## Sf5

Fig. 3.71. Compact system using Mangin secondary and Brachymedial geometry due to Delabre

Schmidt telescope, with apertures up to f/2 and fields up to 5°, but with the advantage of a flat field and shorter overall length. The disadvantage of such solutions is that they require high quality optical glass not only for the front lens, but also for the Mangin mirror, whose optical thickness is doubled by the back reflection. This limits the size of practical application. However, the back reflection permits better protection of the reflecting coat. A number of modifications of the basic system are given in the patent.

In a later patent [3.161], Busack extends the above prime focus system to a Cassegrain version. He refers to a patent by Gallert of a similar system, whereby Gallert uses a positive front lens of convex-concave form, the concave back surface then serving in its reflecting centre as a concave secondary mirror. This system gives good correction at f/3 over a 4° field. Busack's system uses a similar front lens, but has a separated conventional Cassegrain convex secondary, close to the front lens. This is essentially a normal Cassegrain extension of his prime focus system and gives similar excellent correction at f/4 over a 4° field. The advantages claimed over the Gallert system are a shorter overall length, a longer back focal distance, a smaller central obstruction and correction of distortion. If some field curvature is permitted, the central obstruction can be so far reduced that the system is considered eminently suitable for visual observation. All surfaces are again spherical and only one glass type is used.

3.6.5 Three- or multi-mirror telescopes (centered)

3.6.5.1 Various three-mirror solutions. Most designs using 3 mirrors are unattractive in practice because of obstruction problems. However, there are two solutions due to Korsch [3.73] of considerable practical interest. In general, the theory of 3-mirror systems is of fundamental importance for the extension to 4 mirrors.

By analogy with the theory of 2-mirror-plate telescopes above and from Eqs. (3.220), it is clear that any axial distribution of 3 powered, aspheric mirrors can give correction of Sj, Sjj and Sjjj (see §§ 3.6.2.1 and 3.4, and also [3.13]). The general analytical formulation is given by Schroeder [3.22(b)] and inevitably has a complexity exceeding that of Eqs. (3.220) because the third mirror has power as well as asphericity in the general case. A closed-form solution for centered 3-mirror telescopes giving correction of all 4 third order conditions

has been given by Korsch [3.73]. His formulation, lightly modified to bring it into line with our notation and sign convention, is reproduced here. Korsch's formulae assume the entrance pupil is at the primary and the object distance is infinite, i.e. = 0. His free design parameters are then m2,m3 and p2

where mv is the object to image magnification of surface v, and pv is the pupil object to image magnification of surface v. mv is determined by the paraxial ray, pv by the paraxial principal ray. For the formulation of a 2-mirror system in Table 3.5 we used the strict sign convention of Tables 2.2 and 2.3. The Korsch formulae, adapted to this system, are:

## Telescopes Mastery

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