A Semianalytical Method of Frequency-average Smearing for Radio Interferometers based on Point Source

Abstract Next-generation radio interferometers, with their enhanced spatial, temporal, and high-frequency resolution, will pose considerable challenges to data processing and storage. Frequency averaging reduces the volume of data, but would cause smearing of the bandwidth. The examination of bandwidth smearing is essential in the processing of radio interferometer data to achieve scientific objectives. Existing analysis methods can quantify parameters such as peak intensity loss in restored images under ideal assumptions. However, determining the shape of the source smearing in dirty images requires using complex observational simulation methods, which limits comprehensive studies of bandwidth smearing from frequency averaging and its optimal application. In this paper, we introduce a semianalytical method (SAM) and validate its accuracy through the simulation method. The SAM efficiently and precisely evaluates the impact of the smearing effect from frequency averaging for various telescope pointing positions, offering a plausible “distorted beam” representation of the non-phase-centered beam shape of point sources in the dirty image. Based on this beam shape, the specific shape of smearing after frequency averaging can be accurately and comprehensively described. This not only enables the determination of the extent of smearing, prediction of accuracy loss, and formulation of effective observation and data processing strategies prior to data processing, but also facilitates the development of more advanced frequency averaging methods.