A Spherical Harmonic Analysis of the Ooty Wide Field Array (OWFA) Visibility Signal

Considering redshifted 21-cm intensity mapping with the upcoming Ooty Wide Field Array (OWFA) whose field of view subtends similar to 57 degrees in the north-south (N-S) direction, we present a formalism which relates the measured visibilities to the spherical harmonic coefficients of the sky signal. We use this to calculate window functions which relate the two-visibility correlations i.e. the correlation between the visibilities measured at two baselines and two frequencies, to different multipoles of the multifrequency angular power spectrum C-l (nu(1), nu(2)). The formalism here is validated using simulations. We also present approximate closed form analytical expressions which can be used to calculate the window functions. Comparing the widely adopted flat sky approximation, we find that its predictions match those of our spherical harmonic formalism to within 16 per cent across the entire OWFA baseline range. The match improves at large baselines where we have <5 per cent deviations.