  The photon spectrum from free-electron laser (FEL) light sources offers
valuable information in time-resolved experiments and machine optimization in
the spectral and temporal domains. We have developed a compact single-shot
photon spectrometer to diagnose soft X-ray spectra. The spectrometer consists
of an array of off-axis Fresnel zone plates (FZP) that act as
transmission-imaging gratings, a Ce-YAG scintillator, and a microscope
objective to image the scintillation target onto a two-dimensional imaging
detector. This spectrometer operates in an energy range which covers absorption
edges associated with several atomic constituents carbon, nitrogen, oxygen, and
neon. The spectrometer's performance is demonstrated at a repetition rate of
120 Hz, but our detection scheme can be easily extended to 200 kHz spectral
collection by employing a fast complementary metal oxide semiconductor (CMOS)
line-scan camera to detect the light from the scintillator. This compact photon
spectrometer provides an opportunity for monitoring the spectrum downstream of
an endstation in a limited space environment with subelectronvolt energy
resolution.
