Halliday & Matthiessen (2014: 330):
This also involves prepositional phrases functioning as participants; but here there is no alternation between prepositional phrase and nominal group. Instead, the preposition is closely bonded with a verb, so that it is functioning as part of the Process, as with turn into; similarly look at the sky consists of Process look at + Phenomenon the sky. There is no simple diagnostic criterion for deciding every instance; but a useful pointer is provided by the thematic structure, which gives an indication of how the clause is organised as a representation of the process.
To be clear, it is not the prepositional phrase that functions as participant, but the nominal group that serves as the Range of the prepositional phrase.
Process: mental: perception