Field-dependent averaging losses in radio interferometry ($\delta \nu B\theta /c\ll 1,\Delta t{\Omega }_{E}B\theta /\lambda \ll 1$)

After delay tracking and fringe stopping at a phase center, an off-axis direction retains delay of order $B\theta /c$ and rotation-induced fringe-rate offset of order ${\Omega }_{E}B\theta /\lambda$. Averaging across a wide channel or long integration then decorrelates that direction. The displayed inequalities give order-of-magnitude small-smearing conditions; exact coefficients depend on baseline geometry, averaging window and allowed loss. A larger field or longer baseline therefore demands finer frequency and time sampling.