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The authors have identified an important source of line broadening in transition edge sensors used as optical photon detectors. It arises through the loss of high energy phonons into the substrate during the initial photon energy downconversion stage. Because of the relatively small number of phonons involved, the loss rate is subjected to large fluctuations due to the statistical nature of the energy exchange processes. They show that the resulting noise may represent a significant limitation to the resolving power of current detectors.