A near-infrared spectrometer optimized for an adaptive optics system

An optical design for a compact near-infrared (0.8-2.5 mu m) spectrometer is presented, optimized for use with an adaptive optics system on a 4-m class telescope. The various observing modes of the design accommodate a large fraction of the spectroscopic observations desired for this region of the spectrum. The design does not contain any radical optical concepts, but demonstrates that a small instrument without exotic components is well suited to the application. While designed specifically for the NAOMI adaptive optics system on the William Herschel 4.2-m telescope, the basic concepts used - a slow/small-diameter beam allowing a small cryostat volume, single-element off-axis focusing mirrors, and a small collection of cross-dispersed spectroscopic modes selected to provide complete wavelength coverage without exchanging gratings in and out of the cryostat - are valid for other telescope/adaptive optics systems. Most of these advantages are not available for dual-purpose spectrometers designed to accommodate both uncorrected and corrected images. Two issues critical to infrared spectroscopy with adaptive optics are investigated in some detail. The first is the relation between spectral resolving power and system sensitivity. We arrive at a range of optimum resolutions to be used even with astronomical targets that require low resolution. We also show that adaptive optics do not provide substantial gains iii point-source sensitivity where the sky emission is dominated by OH- lines, the contributing factors including the adaptive optics system throughput, less than ideal Strehl ratios, and losses associated with real optical systems operating at the diffraction limit. The second issue critical to spectroscopy with adaptive optics is the light losses resulting from slit diffraction. We present plots showing the relation between slit size, the size of the optical elements downstream of the slit, and the vignetting associated with both. Performance estimates are presented for the design. The combined system sensitivity compares favourably with a similar spectrometer mounted on the Hubble Space Telescope.