A Matter of Perspective

In this episode, Commander Riker is accused of murdering a scientist and faces an extradition hearing aboard the Enterprise,[2] where everyone's version of what transpired is re-created in the holodeck.

The episode involves themes of subjectivity in perception and memory, as well as the principle of presumed innocence in legal proceedings.

With a routine planetary survey ahead, the Federation starship Enterprise drops Commander Riker (Jonathan Frakes) and Chief Engineer La Forge (LeVar Burton) at the Botanica Four research space station orbiting Tanuga Four to check on the progress of the work of Dr. Nel Apgar (Mark Margolis), a Tanugan who has been working on Krieger waves, a new promised energy source for the Federation.

Captain Picard requests that they hold a hearing aboard the Enterprise to determine Riker's guilt.

This involves the use of a holodeck, recreating the events on the station from data logs and testimony from Riker, Dr. Apgar's wife Manua (Gina Hecht) and his research assistant Tayna (Juliana Donald).

In the holodeck recreation, Krag demonstrates that a directed energy beam – from Riker's location prior to transport – struck the Krieger wave converter, destroying it and the station, but his theory is that Riker fired a phaser just before beaming out.

In Manua's version of the events, she is a doting wife, with her husband promising rich rewards coming from the project.

Meanwhile, the crew of the Enterprise find highly focused pulses of an unknown, intense radiation striking parts of the ship, putting holes through the bulkheads.

With Krag, Manua, Tayna and Riker all present, Picard demonstrates through a combination of the testimonies that Apgar was more interested in the potential financial success of completing the Krieger wave converter; he would not get this through the Federation, and Picard postulates that he in fact was trying to weaponize the project to make money, thus explaining his hostility towards Riker's presence.

Further, Picard suggests that Apgar had successfully built the converter; the holodeck simulation of it, also being fully functional, has been focusing the energy from the generator on the planet, resulting in the damaging radiation experienced on the ship, which La Forge identified as Krieger waves.

Picard completes his explanation by running the holodeck simulation of the moment of Riker's transport, synchronized with the planetary generator – the holodeck simulation shows that Apgar had aimed the Krieger wave generator at Riker, but when the energy beam struck him, the beam bounced off the transporter field and hit the converter, destroying it and the station.