Revisiting the radio interferometer measurement equation. I. A full-sky Jones formalism

  title={Revisiting the radio interferometer measurement equation. I. A full-sky Jones formalism},
  author={Oleg M. Smirnov},
  journal={Astronomy and Astrophysics},
  • O. Smirnov
  • Published 10 January 2011
  • Computer Science
  • Astronomy and Astrophysics
Context. Since its formulation by Hamaker et al., the radio interferometer measurement equation (RIME) has provided a rigorous mathematical basis for the development of novel calibration methods and techniques, including various approaches to the problem of direction-dependent effects (DDEs). However, acceptance of the RIME in the radio astronomical community at large has been slow, which is partially due to the limited availability of software to exploit its power, and the sparsity of… 

Revisiting the radio interferometer measurement equation. II. Calibration and direction-dependent effects

This paper aims to describe both classical radio interferometric calibration (selfcal and related methods), and the recent developments in the treatment of DDEs, using the RIME-based mathematical framework developed in Paper I, and demonstrates the ease with which the various effects can be described and understood.

Revisiting the radio interferometer measurement equation - IV. A generalized tensor formalism

A more general formalism that can be used to both clearly define the limitations of the matrix RIME, and to describe observational scenarios that lie outside these limitations is developed.

Generalized formalisms of the radio interferometer measurement equation

The Radio Interferometer Measurement Equation (RIME) is a matrix-based mathematical model that describes the response of a radio interferometer. The Jones calculus it employs is not suitable for

Nonlinear Kalman filters for calibration in radio interferometry

The data produced by the new generation of interferometers are affected by a wide variety of partially unknown complex effects such as pointing errors, phased array beams, ionosphere, troposphere,

Robust Calibration of Radio Interferometers in Non-Gaussian Environment

A robust calibration algorithm is presented based on the design of an iterative relaxed concentrated maximum likelihood estimation procedure that allows to obtain closed-form expressions for the unknown parameters with a reasonable computational cost andumerical simulations reveal that the proposed algorithm outperforms the state-of-the-art calibration techniques.

Validation Solutions to the Full-sky Radio Interferometry Measurement Equation for Diffuse Emission

Low-frequency radio observatories are reaching unprecedented levels of sensitivity in an effort to detect the 21 cm signal from the Cosmic Dawn. High precision is needed because the expected signal

Improving the direction-dependent gain calibration of reflector antenna radio telescopes

Utilising future radio interferometer arrays, such as the Square Kilometre Array (SKA), to their full potential will require calibrating for various directiondependent effects, including the

An Eigenvector-Based Method of Radio Array Calibration and Its Application to the Tianlai Cylinder Pathfinder

We propose an eigenvector-based formalism for the calibration of radio interferometer arrays. In the presence of a strong dominant point source, the complex gains of the array can be obtained by

Polarization calibration techniques for the new-generation VLBI

This paper presents new software that is able to perform a simultaneous fit of multiple calibrator sources, include nonlinear terms in the model of the instrumental polarization and use a self-calibration approach for the estimate of the polarization leakage in the antenna receivers.



Understanding radio polarimetry. I. Mathematical foundations

The measurement of polarized radiation uses entirely different methods at optical and radio wavelengths. As a result, the algebraic analysis of polarimeter performance differs and, in the case of

The MeqTrees software system and its use for third-generation calibration of radio interferometers

The technical goal of MeqTrees is to provide a tool for rapid implementation of numerical models, while offering performance comparable to hand-written code, and is pursuing the wider goal of increasing the rate of evolution of radio astronomical software.

Understanding radio polarimetry. II. Instrumental calibration of an interferometer array

In a companion paper, a mathematical formalism to describe the polarimetric response of a radio interferometer was presented. Some of the instrumental parameters, however, are either unknown or

A generalized measurement equation and van Cittert‐Zernike theorem for wide‐field radio astronomical interferometry

We derive a generalized van Cittert-Zernike (vC-Z) theorem for radio astronomy that is valid for partially polarized sources over an arbitrarily wide field of view (FoV). The classical vC-Z theorem

Understanding radio polarimetry. III. Interpreting the IAU/IEEE definitions of the Stokes parameters.

In two companion papers (Paper I, Hamaker et al. 1996; Paper II, Sault et al. 1996), a new theory of radio-interferometric polarimetry and its application to the calibration of interferometer arrays

Correcting direction-dependent gains in the deconvolution of radio interferometric images

Astronomical imaging using aperture synthesis telescopes requires deconvolution of the point spread function as well as calibration of instrumental and atmospheric effects. In general, such effects

The Noncoplanar Baselines Effect in Radio Interferometry: The W-Projection Algorithm

A novel interpretation of the noncoplanar baselines effect as being due to differential Fresnel diffraction in the neighborhood of the array antennas is presented, and a new algorithm to deal with this effect is developed, which has markedly superior performance.

Advances in Calibration and Imaging Techniques in Radio Interferometry

This paper summarizes some of the major calibration and image reconstruction techniques used in radio interferometry and describes them in a common mathematical framework. The use of this framework

A New Calculus for the Treatment of Optical SystemsI. Description and Discussion of the Calculus

The effect of a plate of anisotropic material, such as a crystal, on a collimated beam of polarized light may always be represented mathematically as a linear transformation of the components of the

Understanding radio polarimetry. IV. The full-coherency analogue of scalar self-calibration: Self-al

An operation state monitoring apparatus for monitoring an operation state of a controlled object is disclosed. The apparatus compares actual operation state data of the controlled object with