  We have developed a photon detection system for muonic X-ray spectroscopy.
The detector system consists of high-purity germanium detectors with BGO
Compton suppressors. The signals from the detectors are readout with a digital
acquisition system. The absolute energy accuracy, energy and timing
resolutions, photo-peak efficiency, the performance of the Compton suppressor,
and high count rate durability are studied with standard $\gamma$-ray sources
and in-beam experiment using $^{27}\mathrm{Al}(p, \gamma){}^{28}\mathrm{Si}$
resonance reaction. The detection system was demonstrated at Paul Scherrer
Institute. A calibration method for a photon detector at a muon facility using
muonic X-rays of $^{197}$Au and $^{209}$Bi is proposed.
