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Fig. 4.15. 3-lens prime focus corrector designed by Richardson et al. [4.34] for the then proposed 7.6 m, f/2 primary of University of Texas. (After Richardson et al.)

The front meniscus lens of Fig. 4.15 is about the same size as the same authors' design for the 3.9 m AAT, i.e. the size relative to the primary (g—value above) is much larger in the latter case. The AAT primary has f/3.25 compared with f/2.0 proposed for Texas. As a result, while the first two lenses of the AAT design are excellently robust, those for the f/2.0 Texas primary are markedly more curved, above all the front lens. With the diameter proposed, 613 mm, it seems possible that flexure problems would appear, as discussed by Cao and Wilson [4.16]. This system was never manufactured as the telescope project did not come to fruition.

The work of Richardson et al. showed, above all, the gain achievable by increasing the size of the corrector. This was pointed out by Wynne [4.28] in connection with correctors for paraboloids. A significant increase in size of the front lens was also applied in the 3-lens paraboloid corrector, using an aspheric on the second lens, by Faulde and Wilson [4.30]. Wynne's scaling law with (bs1 + 1) corresponds, according to Eq. (3.115) to a proportionality to the inverse cube of the secondary magnification (1/m2). Modern RC telescopes tend to steeper primaries with larger values of m2. For one Texas design by Richardson et al. [4.34], m2 = —6.75 giving bs1-values hardly departing from the parabola. In contrast with the early RC designs discussed by Paul [4.4], the modern RC form of primary hardly contributes any overcorrection of spherical aberration. This is the reason why the aspheric on the concave surface of the second lens, as proposed by Faulde and Wilson [4.30] for the paraboloid, is increasingly valuable for modern RC correctors. However, as Richardson et al. [4.34] correctly point out, the larger the system, the less the aspheric is needed. Faulde and Wilson allowed a front lens diameter of 471 mm with a 3.5 m primary, compared with 360 mm for the equivalent RC corrector. The resulting aspheric was, to a third order, quite weak. Conversely, for the smaller correctors used earlier by Wynne [4.14] and considered with only modest increase in diameter by Cao and Wilson [4.16] for less extreme m2-values such as —2.7 for the ESO 3.6 m telescope, three aspheric surfaces are required to obtain a significant gain. This supports the design direction of Richardson et al. to go to the limit in corrector size. In such cases, though, flexure problems may set the practical limits [4.16].

As discussed above in connection with paraboloid correctors, the only theoretically complete solution to the limitations of higher order chromatic aberrations would be achromatism of each lens with 2 glasses. Apart from problems of secondary spectrum, this is impossible in practice for the reasons given above. Furthermore, the larger systems become, the less practicable such achromatism becomes. In this sense, no further major advance over existing systems seems possible with refracting elements.

Much work on PF correctors for recent telescopes, often with extremely steep primaries, has been done by Epps and collaborators. A good example is the design for the 10 m Keck telescope segmented primary (at that time still an RC design) by Epps, Angel and Anderson [4.36]. Figure 4.16 is reproduced from their paper and shows that the front meniscus is used with an interchangeable "blue" or "red" unit which contains the two smaller lenses of the 3-lens corrector and the flat window of the detector. The blue unit also contains an atmospheric dispersion corrector (ADC), a subject we shall deal with in § 4.4. The primary is very steep with f/1.75 and correspondingly only slightly hyperbolic (bs1 = -1.0038). Very complete spot-diagrams are given for four spectral ranges, with refocusing for the blue system. Figure 4.17 gives results for 2 of the 4 spectral bands shown. The middle and rear lenses each have an aspheric. The form of the spot-diagrams off-axis is complex, no doubt a result of the high relative aperture of the primary and the

Hyperbolic Corrector
Fig. 4.16. 3-lens PF corrector for the 10 m Keck primary (after Epps et al. [4.36])
Hyperbolic Lens Corrector
Fig. 4.17. Spot-diagrams for the system of Fig. 4.16 for two of the four spectral bands given (after Epps et al. [4.36])

effects of the aspherics. The worst spot-diagrams have a spread of the order of 3 arcsec, which the authors consider, in tentative conclusions, to fall short of requirements.

Earlier in 1982, the same authors [4.37] [4.38] had favoured a Paul-Baker reflecting type corrector. This, as was shown in Chap. 3, can give superb imagery and is completely achromatic. However, as Richardson and Morbey [4.39] pointed out, the corrector has anyway to work with refracting elements such as wide-band filters, detector faceplates and cold-box windows whose refractive effects cannot be compensated in purely reflective correctors. This is a major advantage of refractive correctors, in spite of their limitations.

Brodie and Epps [4.40] have also designed improved correctors for an older telescope, the 120-inch Shane telescope of the Lick Observatory. This has a parabolic f/5.0 primary. Depending on geometrical space constraints, 3-lens (quartz) solutions with spherical surfaces were set up for fields of 30, 40, 50 and 60 arcmin diameter. Other solutions for 60 arcmin field diameter used larger elements (front lens 24.7 inch diameter) with spherical surfaces, and "normal" sized elements (front lens 19.3 inch diameter) with one aspheric on the second lens. The aspheric gives improved performance, for lenses of this size, over the equivalent all-spherical solution, in agreement with the conclusions above.

Modern designs confirm that the optimum type of corrector will depend on the Schwarzschild (conic) constant and f/no of the primary, and on the permissible size of the front lens relative to that of the primary. This latter may well be limited by flexure, above all if the primary has a high relative aperture. Depending on the above parameters, an aspheric surface (or surfaces) may or may not be worthwhile. Supplementary conditions can greatly complicate the problem. For example, Epps (private communication) has attacked the problem of maintaining a telecentric output for use of the corrector with fibres for a multi-object spectrograph. This condition is in conflict with a flat-field requirement. For the Shane telescope, he obtained a good design with all spherical surfaces if a strongly concave, hyperbolic field is accepted. This forced the use of a strong aspheric. Other constraints he mentions in retrofit designs for existing telescopes are parfocality with the naked focus, limited allowed change in f/ratio and long back focus.

The Wynne design for the RC prime focus correctors goes back to 1968 and has set the standard for many years. This (and virtually all subsequent variants discussed above) used only one glass, normally Schott UBK7, for cost reasons and with optimum transmission for materials available at that time in the required diameters. This situation was determinant for the design, above all the relatively wide spacing of the 3 lenses. As discussed above, since the lenses are not themselves achromatized, the separations lead to serious higher order chromatic effects, notably chromatic difference of coma and astigmatism. Thus two correctors were necessary to cover the spectral range from 334 nm to 1014 nm with a quality more or less meeting the 1 arcsec requirement over a 1° field. The finite thicknesses of the first two lenses also impair the chromatic performance, so these thicknesses were held to what was deemed a reasonable minimum. In fact, the image quality of the ESO Wynne-type corrector has been constantly impaired by flexure astigmatism of these two elements, as discussed above in connection with the work of Cao and Wilson.

More recently (1996) the whole problem has been approached with different premises by Delabre [4.75]. Special glasses are now available in adequate diameters, notably fused silica and Schott FK5. Figure 4.18 shows the Delabre system with its performance and data in the standardized format of Fig.4.6. In fact, it is no longer a triplet corrector, but a 4-lens corrector. However, this does not involve an extra lens since the fourth lens is simply the cryostat window, which is given some optical power, of the CCD detector. The figure shows that the first three lenses are in a compact group of axial length 152 mm instead of 490 mm in the old Wynne-type corrector. The front lens is about 19% smaller than the old front lens. More significantly, the front lens is nearly plano-convex and much thicker relative to its diameter, while the second lens no longer has the flexure-sensitive meniscus form and is also much thicker. The new corrector is therefore completely robust against flexure-induced astigmatic images. The chromatic correction is so much better, above all because of the design possibilities provided by the fourth lens (window), that a single corrector can operate over the whole spectral range from 320 nm to 1100 nm. The system delivers a final image of f/3.02 and has an average optical quality with 80% energy concentration liÜe! C Date : TUE JUL 1

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