How are doppelgänger used in vertigo?

A doppelgänger is a ghostly double of a person that haunts its living counterparts. They are commonly used in film and literature as a psychomachina, this is because it allows story tellers to visualise the different aspects of a characters personality. In Hitchcock's vertigo Madeline and Judy are mirror images of the same character that represent the vices and virtues within Scottie. Madeline brings out the virtuous side of Scottie. From the moment Scottie saw Madeline he was obsessed, this is signified through the camera and music the moment he first saw her. This is where is obsession for the perfect women awakened, he's sees this possession of the ideal women as a cure for is castration, however his attempt fails and madeline dies. It is then after retracing his steps he sees Judy, the camera angels and diegetic angelic music are repeated and mirror the first ones reinforcing that he has met Madeline's doppelgänger. Freud claimed the arrival of a doppelgänger represents the return of the repressed