This means there must be a moment in Empire Strikes Back when Vader realizes he has a son. The question is, when?

After I watched Episode III, I immediately went home and watched the (original) Episodes IV and V, and it seemed obvious to me that Vader had figured out Luke's relationship to him between the two movies (or possibly during the Death Star battle. I was also curious about the kids -- it seems Vader didn't know about them, possibly until he saw Luke.