2 Scrambling properties of fiber

A review of fibers in astronomy has been given by Heacox & Connes (1992). Fiber-fed spectrographs use multi-mode (MM) step-index fibers with core sizes typically in the 50- to 500-$\mu$m range. One property of fibers, discussed by Ramsey (1988) and Barden (1995), is focal ratio degradation (FRD). A fiber tends to increase the divergence (or "speed'') of the beam it carries. This causes either a loss of light if the exiting cone of light overfills the spectrograph collimator, or a loss of resolution if the collimator is replaced with one matching the faster focal ratio. Larger-core fibers do appear to have better FRD characteristics than smaller-core ones. Faster input focal ratios are better preserved than slower ones. One other significant characteristic of fiber optics is their ability to scramble the input image. The geometry of cylindrical fibers introduces two dimensions of scrambling, azimuthal and radial. Both theory (Heacox 1987) and experiments (Hunter & Ramsey 1992) suggest that step index MM fibers provide a high degree of azimuthal scrambling but an incomplete radial scrambling. Image scrambling improves with an increase of the fiber FRD. If the input focal-ratio is fast enough to give little FRD (and this is the case in fiber-fed spectrographs), then the input image will be poorly scrambled, and the output beam preserves some memory of the input beam shape and position.

Our laboratory tests on a 50 $\mu$m step index MM fiber, and also tests by Casse (1995) on a 300 $\mu$m fiber, both measure the photocenter of the near-field versus a known displacement of the input beam. We found independently that the motion of the output photocenter may be of the order of 100 times smaller than that of the input photocenter, with adequate beam and fiber parameters.

This imperfect scrambling is inadequate when the goal is 1 m/s precision. The near-field pattern of a fiber is defined as the brightness distribution across the output face of the fiber. In most cases a spectrograph images this output face directly onto the detector; then variations in illumination introduce small changes in pixels illumination which lead to radial velocity shifts. A higher-resolution spectrograph reduces these errors, because given image shifts on the pixels induce smaller wavelength shifts than in a lower-resolution spectrograph.

The far-field pattern is defined as the cross-section of the beam far from the output face. Far-field variations are projected onto the spectrograph collimator, and cause changes in grating illumination. Then, spectrograph aberrations and grating imperfections induce small varying RV shifts. To increase scrambling, one may incorporate a double-fiber scrambler (Brown 1990), in which a pair of fibers is coupled together using a pair of microlenses, separated by their common focal lengths. The fibers then see each other at infinity, causing the near- and far- fields to be interchanged. Brown et al. (1991) found that their double-scrambler eliminated temporal variations in grating illumination that were responsible for roughly 5 m/s RMS velocity noise in their spectrograph and increased the precision of radial-velocity observations by a factor of about 3 over a single fiber, to the expected shot-noise-limit. The same double scrambler was laboratory-tested by Hunter & Ramsey (1992). Their results show that intensity variations across the near- and far-field patterns due to both angular and positional changes in the input beam were reduced by a factor ranging from 2 to 10. Casse (1995) laboratory-tested a similar double-scrambler and found a scrambling gain of about 5 in the near-field pattern. The decreased radial-velocity noise provided by these double-scramblers is not without drawbacks: the main problem is low throughput. The transmission estimated both by Hunter & Ramsey (1992) and Casse (1995) is between 20 and 25%; Brown (1994) mentioned 66%. A somewhat different double-scrambler was incorporated in March 1997 at the input of the fiber-fed ELODIE spectrograph by D. Kohler. Its throughput is about 75% but the overall gain in radial-velocity precision deduced from our own observations is only about 1.5. According to Mayor and Queloz (private communication) the current long-term precision limit of ELODIE is now not due to the scrambler but related to the thermal and mechanical variations of the instrument. Probably their relative long exposures (greater than 10 minutes) averages the scrambler noise. In our case, with time exposure less or equal to 1 minute, we are not convinced that a double-scrambler is sufficient.

Another solution (proposed by Connes et al. 1996), will cancel "scrambler noise'' altogether. It makes use of a single-mode (SM) fiber which (unlike a MM fiber) acts as a perfect SM spatial filter: all cross-sections of the output beam are quasi-Gaussian and preserve no memory of the input beam geometry. Hence a SM fiber behaves as an ideal scrambler. It may be matched to the Airy pattern at the focus of a diffraction-limited telescope, irrespective of its diameter, with an efficiency of about 80%. On the ground, this solution is limited to a telescope pupil smaller than the "Fried diameter'' (roughly 12 cm in the visible for 1 arcsec seeing), or requires AO. Such systems are so far limited to the infrared. Altogether, while the association of an SM fiber and AO offers a definitive solution of our problem, it cannot be tried presently.