We develop a general framework for quantifying the many different contributions to the noise budget of an image made with an array of dishes or aperture array stations. Each noise contribution to the visibility data is associated with a relevant correlation timescale and frequency bandwidth so that the net impact on a complete observation can be assessed. All quantities are parameterised as function of observing frequency and the visibility baseline length. We apply the resulting noise budget analysis to a wide range of existing and planned telescope systems that will operate between about 100 MHz and 5 GHz to ascertain the magnitude of the calibration challenges that they must overcome to achieve thermal noise limited performance. We conclude that calibration challenges are increased in several respects by small dimensions of the dishes or aperture array stations. It will be more challenging to achieve thermal noise limited performance using 15 m class dishes rather than the 25 m dishes of current arrays. Some of the performance risks are mitigated by the deployment of phased array feeds and more with the choice of an (alt,az,pol) mount, although a larger dish diameter offers the best prospects for risk mitigation. Many improvements to imaging performance can be anticipated at the expense of greater complexity in calibration algorithms. However, a fundamental limitation is ultimately imposed by an insufficient number of data constraints relative to calibration variables. The upcoming aperture array systems will be operating in a regime that has never previously been addressed, where a wide range of effects are expected to exceed the thermal noise by two to three orders of magnitude. Achieving routine thermal noise limited imaging performance with these systems presents an extreme challenge. The magnitude of that challenge is inversely related to the aperture array station diameter.
Synthesis imaging with a lunar orbit array: III. Augmented lagrangian Multiplier Imaging using Gradient descent Optimization (AMIGO)
National Astronomical Observatories, CAS（中国科学院国家天文台）；School of Astronomy and Space Science, University of Chinese Academy of Sciences（中国科学院大学天文与空间科学学院）；Center of High Energy Physics, Peking University（北京大学高能物理中心）
Synthesis imaging with a lunar orbit array: II. Impacts of instrument-induced phase errors
State Key Laboratory of Radio Astronomy and Technology, National Astronomical Observatories, CAS（中国科学院国家天文台射电天文与技术重点实验室）；School of Astronomy and Space Science, University of Chinese Academy of Sciences（中国科学院大学天文学与空间科学学院）；National Space Science Center, Chinese Academy of Sciences（中国科学院国家空间科学中心）
Multifrequency Synthesis via CHIBI: Colorful Hierarchical Interferometric Bayesian Imaging
Black Hole Initiative, Harvard University（黑洞倡议项目，哈佛大学）；Shanghai Astronomical Observatory, Chinese Academy of Sciences（中国科学院上海天文台）；Center for Computational Sciences, University of Tsukuba（筑波大学计算科学中心）
PhySR: Physics-Informed Neural Network for Super-Resolution Reconstruction in Radio Synthesis Imaging
Guizhou University（贵州大学）；Xinjiang Astronomical Observatory, Chinese Academy of Sciences（中国科学院新疆天文台）；Key Laboratory of Radio Astronomy, Chinese Academy of Sciences（中国科学院射电天文重点实验室）；Nanjing University（南京大学）
