Tarquin and his amplifier

The telepathic amplifier was a multifaceted object which helped Tarquin, who kept it on his desk, extend the range of his telepathy. A humanoid used the tool by placing a hand atop the object and the person closing his or her eyes. The telepathic amplifier glowed internally while being used.

When Tarquin was exiled to a particular planet in the Delphic Expanse because his species treated telepaths as outcasts, the telepathic amplifier was passed down from his family to Tarquin himself.

In 2153, the telepathic amplifier enabled Tarquin to find Human Starfleet Ensign Hoshi Sato, who was meanwhile serving on board Enterprise NX-01. Tarquin believed his discovery of her wouldn't have been possible without the telepathic amplifier. During a visit to his planet, she once tried to use the tool herself, Tarquin showing her how he used it, though the resultant telepathic stimuli proved overwhelming for her. Later, when Tarquin proved extremely reluctant to let her go, Sato threatened to destroy the telepathic amplifier, until he finally did release her. (ENT: "Exile")

This tool is not named on screen; its designation as a "telepathic amplifier" comes from the final draft script of "Exile". In that teleplay, it was described as "a glowing, multi-colored object".
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