Phasing cloaking device

The phasing cloaking device, was an experimental technology developed by a secret group in Starfleet Security in the 2350s. An expansion on the more traditional cloaking device, it was designed to phase sequence the structure of matter and energy to such a rate that it was possible to allow any vessel utilizing the device to pass through normal matter in the phased state. A direct violation of the Treaty of Algeron, which banned cloaking technology aboard Federation starships, the phasing cloak was first tested aboard the USS Pegasus in 2358, under the command of Captain Erik Pressman.

In response to the illegal use of this device, the crew of the Pegasus mutinied against Pressman, forcing Pressman and a small group of officers who sided with him, including a young Ensign Will Riker, to flee the ship. Afterwards, the Pegasus drifted into an asteroid field in the Devolin system while still in a phased state. The cloak blew out the plasma relays aboard the ship, and when it passed through a particularly large asteroid, the cloak failed, causing the Pegasus to partially materialize inside solid rock. The crew dead, the Pegasus remained entombed in the asteroid for the next twelve years. A Judge Advocate General's investigation into the mutiny was initiated, but, in order to conceal the illegal test, Starfleet Intelligence classified the file.

In 2370 Pressman, now an admiral at Starfleet Intelligence, boarded the USS Enterprise (NCC-1701-D) and mounted a mission to retrieve the phasing cloak. It had been determined that the Romulans had learned about the cloaking device and were attempting to retrieve it themselves, and Pressman was determined not to let it fall into their hands. The Pegasus was eventually located and the device retrieved, but not before a Romulan Warbird sealed the Enterprise inside the asteroid. Deciding not to continue to aid Pressman in the illegal activity, Riker, by this point the Enterprise's first officer, revealed the existence of the cloaking device to Captain Picard, and suggested using it to phase the Enterprise and pass through the surface of the asteroid. The plan worked, and Picard ordered the Enterprise to decloak in front of the Warbird, thereby revealing the existence of the phasing cloak to the Romulans. Both Admiral Pressman and Commander Riker were subsequently taken into custody for their respective roles in the illegal experiment. 

Other similar phasing technology
In 2368, on Devidia II, crew of the USS Enterprise-D devised a method of phase-shifting crewmen to a positive phase variance of 0.004 percent. Data was enveloped in a contained subspace force field created by a subspace generator. By adjusting the synchronic distortion of the field with the phase discriminator in his positronic brain, he phase-shifted himself. The procedure was repeated for other members of the crew using a tricorder modified to interface with the subspace generator, containing a custom built phase discrimination. It was theorized in both instances that the phase displacement was not precise enough to synchronize the Enterprise crew to the Devidians' perceptual range, even though the Enterprise personnel could see them when phased. 

To covertly conduct their invasive experiments on other humanoids, the Srivani also used this type of stealth technology for themselves, as well as their equipment and ships. In 2374, when invading the USS Voyager, the technology hid the Srivani to a phase variance of 0.15. Adjusting the Borg sensory node of Seven of Nine for this variance allowed her to see them. Seven also modified her hand phaser to a modulation that would penetrate the cloak.