The new MuSiCoS polarimeter is inspired by the prototype instrument built by Semel et al. (1993). It is designed to be mounted at the Cassegrain focus of a 2 m telescope through an interface module which contains all of the usual spectroscopic calibration (halogen and thorium/argon lamps) and guiding facilities.

The optical layout of the instrument is shown in Fig. 1. A detailed description of the different optical components, as well as of the mechanical and electronic design is given in the following paragraphs. All optical surfaces are coated with multilayer antireflection films ensuring a reflectance everywhere lower than 1.5% (and lower than 1% in average) throughout the whole spectral domain (390 to 870 nm).

The stellar light is collected through a 2 $^{\prime\prime}$ circular aperture placed at the Cassegrain focus, which is followed by a short focal length doublet that converts the beam to a speed of f/25. In the particular case of the TBL (which already has an f/25 Cassegrain beam), this aperture is 500 $\mu$ m in diameter and no attendant doublet is used. For an hypothetic f/8 Cassegrain beam for instance, a 160 $\mu$ m aperture should be used, and a Melles Griot achromatic doublet LAO001 (with 10 mm focal length) located 4.44 mm behind would achieve the requested beam speed conversion.

2.2 Polarisers

Two sheet polarisers (installed in a rotatable wheel with three positions) can be inserted into the beam (slots 1 and 3 correspond to the circular and linear polariser respectively, while slot 2 is left empty). The linear polariser is oriented at a fixed azimuth in the polarimeter frame, defining a reference azimuth throughout the whole instrument.

2.3 Wave plates

Two wave plates (installed in a second rotatable wheel with three positions) can also be inserted into the beam (slots 1 and 3 correspond to the quarter-wave plate and half-wave plate respectively, while slot 2 is left empty). The half-wave plate can be rotated to angles of 0 $^\circ$ , 22.5 $^\circ$ , 45 $^\circ$ and 67.5 $^\circ$ with respect to the reference azimuth (see Sect. 2.2), while the quarter-wave plate can be oriented at angles of -45 $^\circ$ , 0 $^\circ$ and 45 $^\circ$ . Note that the beam aperture (f/25) is sufficiently small that the associated error in wave plate retardance can be neglected.

The superachromatic wave plates built by the German company Bernard Halle Nachfl. (made of three pairs of quartz and MgF₂ plates cemented between parallel plates of fused silica, following the design of Serkowski 1974) are the only commercial crystalline retarders with close to nominal retardance and fast axis direction (within about 1% and 4% for the half-wave plate and quarter-wave plate respectively) throughout the whole spectral domain of interest (390 to 870 nm). However, we discovered that these wave plates introduce large ripples both in polarisation and intensity spectra (with respective peak-to-peak amplitudes of about 1% and 2% respectively), most likely due to interference within the multiple cement layers of the retarders. This is very likely a general problem of all Halle superachromatic retarders (rather than a specific defect of ours as we first thought), since all similar plates that we know of (used in the polarimetric modules at the Anglo-Australian Telescope and William Herschell Telescope) also generate such ripple (e.g. Harries & Howarth 1996). The analytical modeling proposed by Harries & Howarth (1996) to correct the spectropolarimetric data from this ripple, although successful at a spectral resolution of 5000, turns out to be insufficient at spectral resolution of 35000 given the very complex shape and multiperiodic behaviour of the fringe pattern (see Fig. 2). Moreover, this ripple is found to vary significantly in position and shape on a timescale of only a few hours (probably with dome temperature); removing this effect using spectra of a bright unpolarised standard is therefore not a viable solution either.

We therefore decided (as a temporary solution, hoping that the Halle wave plate problem is correctable) to use an achromatic retarder built by the French company Optique Jean Fichou (made of one quartz and one MgF₂ crystal plate cemented together with axes at right angles) as a quarter-wave plate, whose deviation from nominal retardance is lower than about 3% in a more restricted spectral domain (i.e. 400 to 700 nm in our particular case). Observations of bright unpolarised standard stars indicate that any ripple generated by this retarder is smaller than 0.05% peak-to-peak, i.e. more than 20 times weaker than those induced by Halle retarder. Instead of using a half-wave plate, we rotate the polarimeter as a whole (by angles of 0 $^\circ$ , 45 $^\circ$ , 90 $^\circ$ and 135 $^\circ$ ); although slightly slower, less convenient (as automatic guiding needs to be retuned after each instrument rotation) and less accurate (see Sect. 3.1), this procedure turns out to be more achromatic than the original solution involving the Halle wave plate. Note that circular spectropolarimetry is only accurate within 400-700 nm in this temporary solution, and therefore requires a special "intermediate'' setup of the MuSiCoS spectrograph between the two nominal "blue'' and "red'' configurations (Baudrand & Böhm 1992). In this new setup, we can cover for instance the whole 450 - 660 nm range in a single exposure.

$\begin{figure} \flushleft{ \psfig {file=pol_fig2.ps,angle=270,height=7cm} }\end{figure}$

Figure 2: Polarisation ripple in Stokes V spectra generated by the Halle superachromatic quarter-wave plate

2.4 Beamsplitter

Once the stellar polarisation of interest is converted (by means of retarders or polarimeter rotations) into a reference linear polarisation (with an electric field oriented along the reference azimuth defined in Sect. 2.2), we use a combination of birefringent crystals to split the stellar light into two beams corresponding respectively to polarisation along and perpendicular to the reference azimuth.

This beamsplitter (see Fig. 3) is made of two crossed calcite blocks (Savart plate). The advantage of such a design with respect to a conventional single block is that both beams emerging from the analyser are shifted by the same amount with respect to the incident beam. In particular, the chromatic variation of this splitting equally affects both beams, whose symmetry is therefore enhanced compared to the single block solution. The thickness of each calcite block (3.84 mm) ensures that both emerging beams are separated by $0.60\pm0.03$ mm and shifted by $0.42\pm0.02$ mm each with respect to the incident beam, throughout the whole spectral domain (390 to 870 nm). This shift corresponds to the minimum possible separation between the two fibres in the image plane.

$\begin{figure} \includegraphics [angle=90,height=7.5cm]{pol_fig3.eps}\end{figure}$

Figure 3: Beamsplitter of the MuSiCoS polarimeter. The arrows depict the direction of the optical axes in each calcite block, while the hatch marks represent the direction of the electric field vibration of both ordinary and extraordinary rays. The two crystals and plates are glued together with an epoxy cement

Note that a Savart plate is not free of astigmatism (e.g. Semel 1987). However, the large focal reduction the beam is subject to after the polarisation analysis (see Sect. 2.5) ensures that both tangential and sagittal images always fall within 3.2 $\mu$ m of the double fibre focal plane throughout the whole spectral range, implying that astigmatism can be easily neglected.

2.5 Focal reducer

We then need a focal reducer to speed the beam up to an aperture of f/2.5, at which fibres behave satisfactorily.

Given the large desired magnification factor and the space into which all of the above optical components and mountings must be placed (see Fig. 1), a dedicated focal reducer had to be specially designed to minimise longitudinal chromatic aberrations. The selected design (see Fig. 4) includes three single lenses and ensures that the multicolour spot diagram is smaller than 5 $\mu$ m up to an object off-axis distance of 670 $\mu$ m (corresponding to the beamsplitter shift increased by the radius of the entrance aperture at a beam speed of f/25), only slightly larger than the diffraction limit.

$\begin{figure} { \psfig {file=pol_fig4.ps} }\end{figure}$

Figure 4: Focal reducer of the MuSiCoS polarimeter. The Cassegrain beam comes from the top and the horizontal line at the bottom depicts the focal plane of the double fibre. R1 and R2 denote the curvature radii of the upper and lower surface of each lens respectively

This focal reducer and its mounting were built and assembled by Soptel Technologies in France.

$\begin{figure} \psfig {file=pol_fig5.eps,angle=270,height=6cm}\end{figure}$

Figure 5: Internal transmission of H-treated low-OH Ceram-Optec Optran fibres for 50/60 $\mu$ m (full line) and 200/220 $\mu$ m (dashed line) core/cladding diameters. The dotted line depicts the theoretical Rayleigh dispersion limit. All these curves correspond to 25 m fibres

2.6 Optical fibres

Two optical fibres with core/cladding diameters of 50/60 $\mu$ m (mounted side by side in a special connector) finally collect the two orthogonally polarised beams and send them to the MuSiCoS spectrograph.

The optical fibre we selected is the prototype H-treated low-OH Ceram-Optec Optran fibre whose transmission is optimised in the 350-1100 nm wavelength band. Measurements at the European Southern Observatory (Garching laboratories) and Observatoire de Meudon have confirmed that the transmission of such fibres is very close to the Rayleigh limit all the way from 350 to 1000 nm for fibre core/cladding diameters of 200/220 $\mu$ m (see Fig. 5). The 50/60 $\mu$ m fibre we purchased for our purpose is just as good up to 500 nm, but gets progressively worse at red and infrared wavelengths with an internal transmission as low as 50% at 1 $\mu$ m (for a 25 m fibre). According to Ceram-Optec engineers, this problem is very likely due to small fibre stresses induced by the acrylate jacket. Despite all efforts to date (in particular, attempting to employ a more flexible epoxy jacket), Ceram-Optec has not yet succeeded in producing a better fibre with the same core/cladding diameters. In the meantime, we have been using this preliminary fibre whose transmission turns out to be reasonably good in average in the restricted wavelength domain imposed by the Fichou quarter-wave plate (400-700 nm, see Sect. 2.3).

2.7 Mechanical and electronic design

The mechanical structure of the polarimeter has been made as rigid as possible to ensure that the entrance hole and double fibre remain optically aligned for all positions of the polarimeter and the telescope. This is indeed an important constraint for the overall instrument transmission, as any relative shift between the entrance aperture and fibre can generate a significant light loss. This loss reaches for instance 13% for a relative aperture/fibre shift of 10% of the aperture/fibre size (i.e. 50 $\mu$ m at the TBL entrance aperture or 5 $\mu$ m at fibre level). Therefore, the two fast beam portions of the instrument (entrance aperture/attendant doublet and focal reducer/fibre) have each been designed as two separate tight compact blocks. Both are fixed onto a larger parallelepiped structure (on the upper and lower sides, respectively) which supports the two rotatable wheels (holding the polarisers and retarders) and the beamsplitter. This structure is rigid enough to ensure that differential deformation between the upper and lower sides remains smaller than 10 $\mu$ m in all directions and for all telescope positions.

Two stepper motors (mounted on the main structure) are used to rotate the two wheels, while a third one (fixed on the wave plate wheel) rotates (through a gear chain) the two retarders simultaneously. Each motor is associated with a proximity detector defining a reference azimuth for the motor axis. Several solutions are usually available to check that no step is skipped during the rotation. The most obvious one, which consists in using potentiometers to measure the angular position of each rotatable unit, could not be applied here for lack of space. We decided instead to drill several notches in the circular edge of each of the four rotatable units (two wheels and two plate holders), one for each position at which each unit can be positioned (i.e. three for the polariser wheel, three for the retarder wheel, three for the quarter-wave plate holder and four for the half-wave plate holder); a small wheel (maintained with a spring onto the circular edge of each rotating unit) then indicates (through a microswitch) whether it is embedded into a notch, i.e. whether the unit has reached the correct angular position. Note that, in this second solution, the fine angular unit positioning is actually obtained through the wheel/notch interactions (if we allow enough gear backlash) rather than with the stepper motors themselves (only used here to drive units to an approximate azimuth).

The three stepper motors (purchased from the Swiss company ESCAP) are remote controlled through a commercial MCU11-STD microcontroller card (built by the French company EPILOG and including a 68HC11A1 microcontroller, a 32 kb EEPROM loaded with dedicated software developed at Observatoire Midi-Pyrénées, a 24 kb RAM and an input/output port controller) as well as an interface card (developed at Observatoire Midi-Pyrénées and involving in particular L297 and L298N SGS-Thomson clock and power drivers). Thirteen two-character commands (sent from a terminal to the microcontroller through a serial port) enable one to obtain all possible instrument configurations (p1 and p3 for the circular and linear polarisers respectively, p2 for no polariser; l1 and l3 for the quarter and half-wave plates respectively, l2 for no wave plate; q1, q2 and q3 for quarter-wave plate azimuths -45 $^\circ$ , 0 $^\circ$ and 45 $^\circ$ respectively; d1, d2, d3 and d4 for half-wave plate azimuths 0 $^\circ$ , 22.5 $^\circ$ , 45 $^\circ$ and 67.5 $^\circ$ respectively). For each command, the corresponding stepper motor first rotates back to its axis reference azimuth (see previous paragraph), switches direction and does a preset number of steps. Once the stepper motor has stopped, the microcontroller then automatically checks (through the corresponding microswitch) whether the instrument has safely reached the requested position. An error message is sent to the user if any problem is encountered (e.g. wrong command, no microswitch contact).

2.8 Tuning procedure

Tuning the instrument consists in aligning the axes of the various birefringent optical components, then perfectly aligning the entrance aperture of the polarimeter with the two optical fibres. This is achieved with the four following steps.

We first mount the instrument on an optical bench, send light through the instrument aperture, remove the fibre and look at the double image with a microscope. We then set the linear polariser of the polarimeter inside the beam leaving the two retarders out (p3 l2 configuration). We then manually rotate the beamsplitter to achieve the best possible extinction of one beam, i.e. to align its optical axes with those of the linear polariser.

In a second step, we insert the half-wave plate in the beam and set its holder to an azimuth of 0 $^\circ$ (l3 d1 configuration). We then rotate the plate manually within its holder to restore the beam extinction obtained in the previous step. We repeat the same operation with the quarter-wave plate in the beam, with its holder set to an azimuth of 0 $^\circ$ (l1 q2 configuration).

In a third step, we mount the double fibre back in position onto the polarimeter and send light through it from its other end. Both polarisers and retarders are removed from the beam (p2 l2 configuration). We then dismount the entrance aperture/attendant doublet block from the main polarimeter structure and observe with the microscope the image of the double fibre duplicated by the beamsplitter. Superimposing two of the four images by rotating the fibre/focal reducer block with respect to the main polarimeter structure ensures that the two fibres are aligned onto the analyser duplication direction.

The last step consists in adjusting very precisely the entrance aperture/attendant doublet block onto the two overlapping central images of the double fibre, in both lateral and longitudinal directions. In a final check, we verify that inserting the polarisers and retarders into the beam or rotating the wave plates generate no apparent beam deviation.

2 Description of the instrument