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Apochromatic Lenses for Near-Infrared Astronomical Instruments

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Apochromatic Lenses for Near-Infrared Astronomical Instruments Apochromatic lenses for near-infrared astronomical instruments Deqing Ren Abstract. A method based on the Herzberger approach has been in- Jeremy R. Allington-Smith vestigated for the selection of glasses for the apochromatic correction at University of Durham near-infrared (NIR) wavelength. The method avoids the algebraic com- Department of Physics plexity and simplifies the glass selection processes. Doublet and triplet Durham DH1 3LE glass combinations can be chosen directly from the plot of partial disper- United Kingdom sion versus V number. Good combinations of NIR doublets and triplets E-mail: [email protected] are given. Design examples show that the method is practical and effi- cient. © 1999 Society of Photo-Optical Instrumentation Engineers. [S0091-3286(99)02103-0] Subject terms: optical design; infrared; lenses; optical glass; camera. Paper 980318 received Aug. 24, 1998; accepted for publication Oct. 21, 1998. 1 Introduction 2 Partial Dispersion and V Number of Glasses In optical design, the first step is to choose optical glasses For NIR glasses, the Sellmeier and Herzberger dispersion to correct chromatic aberration. The control of chromatic formulas are used to calculate the index of refraction. The aberration through the selection of glasses is one of the glass catalogs of various manufacturers, available in digital most extensively studied subjects in the field of lens form, can be used to fit the index data and calculate the design.1–14 Different glass selection methods have been in- coefficients of the dispersion formulas. Then, the dispersion vestigated at visible wavelengths that can yield apochro- formulas can be used to calculate the optical index at any matic and superachromatic lens systems. The term apochro- wavelength. The more data one enters, the more accurate matic and superachromatic mean paraxial color correction will be the fit. The glass index data in this paper are from the infrared glass catalog published with the Zemax optical at three and four wavelengths, respectively. One approach design program.15 These data are provided by Schott16 or uses the Buchdahl glass dispersion equation to select compiled from published sources,17 and their accuracy has glasses for systems of thin lenses that yield apochromatic been confirmed by Albert Feldman’s measurements.18 and superachromatic color correction. Robb and Mercado1 2 For infrared glasses, the Herzberger dispersion formula and Buchdahl use this method to choose two kinds of ma- is often used to calculate the glass index14: terials for a doublet. Another approach uses Herzberger’s relative-partial-dispersion–Abbe-number equation, which can also yield apochromatic and superachromatic color cor- n5A1BL1CL21Dl21El41Fl6, ~1! rection. Herzberger and Salzberg14 used this method to se- lect glasses that can yield the same performance. where L51/(l220.028). Schott uses the Herzberger for- However, most of these studies were done at visible mula to calculate its glasses for NIR. The three-term Sell- wavelengths. Little attention has been given to the near- meier dispersion formula can also be used to calculate the 19 infrared ~NIR! wavelengths ~1to2.5mm!. The use of dou- index of infrared glass with adequate accuracy : blets is often limited by the small number of available glasses and the inability of a doublet to achromatize over K l2 K l2 K l2 the whole NIR wavelength range. We have not found any 2 1 2 3 n 215 2 1 2 1 2 . ~2! paper about the choice of glasses for triplets for NIR astro- l 2L1 l 2L2 l 2L3 nomical instruments. The Buchdahl glass dispersion equa- tion is mathematically too complex for the selection of As is done for visible optical wavelengths, for infrared glasses for doublets. From the point of view of optical en- wavelengths the V number and partial dispersion are de- gineering, it is important to find a simple and practical fined for a stated spectral region l1,l2,l3 as method to choose glasses for chromatic-aberration correc- tion. n221 This paper investigates a method that uses Herzberger’s V5 , ~3! approach to choose glasses to design doublets and triplets n12n3 for apochromatic correction in the NIR wavelength range. Doublet glasses or triplet glasses can be chosen directly n22n3 form the partial-dispersion–V-number plot, without alge- P5 , ~4! braic complexity. Finally, two design examples are given. n12n3 Opt. Eng. 38(3) 537–542 (March 1999) 0091-3286/99/$10.00 © 1999 Society of Photo-Optical Instrumentation Engineers 537 Downloaded From: http://opticalengineering.spiedigitallibrary.org/ on 06/28/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx Ren and Allington-Smith: Apochromatic lenses... Table 1 Refractive indices, V number, and partial dispersion of NIR glasses at 20°C. The refractive indices of IRG2, IRG3, IRG7, IRG9, and ZnSe were calculated with the Herzberger formula; the others, with the Sellmeier formula. The silica is fused silica; the ZnSe and ZnS are chemical vapor deposited. n1 n2 n3 V Glass (1.25 mm) (1.65 mm) (2.2 mm) number P silica 1.44748 1.44280 1.43501 35.5110 0.6246 LiF 1.38512 1.38190 1.37659 44.7701 0.6217 MgF2-O 1.37214 1.36995 1.36648 65.3879 0.6128 IRG9 1.47745 1.47461 1.47031 66.4437 0.6028 IRG7 1.54755 1.54279 1.53584 46.3737 0.5929 CaF2 1.42746 1.42556 1.42280 91.4696 0.5907 MgO 1.71941 1.71449 1.70762 60.6185 0.5824 IRG11 1.66140 1.65675 1.65060 60.8103 0.5699 Fig. 1 Plot of partial dispersion P versus V number for NIR glasses IRG3 1.81383 1.80709 1.79841 52.3309 0.5627 at wavelengths 1.25, 1.65, and 2.2 mmat20°C. BaF2 1.46719 1.46571 1.46396 144.4753 0.5412 IRG2 1.85741 1.85088 1.84321 59.9108 0.5400 SrTiO3 2.29795 2.28014 2.26082 34.4813 0.5203 ZnS 2.27935 2.26973 2.26338 79.4784 0.3974 NIR astronomical instruments work in the J, H, and K ZnSe 2.46802 2.45278 2.44368 59.7034 0.3739 bands ~which are also standard atmospheric windows of transparency21!. In order to avoid refocusing in the three bands, we choose the infrared wavelengths as l151.25 mm, l251.65 mm, l352.2 mm. where n1 , n2 , and n3 are the indices of refraction at the short wavelength l1 , central wavelength l2 , and long wavelength l3 , respectively. It is important to note that Using Eqs. ~1!, ~2!, ~3!, and ~4!, we can calculate the indi- l1 , l2 , and l3 are also the wavelengths to be corrected for ces, V number, and partial dispersion P of the most-used chromatic aberration. glasses in the NIR wavelength. The results are given in The plot of partial dispersion versus V number is ex- Table 1. All of these indices are for room temperature tremely important in choosing glasses that will permit sec- ~20°C!, and all of these glasses have high transmission. ondary color correction in a lens. Unfortunately, many A plot of V number versus partial dispersion at 20°C is glass catalogs provided with computer design programs shown in Fig. 1. It can be seen that BaF2, ZnS, and ZnSe ~such as Zemax! or by glass companies only provide glasses are far away from other glasses on the plot. This is V-number and P data that are calculated at the F-d-C wave- important in the choice of glass, as will be shown in Secs. lengths. In fact, these data are useless for glass selection, as 3 and 4. As NIR instruments are often operated at cryo- they will be different at visible and NIR wavelengths. genic temperatures, we also calculated the partial disper- Shannon20 has calculated V-number and P values of some sion and V number of all these glasses at 77 K and found visible optical glasses in different wavelength ranges. He that their relative values are almost unchanged. So the plot also compared the plots of V number versus P for these of V number versus partial dispersion at 20°C can be used glasses in the visible F-d-C and the infrared wavelength as a standard map for glass choice at other temperatures. ranges, and found that the glass distributions change dra- matically when the wavelength shifts to the infrared. Herzberger and Salzberg14 calculated the partial disper- 3 Selection of Glass for a Two-Material Doublet sion P of some infrared glasses in the wavelength range 1.5 For simplicity in application, only axial chromatic aberra- to 5.0 mm. He used 3.5 mm as the central wavelength l2 . tion will be considered. For thin lens doublets in close con- We find that the distributions of glasses on the V-versus-P tact or with a small air space, the conditions for three- 14 plot for differing short wavelength l1 , central wavelength wavelength color correction are l2 , and long wavelength l3 are also dramatically different, and this has generally been ignored. For example if l1 , l2 , F1 F2 and l3 are 1, 1.75, and 2.5 mm, respectively, the V-number 1 50, ~5! and P of CaF2 glass are 54.6 and 0.488, respectively, com- V1 V2 pared with 91.5 and 0.591 when l1 , l2 , and l3 are 1.25, 1.65, and 2.2 mm, respectively. So the V-number and P F F data must be calculated according to the wavelengths at 1 2 P11 P250, ~6! which one corrects for chromatic aberration. V1 V2 538 Optical Engineering, Vol. 38 No. 3, March 1999 Downloaded From: http://opticalengineering.spiedigitallibrary.org/ on 06/28/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx Ren and Allington-Smith: Apochromatic lenses..
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