This picture of an F4H about to fly under the Golden Gate Bridge appears from time to time, rarely with the explanation. The comments usually include statements that it is a fake, imaginative explanations as to why the landing gear is down, the pilot was grounded thereafter forever, etc.
In actual fact, it is not a fake. It was not authorized per se, but also did not result in the pilot making his last flight as an officer in the U.S. Navy. It did involve cameras, often a incentive for a pilot to do something stupid although not in this case. An AirPac-approved camera crew was on board Ranger (CVA-61) to get footage for a David Wolper documentary, "The Story of a Carrier Pilot". See https://www.youtube.com/watch?v=4MR_bGZrEck
The fact that the footage of this launch is not in the documentary is easily explained by the Navy's unwillingness to appear to condone stupid stunts like flying under bridges, which in any other circumstance would have the pilot's wings removed immediately after landing, assuming that he hadn't screwed up, crashed, and died. The picture above was presumably taken by a member of the public from Vista Point or a boat.
The plan on 19 October 1962 was for XO Ken Stecker of VF-96, The Fighting Falcons, and another pilot in a second F-4 to be launched well before reaching the bridge after the ship departed NAS Alameda. However, the launch was momentarily delayed (the launch officer was reportedly E. Inman "Hoagy" Carmichael who retired as an admiral, so obviously his career wasn't adversely affected either). When it did occur, Stecker decided that going under the bridge was a better option than trying to climb over it. That was not overly challenging because there is at least 220 feet between the bridge and the water. Stecker subsequently became CO of VF-96.
The other pilot was launched just after the carrier passed under the bridge, as documented by this photo taken from a helicopter. The splash is from the bridle used to launch the jet. It was normally retained (that's what the "plank" protruding ahead of the deck in front of each catapult track was for) and reused, but it was limited to a specific number of launches and it was often simply expended when it was one launch short of the limit if it had lasted that long without incurring visual damage.
In response to one nay-sayer that this explanation can't be true because the ship wouldn't have been going fast enough in San Francisco Bay for the first launch, note that the ship does not have much way on but clearly the wind over deck was adequate. In fact, Ranger didn't have any way on for this dockside launch of a lightly loaded Phantom in Yokosuka Harbor in 1963:
For more on aircraft carrier catapults, see https://thanlont.blogspot.com/2011/01/catapult-innovations.html