with additional tabulated parameters that describe the designs of the grisms. The grisms can be seen schematically in Fig. 8 along with an example ray-trace of the spectrograph. The grisms have a square physical footprint with 150 mm sides. The grating layer clear aperture is circu- lar with an over-sized 138 mm diameter as compared to the 125 mm diameter collimated beam to relax the translational position tolerance of the grism within the instrument. We have performed a detailed Monte Carlo analysis of the grism tolerance for each channel including the expected fabrication error, assembly error, and Table 2. LRS2 VPH Grism Properties UV Arm Orange Arm Red Arm Far Red Arm Units (Comments) min , max 370, 470 460, 700 650, 847 823, 1050 nm Dispersion 0.48 1.16 0.95 1.10 ˚ A px 1 (1 ⇥ 1 binning) Spectral Resolution 2.20 5.09 4.24 4.87 ˚ A (FWHM) Resolving Power R 1910 1140 1760 1920 (R = / ) Fringe Density 1770 776 923 797 lines mm 1 Bragg Wavelength 400 590 750 940 nm Angle of Incidence 12.04 6.57 11.17 12.28 (on VPH Layer) Fringe Tilt 1.31 2.00 2.06 2.09 (see Fig. 8) Assembly Physical Tilt ✓ grism 15.3 14.3 15.3 15.3 (see Fig. 8) Prism Wedge Angle 35.5 3.5 30.8 37.4 (see Fig. 8) DCG Optical Thickness 3.5 6.0 4.9 7.5 µm DCG Index Modulation 0.060 0.048 0.074 0.061 (assumed sinusoidal) LRS2-B-UV (“UV” channel) 370 ≤ λ (nm) ≤ 470 LRS2-B-OR (“Orange” channel) 460 ≤ λ (nm) ≤ 700 LRS2-R-NR (“Near Red” channel) 650 ≤ λ (nm) ≤ 842 LRS2-R-FR (“Far Red” channel) 818 ≤ λ (nm) ≤ 1050