What does the vulture eye represent and why do you think it is termed 'vulture eye' in "The Tell-Tale Heart"?

One explanation given by critics about the old man in "The Tell-Tale Heart" is that he is a "doppelganger" for the narrator, a double for him, and the narrator's hatred for the man represents his own self-loathing.  If this be the case, then the focus of the mad narrator goes to the eye that is bluish in its clouding as the object of his problems.  Perhaps, he may believe, it is the eye that is a curse upon him, making him so "nervous."  This eye that resembles a vulture's eye, that has a film which can cover it at times, stares at the narrator as the vulture looms over its prey in anticipation of death.

The fixation upon an object as the curse or reason for one's agony is not uncommon.  Lady MacBeth's fixation on the "damned spot" is the focus of her agonized mind, for example.  So, in order to relieve his psychological torment, the character must rid him/herself of this cursed object. Likewise, the narrator fixates upon the eye. Of course, the horror lies in the old man's realization that the narrator is mad and perceives his eye as this object, for he cries out before he is attacked.  The reader senses horror in the grotesqueness of the bizarre reasoning of the narrator.