I did a fantasy badge a while ago... all of the ones I have seen are fantasy pieces or allegedly made for production but given out at a Japanese premiere.
That particular element appeared in front of Precrime headquarters, while the 3D graphic of it was used numerous places (e.g., posters, flyers, promotional gifts).
Here are photos of it in Washington, DC during filming there:
In the movie, two metal badges appear on screen: 1) what I call the Gideon badge, and 2) the Lamar Burgess lapel badge. As far as I can tell, the Gideon badge can only be seen in the Hall of Containment, while the lapel badge is clearly visible on suited Precrime officers and Lamar Burgess towards the end of the film.
A ton of additional ID material was made for the movie. When they went to iris scans for identification, however, a lot of that other stuff went out the window.
The bigger cooler badge and holographic ID were brokered by me. They were supposedly made for the film but delivered too late for filming. Subsequently, they were given away as premiums at the Tokyo premier of the film. Very few of those were apparently made since I haven't seen any of them show up on the secondary market (I still have one ID and two badges available for sale if anyone's interested).