The crucial requirement for spectro-polarimetry with typical focal reducers is that the polarizing element should be as thin as possible to fit in the filter wheel, this implies that the Wollaston crystals should have a large birefringence.
As lateral chromatism is relatively little important in this mode,
convenient (and probably the cheapest) materials are therefore CaCO
and LiNbO
for visual and IR instruments, respectively.
The latter has 
and is transparent
from 5000 Å\
to beyond 4 
m while Calcite
has 
and is transparent from below 3000 Å
to about 2.0 
m (Oliva et al. 1996).
The entrance wedge can be most conveniently integrated in each Wollaston by cutting the entrance face of the first prism at a suitable angle (cf. Fig. 2 (click here)). A consequence of this choice is that the output images suffer by different lateral chromatism and the outer spectra are much more distorted than the inner one's (cf. Fig. 3 (click here)), but this can be easily taken into account during data reduction. Note that using separate quasi-achromatic wedges would give no practical advantage because the spectra are always distorted although symmetrical, i.e. the chromatism of the Wollaston cannot be corrected by the wedge.
Figure 3:
Simulated spectra using thin WeDoWo devices, the distortion of the dispersed
slit images is a consequence of the lateral chromatism of the wedges and
Wollastons. The Wollaston and wedge angles 
, 
(cf.
Fig. 2 (click here))
and the slit lengths are chosen adopting
15pt 
= 3.5 m, 
= 7.6 cm,
field-of-view = 
15pt 
= 3.5 m, 
= 2.2 cm,
field-of-view = 
for the visual and infrared instrument, respectively
The angles 
and 
required to create four
non-overlapping images of a slit of a given length are plotted
in Fig. 2 (click here) as a function of the projected slit length 
where 
(sky projected angles) is the slit length,
is the telescope diameter and 
is the diameter
of the pupil image. Using the parameters of Fig. 2 (click here) the
slit images are well spaced at all useful wavelengths, i.e.
and 
m for CaCO
and LiNbO
, respectively.
The four spectra are contained within the array if the sky projected
field of view of the detector is 
5 times the slit length
.
Representative examples of dispersed slit images produced by thin
WeDoWo devices coupled with grisms (cf. right panel of Fig. 1 (click here))
are displayed in Fig 3 (click here) where the strong lateral chromatism
of CaCO
at 
Å is particularly evident.
The instrument parameters adopted in Fig. 3 (click here) are
appropriate for the visual low
dispersion spectrograph (LDS)
and for the near infrared camera-spectrometer (NICS) of the Italian
3.5 m telescope TNG (Conconi 1992; Oliva & Gennari 1995).
Lateral chromatism of the Wollaston is a crucial issue for
imaging-polarimetry because this parameter defines the maximum width
of the field which can be reimaged without
introducing a too strong image elongation.
It is therefore convenient to manufacture the Wollastons
using crystals with very low variation of birefringence with wavelengths,
and the best materials which can be found on the market are probably
MgF
and LiYF
(YLF) for visual and IR instruments, respectively.
The latter is a synthetic compound developed for non linear applications
with very interesting optical and mechanical properties.
It is a tough, non-hygroscopic crystal
transparent from 2000 Å to 6 
m and with a low refractive index,
.
The thermo-optic coefficients are very small,
, 
K
(Barnes & Gettemy D.J. 1980). YLF prisms are only slightly deformed
when cooled because the thermal expansion coefficients along the two
crystal axis
are very similar, 13 
K
and 
K
(Tropf et al. 1995).
YLF is twice more birefringent than MgF
\
(
) and, most important,
is a factor >2 less chromatic than MgF
in the J, H, K IR
photometric bands
(for a detailed discussion of IR birefringent materials see also Oliva
et al. 1996).
Figure 4:
Left: schematic representation of a
WeDoWo device useful for imaging-polarimetry at visual
(MgF
prisms) and IR (YLF prisms) wavelengths, the prism of fused silica
is used to achromatize the deviation of the wedge.
Center, right: values of the 
, 
and 
angles
necessary to create four non-overlapping images of a field of view
whose width projected onto the pupil image is 
(Eq. 1).
All computations are based on room temperature refractive indices
of MgF
(Dodge 1980) while those of LiYF
(YLF) are at 77 K
(see text, Sect. 3.2)
As both materials have low birefringence,
relatively large Wollaston angles 
are
therefore required to obtain useful separations, i.e. the prisms
are thick. This should not be a problem however because the WeDoWo devices
can be mounted in the grism wheel which is usually designed to accommodate
thick optical elements.
The lateral chromatism of the wedge must be small compared to that of the
Wollaston. This requirement could be strictly satisfied by manufacturing
the wedge using two or more prisms of materials with different dispersions.
A simpler solution is however that described in Fig. 4 (click here) and which takes
advantage of the fact that both MgF
and YLF are low dispersion optical
materials (i.e. good "crowns") which can be coupled with fused
silica (a cheap "flint" transparent at all 
's
of interest) to produce wedges with very low chromatism.
Table 1:
Parameters of devices for imaging-polarimetry
The angles 
, 
and 
required to create four
quasi-achromatic
non-overlapping images of a field of a given width are plotted
in Fig. 4 (click here) as a function of the projected width of the field
of view 
(Eq. 1). The lateral chromatism is virtually
the same of that of a standard Wollaston and the largest image elongation
(sky projected angles)
for exposures taken through broad band astronomical filters is
for the visual and IR WeDoWo, respectively.
Table 1 (click here) is a list of prisms angles and image elongation for WeDoWo devices designed using the instrumental parameters of LDS and NICS (cf. end of Sect. 3.1). The width of the input field of view is chosen to ensure that the image elongation is less than one pixel in all photometric bands.