Fig. 4.20. Three-element corrector for an f/2.00 to f/5.28 classical Cassegrain designed by Epps et al. [4.36] for a 300-inch telescope, giving f/6.00 with the corrector
1014.00 6S6.30 587.60 546-10 486.10 435-80 404.70 365-00
Fig. 4.22. Spot-diagrams for the 2.2 m MPIA telescope as quasi-RC using a 2-lens corrector of one glass (quartz) (after Wilson [4.15]). Circle 0.47 arcsec
101^-00 656.30 587.60 SM6.10 M86-10 435.80 404.70 365-00
Fig. 4.23. Spot-diagrams for the 2.2 m MPIA telescope as strict RC using a 2-lens corrector of 2 different glasses (PK50 and BaFs) (after Wilson [4.15]) Circle 0.48 arcsec
In [4.36] and [4.46], a large number of such designs are investigated for different f/ratios. Further such studies have been made for the Magellan 315-inch, f/1.20 parabolic primary [4.47] using all spherical surfaces and delivering a mildly curved field. Epps [4.48] has even applied such designs to a 256-inch, f/1.00 to f/3.962 naked classical Cassegrain to give f/4.50.
Lens correctors for RC and quasi-RC telescopes: Many designs have been published. Wynne [4.24] gave a design for the Kitt Peak 150-inch RC telescope. It consists of two separated lenses agreeing with the relaxation principle (c) of § 18.104.22.168. The field given was ± 15 arcmin, with correction within 0.2 arcsec. Later, Wynne [4.14] gave a similar design for a field of ±25 arcmin, the spot-diagrams somewhat exceeding 0.5 arcsec. Wilson [4.15] gives comparisons of a number of designs showing the advantage of relaxation with the principles of § 22.214.171.124. These become rapidly more significant as the field increases towards ±30 arcmin or beyond. Figs. 4.22 and 4.23 reproduce examples of designs for the 2.2 m MPIA telescopes. Out to a field of ±32.5 arcmin, the monochromatic spot-diagrams are within 0.1 arcsec. The chromatic spread is within 0.3 arcsec over the whole field and spectral range (365-1014 nm) in the first case, and even substantially better in the second case apart from secondary spectrum effects of lateral chromatic aberration (C2). Wilson shows another design, for ±27 arcmin field, using a quartz-
LLF1 two-glass corrector in which all spot-diagrams are within 0.1 arcsec, the only significant errors being the secondary spectrum of C2 which amounts to 0.57 arcsec for the edge of the field and extreme wavelength 1014 nm. The effect of this aberration depends, of course, on the bandpass of the filters.
Refsdal [4.49] gave a design for a quasi-RC telescope using a doublet of fused silica with one aspheric giving very good correction over a field of ±45 arcmin. An elegant design by Rosin [4.50] used two glasses (K3 and SK16) in a meniscus form with surfaces either concentric to the image or using the "aplanatic condition" (A (= 0 in Eqs. (3.20)). This is a powerful extension of the singlet, thick meniscus design mentioned above, using relaxation principle (a) of § 126.96.36.199.
For a strict RC telescope, the best design of a doublet corrector of a single glass has been given by Su, Zhou and Yu [4.51] for the Chinese 2.16 m RC telescope, f/3 to f/9. Using a corrector consisting of 2 fused quartz lenses with quite large separation (about 20 cm for diameters of 32.6 and 30.1 cm), they attained the performance shown in Fig. 4.24 for a field of ±26.5 arcmin. This shows the power of the relaxation principle (c) of § 188.8.131.52 (separation of the elements). The spot-diagrams over the whole field and wavelength range from 365 to 1400 nm are within 0.32 arcsec. The lens separation produces small lateral chromatic aberration (C2) effects which are well balanced between the orders.
This design, originally carried out in 1974, sets the standard for normal RC correctors.
Finally, reference must be made to a large number of designs by Epps and collaborators for RC systems. For example, Epps et al. [4.36] give several designs for hyperbolic primaries with small departures from the paraboloid typical of modern RC telescopes with high m2. These are 3-lens designs which, as one would expect, are similar in appearance to that of Fig. 4.20 for a parabolic primary. They also use 2 aspherics and give similar performance to the spot-diagrams of Fig. 4.21. Another example using a much more eccentric primary (bsi = —1.1523) gives an improvement of a factor of about 2 in the spot-diagrams over the whole field of ± 30 arcmin, as shown in Fig. 4.25, also designed for a 300-inch telescope. The improvement due to the higher eccentricity is another example of the gain through relaxation (b) of § 184.108.40.206. Further examples are given by Epps [4.47] for the Magellan and Columbus project designs. Since the primaries are very close to paraboloids, the designs are based on the paraboloid although the Columbus project envisaged an RC telescope. Since m2 = —12.5 (f/1.20 to f/15), the departure from the classical Cassegrain is small. As with his PF designs, Epps also presents designs with reduced non-telecentricity for use with fibre-optics spectrographs. Typical errors of non-telecentricity are of the order of 1° - 2°.
4.4 Atmospheric Dispersion Correctors (ADC)
We have referred above to the Epps designs [4.36] of sophisticated correctors including ADC. All of these included two plane-parallel plates, incorporated into each corrector, to provide material for later design of a pair of counter-rotating zero-deviation prisms serving as an ADC. No further information was given about their nature, but they were considered from an optical design viewpoint as plane-parallel plates. The glasses given were FK5 and LLF2.
The use of prisms for ADC is, according to Wallner and Wetherell [4.52], a concept that goes back to Airy [4.53] and was often used for special observational situations. But systematic analysis for general purpose correction has only recently been carried out.
The classical formula for atmospheric refraction, due to Comstock, is quoted in older books, e.g. Russell et al. [4.54]. In modern units it can be written as
where Z is the zenith distance, b the barometric pressure in mbar, t the absolute temperature in °K and /rej the mean refraction deviation in arcsec. This formula is based on a model treating the atmosphere as successive layers of uniform density and ignoring the curvature of the Earth. It is easily proven [4.55] that, to this approximation, the general form of (4.91) is
where na is the effective refractive index of the atmosphere and is a function primarily of b, t and A, the wavelength. If the curvature of the Earth is taken into account, it was shown by Cassini [4.55] that the more accurate form is
in which h is the height of the equivalent homogeneous atmosphere and R the radius of the Earth. Since R is a small quantity, the term in tan3 Z can be ignored unless tanZ ^ 1. For ADC purposes3, Eqs. (4.91) and (4.92) are sufficient, so that
b giving (na-1) = 0.000 2898 if b = 1013.25 mbar (760 Torr) andt = 273.15°K (0°C). The more accurate formula of Cassini would give a value for (na — 1) nearer to the measured value of the atmosphere for the visual sensitivity maximum at about 550 nm, i.e. (na — 1) ~ 0.000 293 3. Values as given by von Hoerner and Schaifers [4.56] are reproduced in Table 4.1.
3 A more general treatment of atmospheric refraction and dispersion is given in RTO II, Chap. 5.
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