When Facebook opened its Graph API to developers, it allowed apps to read public information. However, as of the last major API update (v19.0+), profile pictures are served in limited resolutions. The API simply does not offer a method to pull the original HD file of a user’s profile picture unless that user has explicitly granted your app user_photos permission.
allow you to paste a URL to retrieve photos in HD without requiring you to log in or register. Developer Workarounds : For technical users, using Graph API calls