under the eyes of [sb]preppreposition: Relates noun or pronoun to another element of sentence--for example, "a picture of John," "She walked from my house to yours."
(observed)
在…的眼皮底下 zài … de yǎn pí dǐ xià
在…的监视之下 zài … de jiān shì zhī xià
Under the eyes of his tutor, James became the smartest kid in his school.