From my own experience I can confirm the usefulness of the fiber shaking. I noticed it when recording flats, the S/N increased from 250 to 350, obtained by measuring the noise resulting from the division of two flat spectra (dividing out fringes and blaze function not related to the fiber). For star spectra the difference was not noticeable at a S/N of about 100 (weaker targets and poor grating efficiency. The moving of the fiber was manual, a slow motion (about 1 Hz).
In case I would need it on a regular basis, I would build a double pendulum attached to a rotating excenter, which gives a chaotic motion, favorable for suppression of mode noise.
Another thing besides fiber noise is the effect of fiber illumination on radial velocity measurements. A good description of the effect is given here:
http://arxiv.org/pdf/1001.0794While the fiber scrambles well the near field, the far field (as described by angle of incidence) is much less scrambled by the fiber. Changes in f-ratio of the illumination (e.g. caused by defocusing the telescope on the fiber) have a measurable effect on the line position. The cause is coma aberration of the spectrograph objective. In my setup this resulted in systematic errors of up to 1km/sec! with a not very good fiber, for a Canon 85mm f1.8 lens, the same as used in the Eshel . I found out about it by comparing the FeAr calibration with a terrestrial H2O line calibration around H-alpha. In order to reduce this effect it is highly recommended for precise radial velocity mesurements to first pay attention how the signal and calibration light is fed into the fiber and second use an optical fiber scrambler, which changes the optical near field and far field.
A description of a fiber scrambler as used with ELODIE is given by Baranne:
http://adsabs.harvard.edu/abs/1999ASPC..185....1BIt is important to note that this second effect (far field illumination of the fiber) cannot be removed by shaking the fiber! Of course the introduction of additional optics introduces additional light loss, which decreases S/N. It has to be tested experimentally if the added precision outweighs the loss in S/N.
A challenge for achieving a 10m/sec precision!
Martin