doi:10.1016/j.newar.2006.09.025 
Copyright © 2006 Elsevier B.V. All rights reserved.
Interferometric polarimetry of the cosmic microwave background: Methodology
S.T. Myersa, 
, 
, J.L. Sieversb, J.R. Bondb, C.R. Contaldic, B.S. Masond, T.J. Pearsone and A.C.S. Readheade
aNational Radio Astronomy Observatory, P.O. Box O, Socorro, NM 87801, United States
bCanadian Institute for Theoretical Astrophysics, 60 St. George St., Toronto, Ont., Canada M5S 3H8
cTheoretical Physics, Blackett Laboratory, Imperial College, London SW7 2BZ, UK
dNational Radio Astronomy Observatory, 520 Edgemont Road, Charlottesville, VA 22903-2475, United States
eAstronomy, Caltech 105-24, Pasadena, CA 91125, United States
For the CBI collaboration (http://astro.caltech.edu/
tjp/CBI/)..
Available online 17 November 2006.
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Abstract
Interferometry has long been used in radio astronomy to enable imaging of astronomical sources with angular resolutions exceeding the diffraction limit of a single aperture. In the past decade, interferometry of the CMB has been carried out with instruments such as the CBI, DASI and VSA which exploited the inherent instrumental stability and simplicity of ell-space analysis of interferometer data. The practice of interferometric polarimetry has been particularly well-developed in the radio astronomical community and DASI and CBI were able to measure the polarization of the CMB over the multipole range 200 < ℓ < 1500. In this talk, I discuss the theory of interferometry and the mathematics of CMB interferometric polarimetry, using the recent polarization observations of the Cosmic Background Imager (CBI) as an example. Topics will also include description of the data pipeline, handling of contaminating signals and sources, and the construction of optimal maps. I will conclude with the possibility of future CMB interferometers with kilo-element arrays and mega-pixel imaging.
Keywords: Cosmology; Observation; Cosmic microwave background; Polarization
Fig. 1. Schematic of a planar interferometer such as the CBI. Signals from pairs of elements are correlated, with the delays set such that the signals from on-axis wavefronts arrive coherently at the multipliers. Wavefronts coming from an angle θ off-axis correlate with a residual phase 2πθB/λ between antenna pairs with projected baseline B at observing wavelength λ. The real and imaginary parts of the complex correlations are computed, and the outputs are complex un-calibrated “visibilities”.
Fig. 2. Left: The physical baseline between a pair of CBI antennas to be correlated. If a correlated signal were transmitted from the pair, it would paint a sinusoidal fringe on the sky with angular wavelength B/λ. This is equivalent to the plane wave that this baseline is sensitive to. Right: In the uv-plane, the baseline is the center of a locus of points of width equal to the sum of the dish diameters in wavelengths. The correlation sums together the complex coefficients of the plane waves whose k-vectors k = 2πu fall in this region. For polarization, the E and B modes are defined with respect to the orientation of the k-vectors in uv-space.
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Fig. 3. Top row (left to right): Images d of the E and B fields on the sky using the CBI 20 h strip data as presented in Sievers et al. (submitted). The color bar shows the flux density scale in mJy/beam. The six dashed circles are the half-power points of the mosaic fields in that strip, with offsets given in degrees on the coordinate axes. A common-mode signal along the scan direction has been projected out. Bottom row (left to right): The uv-plane maps 
for E and B, respectively, corresponding to the sky images in the top row. The maps show the amplitudes of estimators in cells in uv-space, and have been truncated at ℓ = 1200. Coordinate axes are ku, kv in units of ℓ. Because the 20 h strips are oriented E–W, the resolution along the u axis is higher than that along the v axis. About 3× more power is seen in the E uv-maps and images than in the B maps and images, which in turn are consistent with noise. uv-Maps such as this can be used to search for non-Gaussianity (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).
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