Revisiting the radio interferometer measurement equation. I. A full-sky Jones formalism
Revisiting the radio interferometer measurement equation. I. A full-sky Jones formalism
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DOI：
10.1051/0004-6361/201016082
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发表时间：
2011-01
影响因子：
6.5
通讯作者：
O. Smirnov
中科院分区：
文献类型：
--
作者：
O. Smirnov
上下文自Hamaker等人提出以来，无线电干涉仪测量方程（RIME）为开发新的校准方法和技术提供了严格的数学基础，包括解决方向相关效应（DDE）问题的各种方法。然而，在射电天文学界对RIME的接受一直很慢，部分原因是利用其功能的软件有限，以及实际结果的稀疏性。这种情况急需改变。目标。本系列论文旨在将DDE治疗的最新进展纳入一个基于RIME的数学框架，并证明可以轻松描述和理解各种效应。它还旨在展示基于RIME的校准方法的好处。方法.论文我重新推导出的RIME从第一原则，形式主义扩展到全天空的情况下，并纳入DDE。纸二，然后使用的形式主义来描述自校准，既有一个完整的RIME，并与旧的软件包的近似方程，并显示这是如何影响DDE。它还概述了现实生活中的DDE和处理它们的建议方法。最后，在论文III中，这些方法中的一些行使，以实现一个非常高的动态范围的校准WSRT观测3C 147在21厘米，充分治疗的DDE。结果RIME形式主义扩展到全天空的情况下（纸I），并被证明是一个优雅的方式来描述校准和DDE（纸II）。将其应用于WSRT数据（论文III），得到了3C 147周围具有非常高的动态范围（160万）的噪声限制图像，并且没有困扰常规自校准的离轴伪影。所得到的差分增益解包含有关天空模型中的DDE和误差的重要信息。结论. RIME是描述无线电干涉测量的一个强大的形式主义，并支持新的校准方法的发展，特别是那些处理DDE。其中之一是用于3C 147缩减的差分增益方法。差分增益可以消除DDE相关的伪影，并为天空模型的迭代改进提供信息。也许最重要的是，微弱的2 mJy的来源已被证明产生有意义的差分增益的解决方案，因此可以作为潜在的校准信标在其他DDE相关的计划。
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 practical results. This needs to change urgently. Aims. This series of papers aims to place recent developments in the treatment of DDEs into one RIME-based mathematical framework, and to demonstrate the ease with which the various effects can be described and understood. It also aims to show the benefits of a RIME-based approach to calibration. Methods. Paper I re-derives the RIME from first principles, extends the formalism to the full-sky case, and incorporates DDEs. Paper II then uses the formalism to describe self-calibration, both with a full RIME, and with the approximate equations of older software packages, and shows how this is affected by DDEs. It also gives an overview of real-life DDEs and proposed methods of dealing with them. Finally, in Paper III some of these methods are exercised to achieve an extremely high-dynamic range calibration of WSRT observations of 3C 147 at 21 cm, with full treatment of DDEs. Results. The RIME formalism is extended to the full-sky case (Paper I), and is shown to be an elegant way of describing calibration and DDEs (Paper II). Applying this to WSRT data (Paper III) results in a noise-limited image of the field around 3C 147 with a very high dynamic range (1.6 million), and none of the off-axis artifacts that plague regular selfcal. The resulting differential gain solutions contain significant information on DDEs and errors in the sky model. Conclusions. The RIME is a powerful formalism for describing radio interferometry, and underpins the development of novel calibration methods, in particular those dealing with DDEs. One of these is the differential gains approach used for the 3C 147 reduction. Differential gains can eliminate DDE-related artifacts, and provide information for iterative improvements of sky models. Perhaps most importantly, sources as faint as 2 mJy have been shown to yield meaningful differential gain solutions, and thus can be used as potential calibration beacons in other DDE-related schemes.