For 2 separated single lenses, the transverse chromatic condition C2 cannot be fulfilled as well as the longitudinal condition Ci, as was discussed above. Otherwise, the four conditions Si, Sii,^2 Siii and Ci can, in principle, be fulfilled by the parameters: 2 powers, 2 bendings, E2 and (Ei — E2), as was implicit in the work of Paul [4.4]. For 2 separated thin afocal doublets, 2 more parameters are available, 2 bendings. The two extra powers are not free parameters because the thin doublets are each defined as afocal, correcting both Ci and C2 with a single glass without secondary spectrum. This parametric situation is more generous than that of a single afocal doublet with a separated plate which gave the solution of Eq. (4.61) for given E-values. With 2 thin afocal doublets, there are, in principle, an infinite number of solutions for given E-values. Such a 4-lens system is, therefore, clearly promising as a corrector for paraboloids. An intermediate solution would be a 3-lens system consisting of a single afocal doublet and a single afocal meniscus with significantly different E-values, as was chosen by Ross (Fig. 4.7).

If the primary is hyperbolic, this will further relax these systems.

4.3.1.2 Modern correctors for parabolic primaries. Wynne's work [4.24] on improvements to the three-lens designs of Ross has been mentioned above. Although this brought considerable improvement, the limitation from chromatic difference of coma was still larger than desirable. Accordingly, Wynne [4.28] investigated 4-lens correctors for paraboloids. He started from the concept above of two separated, thin, afocal doublets of a single glass (UBK7). Above all, the coma correction was distributed evenly between the two doublets, whereas the 3-lens Ross corrector of Fig. 4.7 achieved the coma correction mainly at one surface of the doublet. The spherical aberration contributions of the doublets are equal and opposite and the astigmatism contributions largely so, giving a sum ^2(Sm)cor balancing that of the primary. The scaling law, mentioned above, can be applied. For the initial design, the ratio gi/g2 of the distances from the focus was taken to be about 3. Since the finite thicknesses disturb the chromatic conditions, the order of powers in the two doublets is reversed to allow compensations. Individual powers were given initially with numerical apertures of about ± 0.3, but this is not critical. This design corrects Cl, C2, Si, Sii, Siii and iv . The system was then optimized for real thicknesses and separations. This leads to separations of the two doublets, above all of the second one. Wynne gave details of such a design for the Palomar 5 m, f/3.34 paraboloid.

Fig. 4.9. Wynne design for a 4-lens corrector of the Palomar 5 m, f/3.34 paraboloid. The cross shows the focus of the naked primary (after Wynne [4.28])

Only spherical surfaces were used. The final corrector had a small negative power, giving f/3.52 in the final image. Figure 4.9 shows the section through the system and Fig. 4.10 the spot-diagrams, both taken from Wynne's paper [4.28]. Later, Wynne showed a similar design for the Isaac Newton 2.5 m, f/3.0 primary with somewhat thicker front lenses. Thinner lenses give better performance in such designs, but can give sag problems. Also, the larger the system, the better its theoretical performance.

The spot-diagrams clearly reveal the limitation of such correctors by chromatic difference of coma, particularly due to the reversal of sign of the residual coma at the edge of the field of 25 arcmin diameter. The spot-diagrams fall within 0.5 arcsec over the whole field for the mean focal position except at the two extreme blue wavelengths.

The higher order chromatic aberrations, mainly chromatic difference of coma and astigmatism, limit all practical correctors. This is inevitable with separated, powered lenses because of the dispersion of ray heights on subsequent elements. The situation is alleviated by inverting powers of successive lenses, as Wynne has done. This limitation could only be removed by achro-matising each lens. Not only would this lead to unacceptable absorption, but also much increased individual powers with serious monochromatic higher order effects as well as secondary spectrum. Such systems would not be practical, so the limitation of higher order chromatic effects will remain.

In the above analysis of the possible correction of all three third order conditions for paraboloids, a solution with 3 lenses (an afocal doublet and a meniscus) was referred to, as attempted by Ross and improved by Wynne [4.24]. Since ghost images are a significant problem with correctors [4.29], a 3-lens solution is of great interest if satisfactory quality can be achieved. Applying the argument discussed above, which had its origins in the work of Paul [4.4], that an aspheric surface can relax a system if it has a different E-value from those of other elements, Faulde and Wilson [4.30] designed a 3-lens corrector for paraboloids with an aspheric surface on the concave side of the central negative lens. The aim was to achieve a similar quality for the paraboloid as was achieved by the 3-lens corrector for RC primaries designed

by Wynne [4.14], which we shall discuss in the next section. The design is shown in section in Fig. 4.11 and the spot-diagrams in Fig. 4.12. This work was suggested by Elsasser and Bahner in the framework of studies for the 3.5 m MPIA telescope. A paraboloid of 3.5 m with f/3.0 and a well corrected, flat field of ±0.5° were requirements using the single glass UBK7.

Since the field is ±0.49° compared with ±0.25° for the Wynne system of Fig. 4.10, and the paraboloid somewhat steeper, the quality of this corrector is not within 0.5 arcsec. The aim was spot-diagrams within 1.0 arcsec over the whole field and for all wavelengths, which was just about achieved.

.Aspheric s

.Aspheric

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