Research on Wide-field Imaging Techniques for Low-frequency Radio Arraytwo

Wide-field imaging of low-frequency radio telescopes is subject to a number of difficult problems. One particularly pernicious problem is the non-coplanar baseline effect. It will lead to distortion of the final image when the phase of $w$-direction called $w$-term is ignored. The image degradation effects are amplified for the telescopes with a wide field of view. This paper summarizes and analyzes several $w$-term correction methods and their technical principles. Their advantages and disadvantages are analyzed after comparing their computational cost and computational complexity. We conduct simulations with two of these methods, i.e., faceting and $w$-projection, based on the configuration of the first-phase Square Kilometre Array (SKA) low-frequency array. The resulted images are also compared with the result of the two-dimensional Fourier transform method. The results show that the image quality and correctness derived from both faceting and $w$-projection are better than the two-dimensional Fourier transform method in wide-field imaging. The effects of the number of facets and the $w$-direction step length on the image quality and running time are evaluated. The results indicate that the number of facets and the $w$-direction step length must be reasonable. Finally, we analyze the effect of data size on the running times of the faceting and $w$-projection algorithms. The results show that the faceting and $w$-projection algorithms need to be optimized before the huge amount of data processing. The research of the present paper initiates the analysis of wide-field imaging techniques and their applications in the existing and future low-frequency arrays, and will foster their applications in even broader fields.