Phrase(s): eagle eye acute eyesight; an intently watchful eye. (From the sharp eyesight of the eagle.) • The students wrote their essays under the eagle eye of the headmaster. • The umpire kept his eagle eye on the tennis match.
McGrawhill's American Idioms And Phrasal Verbs
Unusually keen sight; also, keen intellectual vision. For example, Antiques dealers have an eagle eye for valuable objects, or A good manager has an eagle eye for employee errors. [Late 1500s]
American Heritage Idioms