(covers information from several alternate timelines)
The pattern enhancer (also known as a transport enhancer or transporter enhancer) was a piece of Federation equipment designed to aid in the reception and rematerialization sequence of an in-garrisoned transporter system.
The cylindrical pattern enhancers were typically one meter in height from the surface upon which they rested to their apex. They were composed of four distinct sections, from bottom to top: the trio of legs which were encased within the body of the equipment while not in use, the highly-polished silver-colored main body encasing the primary portion of the actual equipment, the black control cuff upon which controls for specific manipulation of the enhancer were set, and the sensor array contained within the clear, roughly conical top. The casing of the pattern enhancers contained sophisticated and relatively powerful localized sensors as well as powerful and adaptive communication equipment. However, in polarized ionization fields, pattern enhancers do not achieve the desired effect. (DS9: "Heart of Stone")
Typically, the use of a pattern enhancer was dictated by the inability of a transporter chief to acquire a solid transporter lock on the intended subjects at a location not equipped with equitable transporter technology. This inability could be a result of transporter jamming, natural interference, or any other phenomenon that disrupted normal sensor operation. When unable to achieve this requisite lock, pattern enhancers were used to define, scan, and relay information about a small, localized area through varying types of interference to the recipient transporter system. This highly specified and powerful communication to the transporter system allowed it to make a better analytical decision regarding the matter specified for transport as well as location information relative to known markers.
The inclusion of pattern enhancers in an away team's equipment complement was usually left to the discretion of the team commander. However that decision was influenced, when pattern enhancers were used, their operating procedure was very standardized to prevent problematic operation while in a chaotic situation. Pattern enhancers could be used either as a group of three or singularly. (VOY: "Dark Frontier") Used as a trio, the enhancers were set up in an equilateral triangular formation, roughly one to ten meters apart. First the legs were extended by means of a switch or lever on the main body of the device; these allowed for steady placement regardless of terrain. Second, the conical top and the attached control cuff of the device were rotated approximately 70-90° clockwise; once the top was lit, the enhancer was active. Once activated, all pattern enhancers immediately began sensor data transmission of whatever was contained within the confines of the trio of deployed enhancers.
Despite their obvious complexity and value, unless the conditions which necessitated the enhancers use in the first place was expected to dissipate or be negated, the enhancers were remained in place upon successful transport.
On previous versions of the Federation pattern enhancer, once all three were activated they would attach between the group a vibrant blue, permeable strand of energy; however by 2375 this feature had been eliminated for reasons unknown.
In 2263 of the alternate reality, Montgomery Scott came up with the idea of modifying pulse beacons from the USS Franklin to act as pattern enhancers to enable an away team to beam the trapped crew of the USS Enterprise out of Krall's base. These makeshift pattern enhancers successfully enabled Scott and Pavel Chekov to beam the Enterprise crewmembers, twenty at a time, to the Franklin. (Star Trek Beyond)