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Equation (4.90) and the first two equations of (4.89) can give a real solution for a thin doublet in certain circumstances. The most interesting example is the proposal of Rosin [4.43], based on work by Wynne [4.23], to use a parabolic primary with a spherical secondary of the same radius and an afocal, single-glass doublet. Essentially the same system was proposed later by Harmer and Wynne [4.44]. We shall consider the results of this design in the next section.

4.3.2.5 Practical examples of secondary focus correctors using lenses

Field flatteners: A negative lens placed close to the image can flatten the field of an RC telescope in an optimum way for the mean astigmatic field curvature 2S/// + S/V. This solution achieves essentially the same result as bending a photographic plate except for small chromatic differences of C2. Wynne [4.14] gives the gain for a curved photographic plate for typical RC telescopes: for a 3.5 m, f/3-f/8 RC, the semi-field for 0.5 arcsec image spread is increased by bending the plate optimally from 9.2 arcmin to 13.0 arcmin.

Single lens correctors: In spite of the inevitable chromatic aberrations, such simple correctors can be considered in certain circumstances. Kohler [4.12] [4.13] noted that the negative field-flattening lens of the RC telescope can also correct the astigmatism if it is shifted from the image and the as-pheric constants of the mirror system are changed to compensate the coma inevitably introduced by the lens. This is a good practical example of the relaxation (b) in § 4.3.2.3. The properties of this corrector, which was manufactured for the ESO 3.6 m quasi-RC telescope and determined the forms of the mirrors, were discussed by Wilson [4.15]. Figure 4.19 reproduces spot-diagrams given for the best focus of the mean wavelength (546 nm) over a

field of ± 0.25°. The monochromatic correction, as predicted by the third order theory above, is very good, within 0.18 arcsec at the field edge. The uncorrected Ci is modest over a wide spectral band and can be refocused. With optimum focus, the higher order chromatic aberrations are also quite modest. However, the great weakness is the uncorrected C2, the lateral chromatic aberration, which amounts to about 2 arcsec over the whole wavelength band 365 nm-1014 nm. The corrector must therefore be used over relatively narrow spectral bands, which also allows optimum focus. One advantage of this corrector is the reduction of ghost images compared with doublet correctors. Another is that its contribution to Sj is sufficiently low that the telescope can be used without the corrector, although it has some field coma as a quasi-RC system.

The aspheric plate plus field-flattener corrector of Fig. 4.6, as discussed by Schulte [4.17], is much superior in performance, but much more expensive to make.

Another possible single lens solution was mentioned by Wilson [4.45]. It is well known that a meniscus lens, roughly concentric to the image and placed near the image plane, will strongly affect astigmatism without much affecting the aperture aberrations E Sj and E Sjj. If its thickness is finite, it can also correct the field curvature. Because of an inevitable coma contribution, a modification of the mirror constants is also required here. On account of the thickness and bending, the chromatic aberrations are worse than in the thin Kohler singlet above. However, in an achromatised doublet form, the meniscus concept has been applied successfully by Rosin - see next section.

Two- and three-lens correctors for quasi-classical Cassegrain telescopes: In his pioneer paper of 1949, Wynne [4.23] investigated correctors for classical Cassegrain telescopes. Because of the problems referred to in §§ 4.3.2.2 and 4.3.2.3, he concluded that a modification of the asphericity of the secondary mirror was essential for the correction of spherical aberration. The problem of field curvature was solved by giving the secondary the same curvature as the primary - a solution which has only limited use, in practice, because of obstruction. This allowed an afocal doublet corrector of a single glass. For two examples given, the figuring on the secondary was 63% and 15%, respectively, of the classical hyperboloid for a doublet of diameter 1 that of the primary. Of course, the mirror system without corrector is not corrected for spherical aberration. This design principle corresponds to the relaxation (b) of § 4.3.2.3.

Wynne [4.23] mentions the possibility of making the secondary spherical, but does not give an example. Rosin [4.43] was the first to apply this to a finished design. He followed Wynne's proposal of eliminating field curvature by using equal radii on primary and secondary, which leads to either high obstruction or unacceptable image position in most cases.

Harmer and Wynne [4.44] published a similar design with a spherical secondary, suggesting its greatest interest would be for modest-sized telescopes with fields up to 1.5° diameter. The corrector is a nearly afocal doublet in UBK7 glass. Spot-diagrams are shown for two designs, one with the positive lens leading and one with the negative lens leading. They are effectively within 0.5 arcsec for the whole field of ±0.75° and for most of the spectral range from 365-852 nm.

Wynne [4.42] has also given a more general treatment of the possibilities of doublet correctors in classical Cassegrain telescopes or for parabolic primaries with changed secondary asphericity. He also mentions [4.23] corrector designs for classical Cassegrain telescopes with 3 separated lenses, corresponding to the relaxation principle (c) of § 4.3.2.3. He points out that this can lead to problems of high individual powers - exactly the same problem as occurs with 3 aspheric plates, as discussed in § 4.2.

In general, 2-lens correctors will give good solutions for strict classical Cassegrain (or quasi-classical Cassegrain) telescopes with residual field curvature if one or more of the relaxation principles of § 4.3.2.3 is applied, depending on field, m2 and the relative aperture of the primary. If the latter is very steep then the relative aperture of the secondary focus is also appreciable, even with a fairly large m2.

Such extreme systems have been investigated by Epps et al. [4.36]. A strict classical Cassegrain with f/2.0 to f/5.28 has been taken as the basis for the calculation of a 3-lens corrector giving a final f/ratio of f/6.00. The lenses are of a single glass, both in this and similar designs and have an aspheric on the two rear lenses. All such designs (Fig. 4.20) have an ADC (atmospheric dispersion corrector) built in. In a later paper [4.46], Epps indicates the use of fused silica for the lenses for a similar design intended for the MMT conversion. The choice of the glass is uncritical for single-glass designs. Figure 4.21 reproduces the spot-diagrams for the design of Fig. 4.20.

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