Performance of polarimetric beamformers for phased array radio telescopes

The results of four recently introduced beamforming schemes for phased array systems are discussed, each of which is capable to provide high sensitivity and accurate polarimetric performance of array-based radio telescopes. Ideally, a radio polarimeter should recover the actual polarization state of the celestial source, and thus compensate for unwanted polarization degradation effects which are intrinsic to the instrument. In this paper, we compare the proposed beamforming schemes through an example of a practical phased array system (APERTIF prototype) and demonstrate that the optimal beamformer, the max-SLNR beamformer, the eigenvector beamformer, and the bi-scalar beamformer are sensitivity equivalent but lead to different polarization state solutions, some of which are sub-optimal

Efficient Prediction of Array Element Patterns Using Physics-Based Expansions and a Single Far-Field Measurement

A method is proposed to predict the antenna array beam through employing a relatively small set of physics-based basis functions-called characteristic basis function patterns (CBFPs)-for modeling the embedded element patterns. The primary CBFP can be measured or extracted from numerical simulations, while additional (secondary) CBFPs are derived from the primary one. Furthermore, each numerically generated CBFP, which is typically simulated/measured for discrete directions only, can in turn be approximated by analytical basis functions with fixed expansion coefficients to evaluate the resulting array pattern at any angle through interpolation. This hierarchical basis reduces the number of unknown expansion coefficients significantly. Accordingly, the CBFP expansion coefficients can be determined through a single far-field measurement of only a few reference sources in the field of view. This is particularly important for multibeam array applications where only a limited number of reference sources are available for predicting the beam shape. Furthermore, this instantaneous beam calibration is fast, i.e., potentially capable to speed up the array calibration by one or two orders of magnitude, which is particularly important if the antenna radiation characteristics are subject to drifts

Polarimetry With Phased Array Antennas: Sensitivity and Polarimetric Performance Using Unpolarized Sources for Calibration

Polarimetric phased arrays require a calibration method that allows the system to measure the polarization state of the received signals. In this paper, we assess the polarimetric performance of two commonly used calibration methods that exploit unpolarized calibration sources. The first method obtains a polarimetrically calibrated beamforming solution from the two dominant eigenvectors of the measured signal covariance matrix. We demonstrate that this method is sensitivity equivalent to the theoretical optimal method, but suffers from an ambiguity that has to be resolved by additional measurements on (partially) polarized sources or by exploiting the intrinsic polarimetric quality of the antenna system. The easy-to-implement bi-scalar approach assumes that the feed system consists of two sets of orthogonally oriented antenna elements, each associated with one polarization. We assess its sensitivity and polarimetric performance over a wide field-of-view (FoV) using simulations of a phased array feed system for the Westerbork Synthesis Radio Telescope. Our results indicate that the sensitivity loss can be limited to 4.5% and that the polarimetric performance over the FoV is close to the best achievable performance. The latter implies that the intrinsic polarimetric quality of the antennas remains a crucial factor despite the development of novel polarimetric calibration methods

Polarimetry With Phased Array Antennas: Theoretical Framework and Definitions

For phased array receivers, the accuracy with which the polarization state of a received signal can be measured depends on the antenna configuration, array calibration process, and beamforming algorithms. A signal and noise model for a dual-polarized array is developed and related to standard polarimetric antenna figures of merit, and the ideal polarimetrically calibrated, maximum-sensitivity beamforming solution for a dual-polarized phased array feed is derived. A practical polarimetric beamformer solution that does not require exact knowledge of the array polarimetric response is shown to be equivalent to the optimal solution in the sense that when the practical beamformers are calibrated, the optimal solution is obtained. To provide a rough initial polarimetric calibration for the practical beamformer solution, an approximate single-source polarimetric calibration method is developed. The modeled instrumental polarization error for a dipole phased array feed with the practical beamformer solution and single-source polarimetric calibration was -10 dB or lower over the array field of view for elements with alignments perturbed by random rotations with 5 degree standard deviation

Electrodynamics of Abrikosov vortices: the Field Theoretical Formulation

Electrodynamic phenomena related to vortices in superconductors have been studied since their prediction by Abrikosov, and seem to hold no fundamental mysteries. However, most of the effects are treated separately, with no guiding principle. We demonstrate that the relativistic vortex worldsheet in spacetime is the object that naturally conveys all electric and magnetic information, for which we obtain simple and concise equations. Breaking Lorentz invariance leads to down-to-earth Abrikosov vortices, and special limits of these equations include for instance dynamic Meissner screening and the AC Josephson relation. On a deeper level, we explore the electrodynamics of two-form sources in the absence of electric monopoles, in which the electromagnetic field strength itself acquires the characteristics of a gauge field. This novel framework leaves room for unexpected surprises.Comment: LaTeX, 23 pages, 5 figure

Social preferences, accountability, and wage bargaining

We assess the extent of preferences for employment in a collective wage bargaining situation with heterogeneous workers. We vary the size of the union and introduce a treatment mechanism transforming the voting game into an individual allocation task. Our results show that highly productive workers do not take employment of low productive workers into account when making wage proposals, regardless of whether insiders determine the wage or all workers. The level of pro-social preferences is small in the voting game, while it increases as the game is transformed into an individual allocation task. We interpret this as an accountability effect

Risk preference and choice stochasticity during decisions for other people

In several contexts, such as finance and politics, people make choices that are relevant for others but irrelevant for oneself. Focusing on decision-making under risk, we compared monetary choices made for one’s own interest with choices made on behalf of an anonymous individual. Consistent with the previous literature, other-interest choices were characterized by an increased gambling propensity. We also investigated choice stochasticity, which captures how much decisions vary in similar conditions. An aspect related to choice stochasticity is how much decisions are tuned to the option values, and we found that this was higher during self-interest than during other-interest choices. This effect was observed only in individuals who reported a motivation to distribute rewards unequally, suggesting that it may (at least partially) depend on a motivation to make accurate decisions for others. Our results indicate that, during decision-making under risk, choices for other people are characterized by a decreased tuning to the values of the options, in addition to enhanced risk seeking