To catch sight of something is to see it briefly and by chance. A glimpse, and then it is gone.
The brevity and the accident are both essential, which is why you catch sight of somebody in a crowd rather than in a meeting. It is a three-part phrase and stays together. The related noun a glimpse means the same thing in one word. Catching somebody's eye is a different phrase entirely, meaning to attract their attention rather than to see them.
1phrasecatch sight ofTo see something briefly and unexpectedly.
“I happened to catch sight of him on the far platform.”
Practised in A Man Called Ove, Ways of Looking
First appears in chapter 4 of A Man Called Ove.
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