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We are using precise Doppler measurements to detect the presence of extra-solar planetary systems. We desire to achieve radial velocity measurements precise to $\sim$10 $m~s^{-1}$ over a time-scale of decades. We utilize the Hamilton echelle spectrograph at Lick observatory to gather spectra from 5000 to 6200 \AA$~$ of 80 F, G, K, and M type stars. A shift of 0.01 pixel corresponds to 25 $m~s^{-1}$. Correspondingly, 1\% changes in the spectrograph instrumental profile (IP) induce false Doppler shifts of $\sim$25 $m~s^{-1}$. Such tiny changes in the IP are well known to result from changes in (1) the illumination of spectrograph optics, (2) the structure of the optical components (thermal or mechanical effects), (3) non-uniform filling of the slit. We determine the IP for each CCD spectrum by placing an absorption cell of gaseous iodine at the slit of the spectograph. Starlight passes through the cell yielding a composite spectrum of stellar and iodine lines, from which the iodine portion is later extracted by dividing out the stellar spectrum. The IP is deconvolved from this iodine spectrum by comparison with a high-quality FTS spectrum of iodine having high resolution. This deconvolution is performed on a grid of sub-pixels, using non-linear least squares.
To better understand the effects that spectrograph changes have on the IP, and to fine tune our software, we ran tests using day-sky spectra, in which we physically changed some parameters of the spectograph such as slit width, focus, and optical illumination. Our current software accomodates the effects of these changes in IP, and at this time yields Doppler errors of $\sim$10 $m~s^{-1}$. We intend to improve this by a factor of two in the near future.
