however 'pole' (field) can be either w polu or na polu (in the field) but 'do pola' is rather regional and standard Polish is 'na pole'.
There is a clear difference here. 'W polu' has more general meaning and 'na polu' is more specific. It can be explained better with an example:
Rolnik pracuje w polu (no matter what 'pole' that is)
Rolnik jest na polu (on some specific 'pole')
But in other contexts it may be different e.g.:
w polu elektrycznym = in electric field
w polu karnym = in penalty area (in soccer)
w polu widzenia = in field of vision
but:
na polu walki = in battlefield
na polu minowym = in minefiled
Cinek