  Spectrographs nominally contain a degree of quasi-static optical aberrations
resulting from the quality of manufactured component surfaces, imperfect
alignment, design residuals, thermal effects, and other other associated
phenomena involved in the design and construction process. Aberrations that
change over time can mimic the line centroid motion of a Doppler shift,
introducing radial velocity (RV) uncertainty that increases time-series
variability. Even when instrument drifts are tracked using a precise wavelength
calibration source, barycentric motion of the Earth leads to a wavelength shift
of stellar light causing a translation of the spectrum across the focal plane
array by many pixels. The wavelength shift allows absorption lines to
experience different optical propagation paths and aberrations over observing
epochs. We use physical optics propagation simulations to study the impact of
aberrations on precise Doppler measurements made by diffraction-limited,
high-resolution spectrographs. We quantify the uncertainties that
cross-correlation techniques introduce in the presence of aberrations and
barycentric RV shifts. We find that aberrations which shift the PSF
photo-center in the dispersion direction, in particular primary horizontal coma
and trefoil, are the most concerning. To maintain aberration-induced RV errors
less than 10 cm/s, phase errors for these particular aberrations must be held
well below 0.05 waves at the instrument operating wavelength. Our simulations
further show that wavelength calibration only partially compensates for
instrumental drifts, owing to a behavioral difference between how
cross-correlation techniques handle aberrations between starlight versus
calibration light. Identifying subtle physical effects that influence RV errors
will help ensure that diffraction-limited planet-finding spectrographs are able
to reach their full scientific potential.
