I think the Roman eagle became double-headed in Constantinople, possibly in reference to the geographical situation of the city, bridging East and West; though I have read that this motif also occurs earlier in Middle-Eastern mythology (I can't remember where or with what significance). It was then adopted by the "Holy Roman Empire" (hence the Habsburgs) and by the Ottomans, as well as of course by the Tsars. All of these claimed in some sense to be the heirs of Constantinople.