  The quiet Sun internetwork is permeated by weak and highly inclined magnetic
fields whose physical properties, dynamics, and magnetic interactions are not
fully understood. High spatial resolution magnetograms show them as discrete
magnetic elements that appear/emerge and disappear/cancel continuously over the
quiet Sun surface. The 4-m European Solar Telescope (EST) and the Advanced
Technology Solar Telescope (ATST) will obtain two-dimensional, high cadence,
high precision polarimetric measurements at the diffraction limit (30 km).
Here, we compile the basic requirements for the observation of internetwork
fields with EST and ATST (field of view, cadence, instrument configuration,
etc). More specifically, we concentrate on the field-of-view requirements. To
set them we analyze the proper motion of internetwork magnetic elements across
the solar surface. We use 13 hours of magnetograms taken with the Hinode
satellite to identify and track thousands of internetwork magnetic element in
an isolated supergranular cell. We calculate the velocity components of each
element and the mean distance they travel. The results show that, on average,
magnetic elements in the interior of supergranular cells move toward the
network. The radial velocity is observed to depend on the distance to the
center of the supergranule. Internetwork magnetic elements travel 400 on
average. These results suggest that ATST and EST should cover, at least, one
supergranular cell to obtain a complete picture of the quiet Sun internetwork.
