role in this critical circumstellar region. We perform an analysis here of the data model containing the instrumental factors that limit the accuracy of circular polarization measurements in such observations, and present a corresponding data reduction algorithm for their correction. The algorithm is an enhancement of existing spectral line VLBI polarimetry methods using autocorrelation data for calibration, but with innovations in bandpass determination, autocorrelation polarization self-calibration, and general optimizations for the case of low SNR, as applicable at these wavelengths. We present an example data reduction at $\lambda=7$ mm and derive an estimate of the predicted accuracy of the method of m_c < 0.5% or better at lambda=7 mm and m_c < 0.5-1% or better at lambda=3 mm. Both the strengths and weaknesses of the proposed algorithm are discussed, along with suggestions for future work.Comment: 23 pages, 13 figure

Accurate Transfer Maps for Realistic Beamline Elements: Part I, Straight Elements

The behavior of orbits in charged-particle beam transport systems, including both linear and circular accelerators as well as final focus sections and spectrometers, can depend sensitively on nonlinear fringe-field and high-order-multipole effects in the various beam-line elements. The inclusion of these effects requires a detailed and realistic model of the interior and fringe fields, including their high spatial derivatives. A collection of surface fitting methods has been developed for extracting this information accurately from 3-dimensional field data on a grid, as provided by various 3-dimensional finite-element field codes. Based on these realistic field models, Lie or other methods may be used to compute accurate design orbits and accurate transfer maps about these orbits. Part I of this work presents a treatment of straight-axis magnetic elements, while Part II will treat bending dipoles with large sagitta. An exactly-soluble but numerically challenging model field is used to provide a rigorous collection of performance benchmarks.Comment: Accepted to PRST-AB. Changes: minor figure modifications, reference added, typos corrected

The Hyper Suprime-Cam Software Pipeline

In this paper, we describe the optical imaging data processing pipeline developed for the Subaru Telescope's Hyper Suprime-Cam (HSC) instrument. The HSC Pipeline builds on the prototype pipeline being developed by the Large Synoptic Survey Telescope's Data Management system, adding customizations for HSC, large-scale processing capabilities, and novel algorithms that have since been reincorporated into the LSST codebase. While designed primarily to reduce HSC Subaru Strategic Program (SSP) data, it is also the recommended pipeline for reducing general-observer HSC data. The HSC pipeline includes high level processing steps that generate coadded images and science-ready catalogs as well as low-level detrending and image characterizations.Comment: 39 pages, 21 figures, 2 tables. Submitted to Publications of the Astronomical Society of Japa

Image inversion analysis of the HST OTA (Hubble Space Telescope Optical Telescope Assembly), phase A

Technical work during September-December 1990 consisted of: (1) analyzing HST point source images obtained from JPL; (2) retrieving phase information from the images by a direct (noniterative) technique; and (3) characterizing the wavefront aberration due to the errors in the Hubble Space Telescope (HST) mirrors, in a preliminary manner. This work was in support of JPL design of compensating optics for the next generation wide-field planetary camera on HST. This digital technique for phase retrieval from pairs of defocused images, is based on the energy transport equation between these image planes. In addition, an end-to-end wave optics routine, based on the JPL Code 5 prescription of the unaberrated HST and WFPC, was derived for output of the reference phase front when mirror error is absent. Also, the Roddier routine unwrapped the retrieved phase by inserting the required jumps of +/- 2(pi) radians for the sake of smoothness. A least-squares fitting routine, insensitive to phase unwrapping, but nonlinear, was used to obtain estimates of the Zernike polynomial coefficients that describe the aberration. The phase results were close to, but higher than, the expected error in conic constant of the primary mirror suggested by the fossil evidence. The analysis of aberration contributed by the camera itself could be responsible for the small discrepancy, but was not verified by analysis