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

Carozzi, T. and Woan, G. (2009) A generalized measurement equation and van Cittert-Zernike theorem for wide-field radio astronomical interferometry. Monthly Notices of the Royal Astronomical Society, 395(3), pp. 1558-1568. (doi:10.1111/j.1365-2966.2009.14642.x)

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Abstract

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 is the theoretical foundation of radio astronomical interferometry, and its application is the basis of interferometric imaging. Existing generalized vC-Z theorems in radio astronomy assume, however, either paraxiality (narrow FoV) or scalar (unpolarized) sources. Our theorem uses neither of these assumptions, which are seldom fulfiled in practice in radio astronomy, and treats the full electromagnetic field. To handle wide, partially polarized fields, we extend the two-dimensional (2D) electric field (Jones vector) formalism of the standard ‘Measurement Equation’ (ME) of radio astronomical interferometry to the full three-dimensional (3D) formalism developed in optical coherence theory. The resulting vC-Z theorem enables full-sky imaging in a single telescope pointing, and imaging based not only on standard dual-polarized interferometers (that measure 2D electric fields) but also electric tripoles and electromagnetic vector-sensor interferometers. We show that the standard 2D ME is easily obtained from our formalism in the case of dual-polarized antenna element interferometers. We also exploit an extended 2D ME to determine that dual-polarized interferometers can have polarimetric aberrations at the edges of a wide FoV. Our vC-Z theorem is particularly relevant to proposed, and recently developed, wide FoV interferometers such as Low Frequency Array (LOFAR) and Square Kilometer Array (SKA), for which direction-dependent effects will be important.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Carozzi, Dr Tobia and Woan, Professor Graham
Authors: Carozzi, T., and Woan, G.
College/School:College of Science and Engineering > School of Physics and Astronomy
Journal Name:Monthly Notices of the Royal Astronomical Society
Publisher:Wiley-Blackwell Publishing Ltd.
ISSN:0035-8711
ISSN (Online):1365-2966

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
408312SKADS - Square Kilometre Array Design StudiesGraham WoanParticle Physics & Astronomy Research Council (PPARC)PP/E000266/1Physics and Astronomy
459312Investigations in Gravitational Radiation.Sheila RowanScience & Technologies Facilities Council (STFC)ST/I001085/1Physics and Astronomy