Sky reconstruction from transit visibilities: PAON-4 and Tianlai dish array

The spherical harmonics $m$-mode decomposition is a powerful sky map reconstruction method suitable for radio interferometers operating in transit mode. It can be applied to various configurations, including dish arrays and cylinders. We describe the computation of the instrument response function, the point spread function (PSF), transfer function, the noise covariance matrix and noise power spectrum. The analysis in this paper is focused on dish arrays operating in transit mode. We show that arrays with regular spacing have more pronounced side lobes as well as structures in their noise power spectrum, compared to arrays with irregular spacing, specially in the north-south direction. A good knowledge of the noise power spectrum $C^{\mathrm{noise}}(\ell)$ is essential for intensity mapping experiments as non uniform $C^{\mathrm{noise}}(\ell)$ is a potential problem for the measurement of the HI power spectrum. Different configurations have been studied to optimise the PAON-4 and Tianlai dish array layouts. We present their expected performance and their sensitivities to the 21-cm emission of the Milky Way and local extragalactic HI clumps