(written from a Production point of view)
The Science of Star Trek was a documentary produced by PBS and was first broadcast as part of their The New Explorers series on 18 January 1995. The show focused on comparing the fictional science of Star Trek with the present-day reality, exploring subjects including wormholes, robotics, antimatter and tricorders. The show was researched over the course of a year, and the producers noted that the breadth of material could have made for an additional episode. (Star Trek: The Official Fan Club of the UK Magazine issue 10)
The documentary was hosted by Bill Kurtis, and featured interviews with Avery Brooks, André Bormanis, Stephen Hawking, Colm Meaney, Leonard Nimoy, Michael Okuda, Armin Shimerman, Michael Westmore, Herman Zimmerman, and Robert Picardo, amongst others.
Portions of the special (including the interviews with Meaney and Shimerman) were filmed on the set of Star Trek: Deep Space Nine, which Kurtis visited during the filming of "The Search, Part II" in July 1994. Also, the interview with Picardo (along with a few behind-the-scenes shots) was filmed on the set of "Phage" in November 1994. Behind-the-scenes shots from the shooting of "All Good Things..." in March 1994 can also be seen, apparently lifted from Journey's End: The Saga of Star Trek: The Next Generation.