A comic Perfect Evil by Shin-Ichi Hiromoto seems to have been published to answer this question directly. The book tells of events immediately following the destruction of the first Death Star where Vader vows revenge on the rebel pilot who destroyed it (this isn't the main story arc of the comic, but the part that is relevant here).
Upon his return to Coruscant, Vader dispatches an intelligence officer to uncover the identity of the rebel pilot. Some time later, aboard his Star Destroyer (not the Executor), the officer contacts him with a holoprojection containing both the name and picture of the pilot Luke Skywalker. Vader remembers his face as the boy who fired on him after he killed Obi-Wan aboard the Death Star.
Vader then makes the assumption that this boy must be his son born to Padme before her death and changes his vow to "reunite" with him rather than act revenge on him.
I assume that since the comic is officially licensed, it would be considered "C" canon. Although, I can also see why considering it canon would be frowned upon because it seems linked to The Force Unleashed video game.
Information taken from a synopsis of the story at Wookieepedia