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tokens: especially when high consistency is required for large-scale surveys like DESI. Further discussion of the VPH grating physics is given by Barden et al. ( 1998 ). 2.1. Requirements and Specifications The DESI VPH gratings have physical dimensions of 180 × 160 mm 2 × 16 mm (thickness) with varying clear aperture areas. The incident field of view (FOV) of the grating is ±75 from the grating central axis, illustrated in Figure 2 , and is illuminated by a collimated beam of various pupil sizes. All DESI VPH gratings are optimized such that the +1 diffracted order efficiency is maximized. There were no specifications on off-axis FOV efficiency. The performance requirements and specifications for the DESI VPH gratings are detailed in Table 1 . These are driven by both science requirements and optical design limitations. Efficiency requirements listed are averaged over polarization and over the clear aperture. Since the actual measurements of the diffraction efficiency will include transmission losses from the VPH gelatin, glue, antireflection (AR) coating, and the substrate glasses, the “adjusted” efficiencies are used to compare results. A total of 36 full-size gratings (12 per channel) were produced by Kaiser Optical Systems Inc. (KOSI). A preliminary set of measurements was conducted by KOSI on a few points across the clear aperture (Figure 4 ), albeit in a less comprehensive manner compared to our measurements presented here. Based on our measurements, the top performing gratings in each channel with the best efficiencies are chosen for DESI integration. Table 1 DESI VPH Grating Specifications and Requirements for Unpolarized Incidence; Wavefront Specifications at 632 nm Notes. a Incidence angles are to be within an allowed installation range of ±10 from the specified α 0 (Edelstein et al. 2018 ). b Including glue and gelatin losses, not including AR coating and glass transmission losses. c Adjusted for glue, gelatin, AR coating, and glass transmission losses. We compare measurements to these values. 2.2. Preliminary Evaluation of Test Gratings Prior to the full production of the DESI VPH gratings, preliminary performance studies were conducted on full-size test VPH gratings for each bandpass, also produced by KOSI. Measurements were made in all three bandpasss to verify that the gratings met desired design specifications and also to prototype a set of reliable and efficient test procedures discussed in this paper. Efficiency performance at the specified incidence angle and the peak-to-valley (P-V) WFE for power and irregularity met the requirements (DESI Collaboration et al. 2016b ). Performance results of the test gratings were used to constrain the properties of the final DESI VPH gratings discussed in this paper. 3. Measurement Rig We built an automated optical test bench to measure the +1 order diffraction efficiency of the gratings. The design was motivated by the desire to conduct a comprehensive yet efficient performance