Near-field imaging of local interference in radio interferometric data: Impact on the redshifted 21 cm power spectrum

Radio-frequency interference (RFI) is a major systematic limitation in radio astronomy, particularly for science cases requiring high sensitivity, such as 21 cm cosmology. Traditionally, RFI is dealt with by identifying its signature in the dynamic spectra of visibility data and flagging strongly affected regions. However, for RFI sources that do not occupy narrow regions in the time-frequency space, such as persistent local RFI, modeling these sources could be essential to mitigating their impact. This paper introduces two methods for detecting and characterizing local RFI sources from radio interferometric visibilities: matched filtering and maximum a posteriori (MAP) imaging. These algorithms use the spherical wave equation to construct three-dimensional near-field image cubes of RFI intensity from the visibilities. The matched filter algorithm can generate normalized maps by cross-correlating the expected contributions from RFI sources with the observed visibilities, while the MAP method performs a regularized inversion of the visibility equation in the near field to construct image cubes in physical units as a function of frequency. We developed a full polarization simulation framework for RFI and demonstrated the methods on simulated observations of local RFI sources. The stability, speed, and errors introduced by these algorithms were investigated, and, as a demonstration, the algorithms were applied to a subset of NenuFAR observations to perform spatial, spectral, and temporal characterization of two local RFI sources. We used simulations to assess the impact of local RFI on images, the u v plane, and cylindrical power spectra, and to quantify the level of bias introduced by the algorithms in order to understand their implications for the estimated 21 cm power spectrum with radio interferometers. The near-field imaging and simulation codes are publicly available in the Python library nfis.