Improving self-calibration

Response calibration is the process of inferring how much the measured data depend on the signal one is interested in. It is essential for any quantitative signal estimation on the basis of the data. Here, we investigate self-calibration methods for linear signal measurements and linear dependence of the response on the calibration parameters. The common practice is to augment an external calibration solution using a known reference signal with an internal calibration on the unknown measurement signal itself. Contemporary self-calibration schemes try to find a self-consistent solution for signal and calibration by exploiting redundancies in the measurements. This can be understood in terms of maximizing the joint probability of signal and calibration. However, the full uncertainty structure of this joint probability around its maximum is thereby not taken into account by these schemes. Therefore better schemes -- in sense of minimal square error -- can be designed by accounting for asymmetries in the uncertainty of signal and calibration. We argue that at least a systematic correction of the common self-calibration scheme should be applied in many measurement situations in order to properly treat uncertainties of the signal on which one calibrates. Otherwise the calibration solutions suffer from a systematic bias, which consequently distorts the signal reconstruction. Furthermore, we argue that non-parametric, signal-to-noise filtered calibration should provide more accurate reconstructions than the common bin averages and provide a new, improved self-calibration scheme. We illustrate our findings with a simplistic numerical example.Comment: 17 pages, 3 figures, revised version, title change

Parametric high resolution techniques for radio astronomical imaging

The increased sensitivity of future radio telescopes will result in requirements for higher dynamic range within the image as well as better resolution and immunity to interference. In this paper we propose a new matrix formulation of the imaging equation in the cases of non co-planar arrays and polarimetric measurements. Then we improve our parametric imaging techniques in terms of resolution and estimation accuracy. This is done by enhancing both the MVDR parametric imaging, introducing alternative dirty images and by introducing better power estimates based on least squares, with positive semi-definite constraints. We also discuss the use of robust Capon beamforming and semi-definite programming for solving the self-calibration problem. Additionally we provide statistical analysis of the bias of the MVDR beamformer for the case of moving array, which serves as a first step in analyzing iterative approaches such as CLEAN and the techniques proposed in this paper. Finally we demonstrate a full deconvolution process based on the parametric imaging techniques and show its improved resolution and sensitivity compared to the CLEAN method.Comment: To appear in IEEE Journal of Selected Topics in Signal Processing, Special issue on Signal Processing for Astronomy and space research. 30 page

Astrophysical data analysis with information field theory

Non-parametric imaging and data analysis in astrophysics and cosmology can be addressed by information field theory (IFT), a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construction of optimal signal recovery algorithms. It exploits spatial correlations of the signal fields even for nonlinear and non-Gaussian signal inference problems. The alleviation of a perception threshold for recovering signals of unknown correlation structure by using IFT will be discussed in particular as well as a novel improvement on instrumental self-calibration schemes. IFT can be applied to many areas. Here, applications in in cosmology (cosmic microwave background, large-scale structure) and astrophysics (galactic magnetism, radio interferometry) are presented.Comment: 4 pages, 2 figures, accepted chapter to the conference proceedings for MaxEnt 2013, to be published by AI

Suitability of Automatic Photogrammetric Reconstruction Configurations for Small Archaeological Remains

19 p.Three-dimensional (3D) reconstruction is a useful technique for the documentation, characterization, and evaluation of small archeological objects. In this research, a comparison among different photogrammetric setups that use different lenses (macro and standard zoom) and dense point cloud generation calibration processes for real specific objects of archaeological interest with different textures, geometries, and materials is raised using an automated data collection. The data acquisition protocol is carried out from a platform with control points referenced with a metrology absolute arm to accurately define a common spatial reference system. The photogrammetric reconstruction is performed considering a camera pre-calibration as well as a self-calibration. The latter is common for most data acquisition situations in archaeology. The results for the different lenses and calibration processes are compared based on a robust statistical analysis, which entails the estimation of both standard Gaussian and non-parametric estimators, to assess the accuracy potential of different configurations. As a result, 95% of the reconstructed points show geometric discrepancies lower than 0.85 mm for the most unfavorable case and less than 0.35 mm for the other casesS

Image formation in synthetic aperture radio telescopes

Next generation radio telescopes will be much larger, more sensitive, have much larger observation bandwidth and will be capable of pointing multiple beams simultaneously. Obtaining the sensitivity, resolution and dynamic range supported by the receivers requires the development of new signal processing techniques for array and atmospheric calibration as well as new imaging techniques that are both more accurate and computationally efficient since data volumes will be much larger. This paper provides a tutorial overview of existing image formation techniques and outlines some of the future directions needed for information extraction from future radio telescopes. We describe the imaging process from measurement equation until deconvolution, both as a Fourier inversion problem and as an array processing estimation problem. The latter formulation enables the development of more advanced techniques based on state of the art array processing. We demonstrate the techniques on simulated and measured radio telescope data.Comment: 12 page

A photonic crystal Josephson traveling wave parametric amplifier

An amplifier combining noise performances as close as possible to the quantum limit with large bandwidth and high saturation power is highly desirable for many solid state quantum technologies such as high fidelity qubit readout or high sensitivity electron spin resonance for example. Here we introduce a new Traveling Wave Parametric Amplifier based on Superconducting QUantum Interference Devices. It displays a 3 GHz bandwidth, a -102 dBm 1-dB compression point and added noise near the quantum limit. Compared to previous state-of-the-art, it is an order of magnitude more compact, its characteristic impedance is in-situ tunable and its fabrication process requires only two lithography steps. The key is the engineering of a gap in the dispersion relation of the transmission line. This is obtained using a periodic modulation of the SQUID size, similarly to what is done with photonic crystals. Moreover, we provide a new theoretical treatment to describe the non-trivial interplay between non-linearity and such periodicity. Our approach provides a path to co-integration with other quantum devices such as qubits given the low footprint and easy fabrication of our amplifier.Comment: 6 pages, 4 figures, Appendixe

Comprehensive Two-Point Analyses of Weak Gravitational Lensing Surveys

We present a framework for analyzing weak gravitational lensing survey data, including lensing and source-density observables, plus spectroscopic redshift calibration data. All two-point observables are predicted in terms of parameters of a perturbed Robertson-Walker metric, making the framework independent of the models for gravity, dark energy, or galaxy properties. For Gaussian fluctuations the 2-point model determines the survey likelihood function and allows Fisher-matrix forecasting. The framework includes nuisance terms for the major systematic errors: shear measurement errors, magnification bias and redshift calibration errors, intrinsic galaxy alignments, and inaccurate theoretical predictions. We propose flexible parameterizations of the many nuisance parameters related to galaxy bias and intrinsic alignment. For the first time we can integrate many different observables and systematic errors into a single analysis. As a first application of this framework, we demonstrate that: uncertainties in power-spectrum theory cause very minor degradation to cosmological information content; nearly all useful information (excepting baryon oscillations) is extracted with ~3 bins per decade of angular scale; and the rate at which galaxy bias varies with redshift substantially influences the strength of cosmological inference. The framework will permit careful study of the interplay between numerous observables, systematic errors, and spectroscopic calibration data for large weak-lensing surveys.Comment: submitted to Ap

Understanding the saturation power of Josephson Parametric Amplifiers made from SQUIDs arrays

We report on the implementation and detailed modelling of a Josephson Parametric Amplifier (JPA) made from an array of eighty Superconducting QUantum Interference Devices (SQUIDs), forming a non-linear quarter-wave resonator. This device was fabricated using a very simple single step fabrication process. It shows a large bandwidth (45 MHz), an operating frequency tunable between 5.9 GHz and 6.8 GHz and a large input saturation power (-117 dBm) when biased to obtain 20 dB of gain. Despite the length of the SQUID array being comparable to the wavelength, we present a model based on an effective non-linear LC series resonator that quantitatively describes these figures of merit without fitting parameters. Our work illustrates the advantage of using array-based JPA since a single-SQUID device showing the same bandwidth and resonant frequency would display a saturation power 15 dB lower.Comment: 12 pages, 9 figures, Appendices include