  We have designed a fiber scrambler as a prototype for the Keck HIRES
spectrograph, using double scrambling to stabilize illumination of the
spectrometer and a pupil slicer to increase spectral resolution to R = 70,000
with minimal slit losses. We find that the spectral line spread function (SLSF)
for the double scrambler observations is 18 times more stable than the SLSF for
comparable slit observations and 9 times more stable than the SLSF for a single
fiber scrambler that we tested in 2010. For the double scrambler test data, we
further reduced the radial velocity scatter from an average of 2.1 m/s to 1.5
m/s after adopting a median description of the stabilized SLSF in our Doppler
model. This demonstrates that inaccuracies in modeling the SLSF contribute to
the velocity RMS. Imperfect knowledge of the SLSF, rather than stellar jitter,
sets the precision floor for chromospherically quiet stars analyzed with the
iodine technique using Keck HIRES and other slit-fed spectrometers. It is
increasingly common practice for astronomers to scale stellar noise in
quadrature with formal errors such that their Keplerian model yields a
chi-squared fit of 1.0. When this is done, errors from inaccurate modeling of
the SLSF (and perhaps from other sources) are attributed to the star and the
floor of the stellar noise is overestimated.
