2. The selection of Flint glasses

A convenient way to identify the Flint glasses which couple with the alkaline-earth fluoride Crowns is the standard partial dispersion versus Abbe number plot which is displayed in Fig. 1. The most striking result is that SF6 and IRG2 have very similar chromatic characteristics, while SF5 seems an even better match to SrF₂ than IRG3. Other interesting pairs are BaF₂-SF56A and SrF₂-SFL4A.

Here we concentrate on the Flint glasses which couple with BaF₂. Refraction indices and dispersions at room temperatures are listed in the upper panel of Table 1. The values of n for SF glasses are computed using the Sellmeier's parameters of the Schott catalog which interpolate measurements from 0.37 to 2.33 m, the extrapolation to 2.5 m should not introduce significant errors.

 

BaF₂ SF6 SF56A irg2

n n r⁽²⁾ n r⁽²⁾ n r⁽²⁾

0.9 1.46935 -0.00898 1.77935 -0.04287 4.78 1.76007 -0.04111 4.58 1.86710 -0.04147 4.62

1.2 1.46742 -0.00475 1.77034 -0.02174 4.58 1.75138 -0.02117 4.45 1.85834 -0.02126 4.47

1.5 1.46622 -0.00350 1.76490 -0.01567 4.47 1.74604 -0.01553 4.43 1.85301 -0.01539 4.39

2.0 1.46460 -0.00314 1.75771 -0.01404 4.47 1.73883 -0.01421 4.52 1.84596 -0.01368 4.35

2.5 1.46297 -0.00342 1.75035 -0.01572 4.60 1.73134 -0.01606 4.70 1.83886 -0.01499 4.39

BaF₂^a SF6^b SF56A^b irg2^b

n n r⁽²⁾ n r⁽²⁾ n r⁽²⁾

0.9 1.47222 -0.00897 1.77894 -0.04227 4.71 1.75971 -0.04056 4.52 1.86666 -0.04107 4.58

1.2 1.47029 -0.00477 1.77005 -0.02151 4.51 1.75112 -0.02096 4.40 1.85798 -0.02110 4.43

1.5 1.46908 -0.00352 1.76467 -0.01555 4.42 1.74584 -0.01542 4.38 1.85269 -0.01531 4.35

2.0 1.46746 -0.00316 1.75751 -0.01399 4.42 1.73866 -0.01417 4.48 1.84567 -0.01365 4.32

2.5 1.46582 -0.00344 1.75017 -0.01570 4.56 1.73118 -0.01604 4.66 1.83857 -0.01498 4.35

Notes to Table 1
⁽¹⁾ Dispersion, in m^-1.
⁽²⁾ r = glass dispersion/BaF₂ dispersion.
^a From Eq. (1), based on from Feldman et al. (1979), cf. Sect. 2.
^b Using the D₀, D₁, D₂, E₀, E₁, coefficients from the Schott catalog (cf. Eq. 2).  

2.1. Temperature dependence of refraction indices

Table 1 (lower panel) also includes optical parameters at cryogenic temperatures. The values for BaF₂ are based on the accurate measurements by Feldman et al. (1979) which tabulate at 0.46, 0.63, 1.15, 3.39, 10.6 m and many temperatures between +200 and -180 C. The resulting refraction indices at -200 C can be conveniently fitted with a two terms Sellmeier's formula which yields

For the Flint glasses we use the Schott formula

and the D₀, D₁, D₂, E₀, E₁, coefficients from the Schott catalog which are based on data at m and C. The values in Table 1 are therefore extrapolated to wavelengths and temperatures for which no measurement exists. However, this should not necessarily introduce large errors because Eq. (2) is based on a physical representation of the glass properties (i.e. the Sellmeier's formula) and the only important uncertainty could be that Eq. (2) does not include the long wavelength resonance which for SF glasses lies at 11 m.

  
Figure 2: Solid lines: predicted variation of refractive index between room and cryogenic temperatures (= n(C)-n(C)). The curves are based on the T-dependent, Sellmeier equation (Eq. 2) whose parameters are taken from the Schott catalog (cf. Sect. 2). The dashed lines is the value for IRG2 estimated by Doyon et al. (1995) and also confirmed within 10^-4 by direct measurements (van Dijsseldonk 1995)

The predicted total variation of refraction index with wavelength is plotted in Fig. 2 where we also include IRG2, a glass for which other estimates exist in the literature (see the caption of Fig. 2 (click here)). The main result is that is small for glasses, the variation of dispersion is also very low and in practice negligible. This is confirmed by our detailed designs (Sect. 3) where we find that the same systems also give excellent images if the SF glasses have at all wavelengths, the only modification required is to refocus the array by a few 10 m.

In short, the information presently available on SF glasses is probably enough for their use in cryogenic lens systems. However, new measurements of refraction indices at 70 K and IR wavelengths would be useful, and could be essential for the design of multi-objective systems which do not foresee the possibility of refocusing the array.