Determining Spectrometer Instrumental Profiles Using FTS Reference Spectra

We describe a new technique for determining the instrumental profile (IP) of an astronomical spectrometer. A known instrinsic spectrum of a reference source is convoluted with a parameterized IP and then compared to a spectrum obtained with the spectrometer to be characterized. Nonlinear least-squares (NLLS) optimization is used to solve for the analytic IP that best reproduces the observed spectrum. This technique is most effective for characterizing the central portion of the IP, out to 1% of the peak. IP recovery is demonstrated using both the Sun and an I2 absorption cell as reference spectra. We also describe a second technique employing singular value decomposition (SVD) to recover an approximate IP by directly inverting a discretized convolution. This second technique is less contstrained and therefore gives poorer results than NLLS, but it is useful when the form of the IP is unknown. Using the NLLS technique, we demonstrate by example that the IP is a function of position in the format of cross-dispersed echelle spectrometers. We also compare our results with laser and thorium emission line profiles. Finally, we present the IP for a range of positions in the format of the Hamilton echelle spectrograph at Lick Observatory and the HIRES echelle at the Keck 10-m telescope.