Comprehensive Measurements of the Volume-phase Holographic Gratings for the Dark Energy Spectroscopic Instrument

The Dark Energy Spectroscopic Instrument (DESI) is a Stage IV ground-based dark energy experiment that will be employed on the Mayall 4 m Telescope to study the expansion history of the universe. In the era of massively multiplexed fiber-fed spectrographs, DESI will push the boundaries of fiber spectroscopy with a design capable of taking 5000 simultaneous spectra over 360 to 980 nm. The instrument utilizes a suite of three-channel spectrographs, where volume-phase holographic (VPH) gratings provide dispersions. Thirty-six VPH gratings were produced and their performances were evaluated at the Lawrence Berkeley National Laboratory. We present the design and the evaluation tests for the production run of the VPH gratings, verifying the incidence angle, area-weighted efficiency, and wavefront errors (WFEs). We also present the specialized test set-up developed on-site to assess the grating performances. Measurements of the VPH gratings show high consistency in area-weighted efficiency to within an rms of 2% for the red and near-infrared and 6.2% for the blue gratings. Measured WFEs also showed high consistency per bandpass. Comprehensive evaluations show that the VPH gratings meet DESI performance requirements and have been approved for integration