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2. Wollaston prisms and IR birefringent materials

Figure 1 (click here) is a sketch of a Wollaston prism with a schematic ray-tracing. In the first (entrance) prism the "o" light beam vibrating perpendicular to the optic axis has a refractive index tex2html_wrap_inline1165 while the e-ray has a refractive index tex2html_wrap_inline1167. At the prisms interface the refraction index of the o-ray changes from tex2html_wrap_inline1169 to tex2html_wrap_inline1171 and the opposite occurs for the e-ray, and when exiting the second prism the angle between the two rays is increased further.

Figure 1: Schematic representation of a Wollaston prism and ray-tracing (adapted from Fig. 11 of Bennet 1995)

For most practical applications the deviation tex2html_wrap_inline1173 can be considered symmetric around tex2html_wrap_inline1175 (i.e. tex2html_wrap_inline1177) and the separation between the o and e rays is given by:
where tex2html_wrap1371 = tex2html_wrap_inline1183 is the birefringence index of the crystal. For astronomical instruments the separation tex2html_wrap_inline1185 can be most conveniently expressed in sky-projected angles
where tex2html_wrap_inline1189 is the telescope diameter and tex2html_wrap_inline1191 is the diameter of the pupil image inside the instrument. The maximum field of view which can be handled by the Wollaston is tex2html_wrap_inline1193. The deviation tex2html_wrap_inline1195 is chromatic because tex2html_wrap1375 varies with tex2html_wrap_inline1199, this implies that broad-band images taken through a Wollaston are elongated. The amount of lateral chromatism, i.e. the image "blurring" over a given tex2html_wrap_inline1201 wavelength range, follows from Eq. (1) and can be conveniently quantified in terms of the parameter

The image elongation tex2html_wrap_inline1209 is simply given by
and this relationship is independent on the detailed parameters of the prism such e.g. its aperture angle. In the case e.g. of a Calcite Wollaston with a sky-projected separation of tex2html_wrap_inline1211 (i.e. a maximum field of view of 40'') the image blurring in the H band is 0.56'' because V=36 (cf. Table 1 (click here)). Wollaston prisms from crystals with tex2html_wrap_inline1221 could therefore be used to image fields of view >1 arcmin with an image blurring of only <0.3''. These materials are analyzed in some details in the following subsections.

Figure 2: Predicted separations (sky projected angles) between the "`o" and "e" rays in AgGaStex2html_wrap_inline1227 and LiYFtex2html_wrap_inline1229 (YLF) Wollaston prisms inserted at the tex2html_wrap_inline1231 22 mm pupil plane of NICS, the IR instrument for the Italian 3.5 m Galileo telescope. Note the large total separation of the beams, tex2html_wrap_inline1233, and the very small image elongation in the 0.9-1.1, J, H and K bands

   Table 1: Refraction indices and chromatic characteristics of IR birefringent crystals with tex2html_wrap_inline1243 tex2html_wrap_inline1245

2.1. AgGaStex2html_wrap_inline1395 (silver thiogallate)

This crystal has a quite large birefringence (tex2html_wrap_inline1397) which peaks at tex2html_wrap_inline13991.05 tex2html_wrap_inline1401m and decreases very slowly at longer wavelengths. The combination of large tex2html_wrap_inline1403 and low chromatism makes it possible to design Wollaston prisms which can handle large fields of view with sub-seeing image quality. An example is given in Fig. 2 (click here) (left panel) where we plot the computed beam separation for an tex2html_wrap_inline1405 AgGaStex2html_wrap_inline1407 Wollaston inserted at the tex2html_wrap_inline1409 22 mm pupil plane of NICS, the IR instrument for the Italian 3.5m Galileo telescope (Oliva & Gennari 1995). The separation is tex2html_wrap_inline1411 and the field of view is therefore 1 arcmin with an image elongation of only tex2html_wrap_inline1413 in all bands.

From the practical point of view, AgGaStex2html_wrap_inline1415 is considered "one of the most successful materials developed for nonlinear optical laser devices in the infrared'' (Bhar et al. 1983). The thermo-optic coefficients are quite large (tex2html_wrap_inline1417 Ktex2html_wrap_inline1419) but the change of birefringence tex2html_wrap1447 with temperature is small: tex2html_wrap_inline1423 tex2html_wrap_inline1425 (Bhar et al. 1983). No significant change of optical performances is therefore expected when the prism is cooled to 77 K. A potential problem is total reflection at the prisms interface which may be difficult to avoid because of the large refractive index: tex2html_wrap_inline1427. Standard cements with tex2html_wrap_inline1429 could only be used for prisms with tex2html_wrap_inline1431, and their practical use may be further limited by the fact that AgGaStex2html_wrap_inline1433 crystals are significantly deformed by cooling. The thermal expansion coefficients || and tex2html_wrap_inline1437 to the optical axis are +29 and -19 (tex2html_wrap_inline1443 tex2html_wrap_inline1445), respectively.

2.2. LiYFtex2html_wrap_inline1449 (YLF)

This material is transparent from below 3000 Å to beyond 4 tex2html_wrap_inline1451m. It displays a very low chromatism from 1 to 2 tex2html_wrap_inline1453m and also has excellent performances from 0.8 to 2.5 tex2html_wrap_inline1455m. The computed beam separation for an tex2html_wrap_inline1457 YLF Wollaston are displayed in Fig. 2 (click here) (right hand panel) where one can better visualize the chromatic performances of this material which is comparable to AgGaStex2html_wrap_inline1459\ in all bands but K. The thermo-optics coefficients of YLF are very small, tex2html_wrap_inline1463 and tex2html_wrap_inline1465 respectively increase by tex2html_wrap_inline1467 and tex2html_wrap_inline1469 between room temperature and 77 K (Barnes & Gettemy 1980). Practical advantages of YLF are:
- The refractive index of YLF is tex2html_wrap_inline1471 and very close to that of standard optical cements.
- YLF crystals are only slightly deformed by cooling because the thermal expansion coefficients || and tex2html_wrap_inline1475 to the crystal axis differ by only 5 tex2html_wrap_inline1477 tex2html_wrap_inline1479.
- Presently, YLF is much cheaper than AgGaStex2html_wrap_inline1481.

2.3. Other materials

YVOtex2html_wrap_inline1487 is an interesting crystal to which attention was already drawn by Bennet & Bennet (1978) and which is now produced by several companies. It has a large birefringence (tex2html_wrap1553tex2html_wrap_inline1491) and could be therefore useful for manufacturing thin Wollastons when the physical thickness of the prism is limited e.g. by the space available in the filter wheel. Accurate measurement of the refractive indices of YVOtex2html_wrap_inline1493 are not available in the literature and the only information we could find is from the CASIX data sheet which gives the following relationships (tex2html_wrap_inline1495 in tex2html_wrap_inline1497m)



These are probably based on measurements at tex2html_wrap_inline1499 tex2html_wrap_inline1501m and are not necessarily accurate at longer wavelengths.

tex2html_wrap_inline1503 is a well known crystal for quasi-achromatic Wollastons from the ultraviolet to 1 tex2html_wrap_inline1505m but has a very low birefringence (tex2html_wrap1555 = 0.011) and becomes quite chromatic at tex2html_wrap_inline1509 tex2html_wrap_inline1511m (tex2html_wrap_inline1513 in the K band, cf. Table 1).

CdSe has a very low chromatism in J, H, K but is not suited for applications below 1.1 tex2html_wrap_inline1523m. Compared to LiYFtex2html_wrap_inline1525 it has a much higher refractive index (tex2html_wrap_inline1527) and a slightly lower birefringence (tex2html_wrap1557 = 0.020). Both facts make CdSe a not attractive alternative to YLF.

tex2html_wrap_inline1531 is a cheap compound extensively used for non linear applications and which is transparent to well beyond 2.5 tex2html_wrap_inline1533m. It has a quite large birefringence (tex2html_wrap_inline1535) and may be useful to manufacture low cost prisms whose performances are however limited by the relatively large chromatism of the crystal (tex2html_wrap_inline1537).

Rutile (tex2html_wrap_inline1539) is another classical material which could be a good though expensive alternative to tex2html_wrap_inline1541 whenever high birefringence is required.

Calcite, the most widely used birefringent crystal, has the advantage of low refractive index and high tex2html_wrap1559 but displays a large lateral chromatism and cannot be used beyond 2.0 tex2html_wrap_inline1545m because of its large opacity to the ordinary ray (cf. Sect. 3).

Figure 3: Transmission of Calcite, thickness 9 mm, at room temperature (upper panel) and 77 K (lower panel), the solid and dashed lines refer to the ordinary and extraordinary ray, respectively, while the thin lines show the transmission expected including reflection (Fresnel) losses alone

tex2html_wrap_inline1547 has interesting optical properties, large tex2html_wrap_inline1549 and tex2html_wrap_inline1551 in all bands, but is very hygroscopic and therefore unlikely to find practical applications in astronomical instruments.

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