For fiber-fed spectrographs with a stable external wavelength source, scrambling properties of optical fibers and, homogeneity and stability of the instrument illumination are important for the accuracy of radial-velocimetry. Optical cylindric fibers are known to have good azimuthal scrambling. In contrast, the radial one is not perfect. In order to improve the scrambling ability of the fiber and to stabilize the illumination, optical double scrambler are usually coupled to the fibers. Despite that, our experience on SOPHIE and HARPS has lead to identified remaining radial-velocity limitations due to the non-uniform illumination of the spectrograph. We conducted tests on SOPHIE with telescope vignetting, seeing variation and centering errors on the fiber entrance. We simulated the light path through the instrument in order to explain the radial velocity variation obtained with our tests. We then identified the illumination stability and uniformity has a critical point for the extremely high-precision radial velocity instruments (ESPRESSO@VLT, CODEX@E-ELT). Tests on square and octagonal section fibers are now under development and SOPHIE will be used as a bench test to validate these new feed optics.
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