The married couple, who are not being named for legal reasons, knew PC Adrian Pogmore - the officer who filmed them from around 600ft in the air - through the wife-swapping scene.
The couple became involved with the swinging scene after visiting a sex club in Sheffield.
They said they were aware they were being observed when the footage was taken by Pogmore, 51, of Guilthwaite Crescent, Whiston, Rotherham but did not know, or consent to, the filming of their 11-minute romp.
Pogmore later gave the couple a copy of the 11-minute video which showed the couple having sex in a variety of different positions.
The couple turned their back on the swinging scene several years ago, after making a decision to change their lifestyle.
Pogmore will be sentenced for four counts of misconduct in public office relating the making of the footage involving the couple, as well as three other videos which captured nude sunbathers, on Tuesday at Sheffield Crown Court.