EVLA Memo 67 W PROJECTION: A NEW ALGORITHM FOR NON-COPLANAR BASELINES

Wide-field imaging is key to many of the science goals of the EVLA in both Phase I and Phase II. Optimization of wide-field imaging algorithms is therefore vital. In this memo, we consider the existing algorithms for dealing with non-coplanar baselines and propose a new algorithm with markedly superior performance. At roughly equivalent levels of accuracy, this new algorithm, which we call “w-projection”, is about an order of magnitude faster than the corresponding facet-based algorithms. The new algorithm is now available in AIPS++. 1. Overview of the non-coplanar baselines problem The response of a narrow-band phase-tracking interferometer to spatially incoherent radiation from the far field can be expressed by the following relation between the spatial coherence, or ‘visibility’, V (u, v, w), and the spectral intensity, or brightness, I(`,m); (1) V (u, v, w) = ∫ ∫ I(`,m) √ 1− `2 −m2 e−2πi[u`+vm+w( √ 1−`2−m2−1)]d`dm In this equation, the baseline coordinates, (u, v, w), and direction cosines, (`,m) have their usual definitions. When the term 2πw( √ 1− `2 −m2−1) is much less than unity, it may be ignored, and a two-dimensional Fourer relationship results. When this term is comparable to or exceeds unity, a two-dimensional Fourier transform cannot be used. The value of this term is roughly: (2) Bλ D2 where B is the maximum baseline length, D is the antenna diameter, and λ is the observing wavelength. This effect (called “non-coplanar baselines”) is therefore most troublesome for the larger VLA configurations observed at longer wavelengths. Also, as Perley and Clark discuss (2003), this factor worsens for small antennas such as will be used in the Large N, Small D design for the SKA. The non-coplanar baselines effect consists of two related but somewhat distinct parts. First there is a position-dependent phase-shift due to the term 2πw( √ 1− `2 −m2− 1). Second, when the Fourier plane sampling S(u, v, w) is taken into account, the actual size structures sampled by a given physical pair of antennas varies across the field of view. Date: 2003 December 16.