Optical Design of a Versatile FIRST High-resolution near-IR Spectrograph

We report the update optical design of a versatile FIRST high resolution near IR spectrograph, which is called Florida IR Silicon immersion grating spectromeTer (FIRST). This spectrograph uses cross-dispersed echelle design with white pupils and also takes advantage of the image slicing to increase the spectra resolution, while maintaining the instrument throughput. It is an extremely high dispersion R1.4 (blazed angle of 54.74 degrees) silicon immersion grating with a 49 mm diameter pupil is used as the main disperser at 1.4 mu m-1.8 mu m to produce R=72,000 while an R4 echelle with the same pupil diameter produces R=60,000 at 0.8 mu m-1.35 mu m. Two cryogenic Volume Phase Holographic (VPH) gratings are used as cross-dispersers to allow simultaneous wavelength coverage of 0.8 mu m-1.8 mu m. The butterfly mirrors and dichroic beamsplitters make a compact folding system to record these two wavelength bands with a 2kx2k H2RG array in a single exposure. By inserting a mirror before the grating disperser (the SIG and the echelle), this spectrograph becomes a very efficient integral field 3-D imaging spectrograph with R=2,000-4,000 at 0.8 mu m-1.8 mu m by coupling a 10x10 telescope fiber bundle with the spectrograph. Details about the optical design and performance are reported.