标题： 射电望远镜阵列的基本成像极限 显示英文标题

标题： Fundamental Imaging Limits of Radio Telescope Arrays

摘要： 射电天文学图像的保真度通常通过实践经验进行评估，即使用经验法则，尽管某些方面和情况已经得到了严格的处理。 在本文中，我们提出了一种数学框架，能够描述射电天文学成像问题的基本限制。 虽然数据模型假设为单次快照观测，即不考虑时间和频率的变化，但该框架足够通用，可以扩展到综合孔径观测。 利用统计信号处理和线性代数的工具，我们讨论了成像和去卷积问题的可解性，成像和去卷积过程中噪声在图中的重新分布，由于校准误差和热噪声传播导致的图像值的协方差以及自校准可处理的源数量上限。 图像值的协方差和可处理源的数量的结合决定了成像过程中可实现的有效噪声底限。 有效噪声比动态范围提供了更好的性能指标，因为它包括了噪声的空间变化。 我们的结果为通过阵列设计改进成像性能提供了手段。 显示英文摘要

摘要： The fidelity of radio astronomical images is generally assessed by practical experience, i.e. using rules of thumb, although some aspects and cases have been treated rigorously. In this paper we present a mathematical framework capable of describing the fundamental limits of radio astronomical imaging problems. Although the data model assumes a single snapshot observation, i.e. variations in time and frequency are not considered, this framework is sufficiently general to allow extension to synthesis observations. Using tools from statistical signal processing and linear algebra, we discuss the tractability of the imaging and deconvolution problem, the redistribution of noise in the map by the imaging and deconvolution process, the covariance of the image values due to propagation of calibration errors and thermal noise and the upper limit on the number of sources tractable by self calibration. The combination of covariance of the image values and the number of tractable sources determines the effective noise floor achievable in the imaging process. The effective noise provides a better figure of merit than dynamic range since it includes the spatial variations of the noise. Our results provide handles for improving the imaging performance by design of the array.