Richard Wright QC, prosecuting, told a jury: "They used the unique viewing position afforded to them, together with the powerful video camera with which the helicopter is equipped, to video members of the public engaged in private activities in a gross violation of their privacy.
"On three separate occasions they filmed a total of five people sunbathing naked in private and, on another occasion, they filmed a couple having sexual intercourse in their own garden."
As Wright opened the case for the prosecution, the jury was shown graphic footage of the couple shot from the helicopter.
Playing the footage, Wright said: "As you will see in a moment, the couple who were filmed on this occasion were very much aware that they were being observed, indeed they seem to relish it."
The prosecutor explained how the couple featured were friends of Adrian Pogmore, 50, a police officer and an air observer on the helicopter, who has pleaded guilty to offences of misconduct in a public office.
The four men on trial - Matthew Lucas, 42, Lee Walls, 47, Matthew Loosemore, 45, and Malcolm Reeves, 64 - all deny the same offence.
Wright told the jury: "The reason that this couple are so happy to be recorded engaging in sexual intercourse is that they are friends of Pogmore and shared his sexual interest in the swinging scene.
"It was clearly, therefore, no coincidence that the helicopter orbits around their garden while they brazenly put on a show."
The prosecutor said: "You may hope that the police helicopter is chasing down criminals and keeping the community safe.
"You may never imagine that in fact it is being used to film a pair of swingers in the throes of sexual passion for the entertainment of the crew."
Continuing his opening of the case, Wright said: "How then does the prosecution say that we can prove that these recordings are not simply the product of one swinging and sex-obsessed air observer, Adrian Pogmore, but were made with the connivance of the other members of the crew?"
Wright said the incident involving the couple having sex on the patio happened on July 28 2008 when the aircraft was piloted by Loosemore, with Pogmore and Lucas as the observers.
Earlier on the same day, the helicopter was used to film a couple sitting naked by a caravan on a campsite used by naturists, also in South Yorkshire.
The prosecutor said: "Although naturists expect to be seen naked by other naturists, they do not expect to be monitored by the crew of the police helicopter."
The jury was shown the video recording of the naturists shot from the helicopter as well as two more recordings of people sunbathing naked.
Footage shot on August 23 2007 - when the pilot was Reeves and the observers were Pogmore and Walls - appeared to involve the aircraft circling a garden where a woman was sunbathing without clothes on a lawn.
Wright said the woman was with two daughters - aged 18 and 15 - who were wearing bikinis and an 8-year-old daughter, who appeared to be fully clothed in the footage.
The prosecutor said: "There is self-evidently no legitimate policing purpose connected to orbiting her home and using equipment to film her naked body."
Wright said the final incident - again featuring people sunbathing naked - was on July 22 2012, when the aircraft was piloted by Reeves, with Lucas and Pogmore as observers.
The prosecutor said that in the cases of all four recordings there was "no legitimate police purpose" for flying over the homes.
Wright said: "This was a deliberate invasion of their privacy for, at the very least, the inappropriate amusement of the crew and, at worst, for their sexual gratification."
He said that it was also a "gross waste of valuable resource".
The prosecutor told the jury that it may hear attempts to trivialise what happened as "isolated incidents of laddish conduct" but he said the people who were filmed did not see it that way.
Wright said the prosecution stemmed from recordings found in Pogmore's possession at a police station in 2015 and that he was the only person present on all four flights mentioned in the charges.
The trial, which started on Tuesday, is expected to last three weeks.
Pogmore, of Whiston, Rotherham, has admitted four charges of misconduct in a public office.
Wright said the other four men deny the charges and, "in short", blame Pogmore for what happened.
