for chromatic correction. It is easily shown that the secondary spectrum is also reduced compared with a classical full-size achromat because the individual powers of such an achromat are higher than that of the Dialyte singlet. This is true of "normal" glasses: if special glasses are used, the secondary spectrum can be further reduced.

The medial systems of Schupmann took up these principles but used cata-dioptric compensation elements. The first such system was already proposed by Hamilton [3.68] in 1814 and consisted of a singlet objective compensated by a Mangin-type concave mirror (Fig. 3.68). Schupmann [3.69] analyzed such possibilities exhaustively and derived two classic solutions, the Schupmann Brachymedial and Medial forms. The Brachymedial (Fig. 3.69) is, in principle, close to the Dialyte and Hamilton Brachymedial in that the compensating element is nearly half the size of the singlet objective. An important difference from the Hamilton version is the broken contact (air space) between the compensating lens and the mirror. The use of the concave mirror permits virtually complete compensation of secondary spectrum (as well as the compensation of the primary spectrum Ci) because of an important consequence of the theory of secondary spectrum. The secondary spectrum of a "normal" glass was shown in Fig. 3.30 and is simply the departure from linearity of the dispersion function with wavelength. First order chromatic correction (Ci) rotates the function so that two wavelengths Ax and À2 are corrected as shown in Fig. 3.31. The correction of secondary spectrum requires that a third wavelength should also be corrected. It was shown by Konig [3.11(d)]

Fig. 3.69. Brachymedial due to Schupmann (1899)

that correction of the secondary spectrum with "normal" glasses obeying the linear relationship between index n and Abbe number va for the dispersion n = A + BVa , (3.316)

which is roughly true for the main sequence of classical glasses, is only possible for a train of separated "thin" lenses if either object or image are virtual. For telescopic systems, the object is always real, even at infinity. The above law implies, then, in practice, that correction of secondary spectrum in such a refracting system is only possible if the image is virtual. The extension of this theorem to normal glasses not obeying Eq. (3.316) has been given by Kerber [3.70]. The Schupmann systems accept this situation and convert the virtual image of the refracting system into a real image by reflection at a spherical concave mirror, as shown in Fig. 3.69. As in the Dialyte of Fig. 3.67, the lens-mirror corrector is roughly afocal in its final effect except that the magnification is ~ — 1 instead of ~ +1. The third order spherical aberration can be corrected by adjusting the "bending" of the concave corrector lens.

A more sophisticated form due to Schupmann is the Medial telescope (Fig. 3.70). Here the singlet objective is compensated by a double-meniscus compensator with spherical concave mirror placed after the focus. This reimages the primary image without magnification with a slight tilt to make it accessible to one side. Such imagery at a concave sphere without magnification is aplanatic due to symmetry and the astigmatism is small for small tilts. The 90° deviating prism also forms a convex lens. The aperture of the compensating system is about 1/4 of that of the objective. Schupmann investigated four possible compensation systems. The one shown in Fig. 3.70 has a separated meniscus in front of a Mangin mirror, a form used for the 335 mm aperture system built for the Urania Observatory in Berlin in 1902 [3.39(g)]. The secondary spectrum was only 1/20 of that of a normal equivalent refractor. If a further airspace is introduced in front of the mirror, even finer correction is possible.

The Schupmann designs are essentially special forms of the refracting telescope which has not been included in our definition of modern telescope optics. They have been discussed here because they are an elegant example of correction by double-pass Mangin-type compensators. For amateur sizes they certainly retain considerable interest, as indicated by Rutten and van Ven-rooij [3.12(h)]. They quote a modern work by Daley [3.71] dealing with the amateur construction of such systems.

Systems with Mangin secondaries and Medial geometry: Many designs of great variety exist. Fig. 3.71 shows a very compact design with all spherical surfaces due to Delabre [3.72]. Here, the primary is f/2 working in a Cassegrain type arrangement with a plane secondary as the back of a negative Mangin lens. Although the secondary is plane, the obstruction is quite low because of an internal image which is transferred out in the Brachymedial geometry by a 5-element refracting system. The length between the reflecting surfaces of primary and secondary is only 636 mm for an aperture of 400 mm and an equivalent focal length of 3000 mm (f/7.5). The field is about 0.8° diameter for miniature camera format. The quality is limited by coma and transverse chromatic effects, 80% of the energy being within 1 arcsec (14.5 ^m) at a field of ±0.3°. The purpose of such designs is to replace full-aperture menisci by smaller elements: but corrector elements near the pupil are always the most effective.

Further interesting developments of the basic optical concept of the Brachymedial designs of Figs. 3.68 and 3.69 have recently been published by Busack [3.160]. In a normal uniaxial form, an additional convex lens, near the image, is added to the basic design of Fig. 3.68. This enables the removal of the fundamental optical weakness of the Brachymedial, the lateral colour or chromatic difference of magnification (see Eq. (3.223)), using only spherical surfaces. Busack claims that this gives a performance equivalent to the

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