How are Doppelgangers used in Vertigo

A Doppelgänger by definition is a ghostly double of a living person that haunts its living counterpart. Freud declared that the arrival of a doppelganger was "The return of the repressed." 
This is apparent in Vertigo as a way of Scottie curing himself of his castration. MAdeleine and Judy are mirror images of each other and provide Scottie a way of curing himself. Madelience represented Scotties ideal woman, his lust, and his sexual desire. She was his perfect woman, and when he failed to save her from his apparent death. He spiralled out of control, transforming his journey from searching for his cure, to hunting for his cure.
 When he is presented with Judy, Hitchcock constructs the stalking sequence identically to the first half, in order with starting at Madeleine's old home, then Earnies, then the art gallery, and the flower shop.
Scottie sees Judy as his weapon to cure himself, and tries to recreate the image of Madeleine, thus recreating the past and curing himself ultimately in the end.