GRAVITY is a 2nd generation Very Large Telescope Interferometer (VLTI) operated in the astronomical K-band. In the Beam Combiner Instrument (BCI) four Fiber Couplers (FC) will feed the light coming from each telescope into two fibers, a reference channel for the fringe tracking spectrometer (FT) and a science channel for the science spectrometer (SC). The differential Optical Path Difference (dOPD) between the two channels will be corrected using a novel metrology concept. The metrology laser will keep control of the dOPD of the two channels. It is injected into the spectrometers and detected at the telescope level. Piezo-actuated fiber stretchers correct the dOPD accordingly. Fiber-fed Integrated Optics (IO) combine coherently the light of all six baselines and feed both spectrometers. Assisted by Infrared Wavefront Sensors (IWS) at each Unit Telescope (UT) and correcting the path difference between the channels with an accuracy of up to 5 nm, GRAVITY will push the limits of astrometrical accuracy to the order of 10 μas and provide phase-referenced interferometric imaging with a resolution of 4 mas. The University of Cologne developed, constructed and tested both spectrometers of the camera system. Both units are designed for the near infrared (1.95 - 2.45 μm) and are operated in a cryogenic environment. The Fringe Tracker is optimized for highest transmission with fixed spectral resolution (R = 22) realized by a double-prism. The Science spectrometer is more diverse and allows to choose from three different spectral resolutions (R = [22, 500, 4000]), where the lowest resolution is achieved with a prism and the higher resolutions are realized with grisms. A Wollaston prism in each spectrometer allows for polarimetric splitting of the light. The goal for the spectrometers is to concentrate at least 90% of the flux in 2 × 2 pixel (36 × 36 μm~2) for the Science channel and in 1 pixel (24 × 24 μm) in the Fringe Tracking channel. In Section 1, we present the arrangement, direction of spectral dispersion and shift of polarization channels for both spectrometers, and the curvature of the spectra in the science spectrometer. In Section 2 we determine the best focus position of the detectors. The overall contrast of images at different positions of the detector stage is computed with the standard deviation of pixel values in the spectra containing region. In Section 3 we analyze high dynamic range images for each spectrometer and resolution obtained at the afore determined best focus positions. We deduce the ensquared energy from the FWHM of Gaussian fits perpendicular to the spectra.
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