run eye over
run an/(one's) eye over (something)
To look at something, often in its entirety, quickly and perfunctorily. I always run an eye over my desk to make sure I have everything before I leave the office at night. You don't have to read this document in detail—just run your eye over it when you get a chance.
run one's eye over something
Fig. to gaze at the whole of something; to glance at all of something. She ran her eyes over the lines of the automobile and nodded her approval. He ran his eyes over the drawing and decided that he had to have it.