Achromatic Lens Systems for Near Infrared Instruments II

ASTRONOMY & ASTROPHYSICS MARCH II 1998, PAGE 599 SUPPLEMENT SERIES Astron. Astrophys. Suppl. Ser. 128, 599-603 (1998) Achromatic lens systems for near infrared instruments II. Performances and limitations of standard Flint glasses E. Oliva and S. Gennari Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, I–50125 Firenze, Italy Received May 5; accepted July 22, 1997 Abstract. This paper investigates which normal Flint cemented doublets/triplets and the only way to obtain glasses are best suited for the design of lens systems work- a system with good total transmission is using as few ing in the infrared up to about 1.7 µm, and possibly lenses as possible. The choice of optical materials is lim- up to 2.5 µm. Between 0.9 and 2.5 µm the best known ited by the fact that “normal” glasses are quite opaque achromatic pairs are BaF2−IRG2 and SrF2−IRG3 and, in the infrared due to absorption bands of water which to a lesser extent, CaF2−IRG7 (Oliva & Gennari 1995). is normally bound in the glass matrix, and sometimes be- Unfortunately, Schott will most probably stop the produc- cause of absorption intrinsic to the glassy compounds. For tion of these very little used and commercially uninterest- this reason normal glasses were mostly ignored, and the ing IRG glasses. choice of optical materials was traditionally limited to a Here we show that equally good performances can few crystals such as CaF2, ZnS, ZnSe and BaF2. Prior be obtained coupling BaF2 or SrF2 with standard SF to the “re–discovery” of Schott IR glasses (Delabre 1994; glasses. The pairs we analyze in details are BaF2−SF6 and Oliva & Gennari 1995) the only glassy material employed BaF2−SF56A, and we also present new measurements of in near IR astronomical instrument was IR-grade fused transmission for several SF glasses which are quite trans- silica. This glass has high dispersion (i.e. is a good Flint) parent up to 1.65 µm and can be therefore readily em- but has a very high partial dispersion (cf. Fig. 1) and is ployed in fiber–fed spectrographs and other instruments not suited to produce good achromatic pairs with any of which do not extend beyond the H atmospheric window. the Crowns known. At longer wavelengths the use of SF glasses is limited Normal alkaline–earth fluoride crystals have very low by strong water absorption features, but these could be dispersion in the near infrared (cf. Fig. 1). The main eliminated by preparing the glass in vacuum environment. problem faced by those designing IR lenses instruments Although this production is expensive and commercially is therefore to find a high dispersive (“Flint”) material unattractive, we hope however that a large enough group to couple with BaF2,SrF2 or CaF2. The condition for of astronomers will support glass manufacturers in the achromatism requires that the Flint should have a partial production of “IR–grade SF glasses”. dispersion similar to the alkaline–earth fluoride crystals, As a practical application we present representative and this is not satisfied by any of the crystalline materials results of the design of F/2 (4 lenses) and F/1.4 (5 lenses) commonly used. However, an excellent match is provided cameras for near infrared (0.95−2.5 µm) spectrometers. by the Schott IRG glasses which were recently employed in several astronomical instruments working up to 2.5 µm Key words: instrumentation: miscellaneous — (e.g. Oliva & Gennari 1995). Unfortunately, the only peo- instrumentation: spectrographs ple who seem interested in IRG2, IRG3 and IRG7 are astronomers, and there is hardly any commercial profit for Schott to continue the production of these glasses. Finding alternatives to the IRG glasses is the main aim of this paper which is also intended to give relatively simple solu- 1. Introduction tions for the design of very fast cameras for IR spectrographs. The optical design of dioptric systems working in the infrared is complicated by several factors. The lenses must In Sect. 2 we analyze the chromatic characteristics be cooled to cryogenic temperatures, this prevents using of normal SF glasses, define the best Flints to couple to BaF2,SrF2, and briefly discuss the uncertainties on Send offprint requests to:E.Oliva the variation of their refraction indices with temperature. 600 E. Oliva and S. Gennari: Achromatic lens systems for near infrared instruments. II. Fig. 2. Solid lines: predicted variation of refractive index between room and cryogenic temperatures (∆n= n(−200 ◦C)−n(25 ◦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) Fig. 1. Plot of the NIR partial dispersion P =[n(1.5) − n(2.5)]/[n(0.95) − n(2.5)] versus the “NIR Abbe resulting refraction indices at −200 oC can be conveniently number”ν =[n(1.5) − 1]/[n(0.95) − n(2.5)] Achromatic pairs fitted with a two terms Sellmeier’s formula which yields are those with very similar P and large ∆ν. For clarity, the 2 2 glass names are without the prefix “SF” o 1.158534λ 4.056181λ n(BaF2 −200 C) = + λ2 − .08466392 λ2 − 47.547072 λ 0.46 µm. (1) Representative designs of fast cameras for IR spectro- ≥ graphs are discussed in Sect. 3. New measurements of the For the Flint glasses we use the Schott formula IR absorption of SF glasses are presented in Sect. 4. n2(λ, T ) − 1 ∆n(λ, T )= 0 D ∆T + D ∆T 2 + D ∆T 3 2n(λ, T ) 0 1 2 2. The selection of Flint glasses 0 E ∆T + E ∆T 2 + 0 1 (2) A convenient way to identify the Flint glasses which cou- λ2 − λ2 ple with the alkaline–earth fluoride Crowns is the standard TK partial dispersion versus Abbe number plot which is dis- and the D0, D1, D2, E0, E1, λTK coefficients from the played in Fig. 1. The most striking result is that SF6 and Schott catalog which are based on data at λ ≤ 1.014 µm o IRG2 have very similar chromatic characteristics, while and T ≥−100 C. The values in Table 1 are therefore SF5 seems an even better match to SrF2 than IRG3. Other extrapolated to wavelengths and temperatures for which interesting pairs are BaF2−SF56A and SrF2−SFL4A. no measurement exists. However, this should not neces- Here we concentrate on the Flint glasses which couple sarily introduce large errors because Eq. (2) is based on with BaF2. Refraction indices and dispersions at room a physical representation of the glass properties (i.e. the temperatures are listed in the upper panel of Table 1. Sellmeier’s formula) and the only important uncertainty The values of n for SF glasses are computed using the could be that Eq. (2) does not include the long wavelength Sellmeier’s parameters of the Schott catalog which inter- resonance which for SF glasses lies at '11 µm. polate measurements from 0.37 to 2.33 µm, the extrapo- The predicted total variation of refraction index with lation to 2.5 µm should not introduce significant errors. 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). The main result is that dn/dT is 2.1. Temperature dependence of refraction indices small for glasses, the variation of dispersion is also very Table 1 (lower panel) also includes optical parameters at low and in practice negligible. This is confirmed by our cryogenic temperatures. The values for BaF2 are based detailed designs (Sect. 3) where we find that the same on the accurate measurements by Feldman et al. (1979) systems also give excellent images if the SF glasses have which tabulate dn/dT at 0.46, 0.63, 1.15, 3.39, 10.6 µm ∆n = −210−4 at all wavelengths, the only modification and many temperatures between +200 and −180 oC. The required is to refocus the array by a few × 10 µm. E. Oliva and S. Gennari: Achromatic lens systems for near infrared instruments. II. 601 Fig. 4. Monochromatic spot diagrams (neglecting lateral chromatism) at several wavelengths and distances from the ar- Fig. 3. Layout and ray tracing of F/2 and F/1.4 near-IR cam- ray center for the BaF2−SF6 cameras (Fig. 3), the array is eras. Spot diagrams and encircled energies are displayed in a 10242 with pixels of 18.5 µm. The size of one pixel is indi- Figs. 4, 5 while the details of the design are listed in Table 2 cated by the thick squares, while the larger squares are 2 pixels (37 µm) In short, the information presently available on SF glasses is probably enough for their use in cryogenic lens systems. However, new measurements of refraction in- for lateral chromatism because this aberration does not dices at '70 K and IR wavelengths would be useful, and influence the spectrograph performances. could be essential for the design of multi–objective systems which do not foresee the possibility of refocusing the The performances of the BaF2−SF6 cameras are re- array. markably good and virtually identical to those obtained using BaF2−IRG2. The BaF2−SF56A combination is also very good for λ ∼< 2.2 µm but not at longer wavelengths 3. The design of fast cameras for IR spectrographs where their chromatisms decouple, but this limitation is not important for applications to instruments not extend- The combination of large telescopes and IR arrays with ing into the K atmospheric window.

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