Fig. 3.4. (b) Spot-diagrams for an RC aplanatic telescope with the geometry of the ESO 3.5 m NTT (f/11; m2 = field curvature rc = —1881 mm

Cassegrain and an RC aplanatic telescope. The coma in the former case is the dominant field aberration. The form of the spot-diagrams for the basic aberrations is given in § 3.3. The point of the arrow-shaped coma figure points towards the axis (field centre) of the telescope. Such comatic images are common in star-field photographs with older telescopes. Bahner [3.5] gives an example from a PF photograph with an f/4 parabolic primary. By contrast, the spot-diagrams in the RC case are completely symmetrical. This is because the field curvature is chosen to give the best mean focus for the residual astigmatism, giving a round geometrical image (see § 3.3). If the focus is shifted slightly one way or the other, the astigmatic lines appear. The absence of symmetry about the horizontal axis makes the coma pattern the most objectionable of all aberrations.

The Gregory aplanatic form is only interesting if its intermediate image is useful (solar telescopes); or its extra length is unimportant so that the technical simplification of a concave secondary for testing is decisive, or its overcorrected field curvature is considered determinant.

A number of publications deal with the whole range of 2-mirror aplanatic forms. An excellent treatment was given in 1948 by Theissing and Zinke [3.15]. The properties of all aplanatic solutions are given in analytical and graphical form for the case in which the final image is formed in the plane of the primary. A more recent paper by Krautter [3.16] extends this general treatment, covering some systems with corrector plates and also the grazing incidence variants of the Mersenne forms for X-ray telescopes, due to Wolter [3.17]. Lens forms are also treated.

c) Telescopes with a spherical secondary: the Dall-Kirkham (DK) Cassegrain form. As is the case for many practical advances in reflecting telescope technology, the suggestion for a Cassegrain with a spherical secondary came out of the amateur telescope-making movement. It is clear that the Schwarzschild theorem given in § can be applied to the general case of a 2-mirror telescope for which we require the fulfilment of only one condition, E S/ = 0, in the final focus. There are an infinite number of solutions, of which the classical telescope is a special case, for which E S/ = 0 for the prime focus as well as for the final focus. Two other cases are of special technical interest: telescopes with a spherical secondary and those with a spherical primary. As before, both Cassegrain and Gregory forms exist, but again the Cassegrain form is the more important in practice.

Although the first proposal was probably made by Dall, the first clear description was apparently given by Kirkham [3.18]: it is generally known as the Dall-Kirkham (DK) form of the Cassegrain. In Chap. 5 and RTO II, Chap. 1, we shall discuss the problems created by the manufacture and test of the classical convex hyperbolic secondary: for amateurs the task has always been formidable, so the technical advantages of a spherical secondary, tested by a concave negative, are enormous. However, as we shall see, this ease of manufacture is accompanied by a high price in field coma. Nevertheless, in certain circumstances, the DK form has legitimate application even for professional telescopes and a number of such instruments are in use: at the ESO La Silla Observatory, for example, the 1.4 m Coude Auxiliary Telescope (CAT) and the Dutch 0.9 m national telescope.

The condition for spherical aberration requires from Eq. (3.59)

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