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Particle analysis was a scientific procedure that reduced its subject to its constituent atoms.
The Tesh leader Jabel submitted Leela for particle analysis in the hope this would provided the answer to how the Sevateem were able to control the barriers on their planet. Declaring him not to be the Lord of Time, Jabel had the Fourth Doctor submitted for analysis too.
The Doctor used a mirror to reflect some of the analyser's power back on itself, destroying it and freeing them both. (TV: The Face of Evil)