The electric field can be "measured" at any place around the antenna, for the radiation pattern there are limitations with respect to the measuring distance.
The far field radiation pattern is "measured" at distances where the path length difference from any point on the antenna structure to the measuring point no longer depends on the measuring distance (Fraunhofer region). In this region, doubling the distance results in 6 dB reduction of power flux density (so E- and H-field halves).
The radiation pattern mostly shows the ratio between the power flux density of the DUT at certain distance in the far field zone, and the power flux density that would be generated by an isotropically radiating source (mostly expressed in dBi). Orientation (angle) towards the DUT is varied during this procedure
As in the far field E is perpendicular to H, E and H are in time phase, and E/H = 377, power flux density (average pointing vector S) = E^2/377 [W/m^2], in air or vacuum.
Note that that gain generally not equals directivity (because of not all electrically supplied energy is converted to radiation due to loss).