Was That A Hawk, Falcon Or Osprey On Roosevelt Island Main Street Lamp Post Today?

Roosevelt Island Historical Society President Judy Berdy spotted this bird perched on top of a Roosevelt Island Main Street lamp post earlier today

before it flew off into Capobianco Park.

I was told that the bird is not a Hawk or a Falcon but an Osprey who feeds on the Roosevelt Island pigeons and rats. Anybody know for sure?