cy z cy
z struction is only about 0.32 without vignetting. Even for a very large (16m) telescope, the size of Mp remains small enough that a multi-dielectric coating, giving very high reflectivity, should be possible. Part of its dimensional requirements arises from the high spherical aberration, but this has the advantage that it is much less sensitive to dust.
The fact that M3 has become almost parabolic in form (bs3 = -0.951) shows that the parabola has effectively been shifted from M2 to M3 by making M2 spherical. Its spherical form compensates about a quarter of the spherical aberration produced by the primary. The loss of compensation of coma and astigmatism is easily rectified by the aspheric forms of M3 and M4 with appropriate small axial shifts. The coma is above all compensated by M4 while M3 produces a major compensation of astigmatism because it is far from the pupil.
For the initial set-up of the geometry, the entrance pupil was placed at the primary. However, since the final system has effectively Sj = Sjj = Sjjj = 0, the stop position of the complete system is uncritical and can be placed as desired. The field curvature Sjv is small, but not zero. M2 is too weak to
compensate the three concave mirrors, so there is a slight undercorrection in the Schmidt sense. This is (to some extent) favourable for matching the field curvature of instruments. It could be compensated by CCD arrays. In principle, a flat field is possible by weakening M3 and M4: but M3 moves further behind M1 and M4 is further from the axis, giving less compact geometry.
Figure 3.82 shows a symmetrical version with two identical mirrors M4 and M4 fed by appropriate rotation of MF, giving two "Nasmyth foci". Each mirror M4 and M4 baffles with its central hole the final image produced by the other. This 2-axis arrangement is perfectly adapted to active optics, because M4 and M4 are at the pupil and are in a fixed (vertical) plane, unaffected by telescope movements in the alt-az mount. Thus, a push-pull system, independent of cosine effects of the zenith angle, can be applied for the active correction.
The centering tolerances are no more severe than for conventional telescopes with a similar M1 and M2. Active centering can either be done at M2, as with the NTT [3.98] (see RTO II, Chap. 3), or by a rotation of MF, which produces coma by shearing the pupil at M4. The pointing shift can
be corrected by rotating M4 about its pole. Korsch [3.87] has pointed out the advantage of active centering by actuating 2 mirrors in his 4-reflection system of Fig. 3.79.
Analogue to the above first, 2-axis solution, there is a second, 2-axis solution which also uses 4 powered mirrors and a 45° flat. This is an extension of the Korsch 3-mirror solution of Fig. 3.72 (b) in the same way that the first solution is an extension of the Willstrop telescope of Fig. 3.74. Instead of an afocal feeder, a real image is formed after M2 at the alt-axis (Fig. 3.83). M3, again concentric to the pupil P2, is now on the second axis, thereby producing a collimated beam and a real, accessible pupil image P3 at which M4 is placed. The final image is formed behind M3, which acts as a baffle as in Fig. 3.82. The geometrical properties of pupil transfer are thus very similar to those of the first solution.
The optical design data are given in ref. [3.94]. The optical quality is similar to that of the first solution and is shown in Fig. 3.84.
Since the correction potential is similar, the advantages and disadvantages of the first and second solutions depend on the geometry. The second solution has the advantage that the alt-axis can be located at will without regard to the projection of M3 beyond Mi inevitable in the first solution. However, if Mi is very steep, the beam aperture angle from M2 blows up the diameter
of M3 and M4 unless M2 is made small with a larger magnification m2. But this increases the obstruction due to the field at Mp. By contrast, the first solution fixes the diameters of M3 and M4 to be effectively the same as that of M2. These aspects are treated in detail in ref. [3.94]. The broad conclusion is that the second solution is probably better if the primary is not too steep, say f/2.0 to f/1.5. For steeper primaries of about f/1.3 to f/1.0, the geometry of the first solution becomes more and more favourable and compact. Both solutions can still give excellent field performance with f/1.2 primaries, probably even f/1.0. The second solution has the disadvantage that the "double Nasmyth" focus of Fig. 3.82 is not possible.
It is now clear that there are essentially 3 ways of establishing a second axis:
a) The Baker 3-mirror telescope of Fig. 3.75, placing Mp after one reflection;
b) The Korsch 3-mirror telescope of Fig. 3.72 (b) or the 4-mirror telescope of the second solution above (Fig. 3.83), placing Mp after two reflections;
c) The first solution above (Fig. 3.80) for a 4-mirror telescope, placing Mp after three reflections.
There are no other practical possibilities for mirror telescopes, although the idea of a second axis can be realised in many other forms and goes back to
the brachymedial and medial forms of Schupmann [3.69]. The Baker form of Fig. 3.75 is largely of historic interest because steep, modern primaries would lead to mirrors M2 and M3 which are too large relative to the primary to be practicable. However, the basic Baker concept of the concave mirror pair as a corrector system can be used in single-axis systems in the Korsch geometry, as shown in Fig. 3.85, a design by Delabre [3.94]. This design is seen as a fast, wide-field telescope for extending Schmidt-type operations up to sizes of 4 m or more. The image quality has d80 < 0.5 arcsec over the whole field of ±0.75°, as shown in Fig. 3.86. The limitations of this system are the diameter of M3 and the strong field curvature (undercorrected). The transferred pupil is near M4 and the generalised Schwarzschild theorem enables the wide-field correction with the f/1.2 spherical primary.
The system of Fig. 3.85 has been widely used in designs given in the literature. Already in 1979, Robb [3.99] clearly recognized the advantages of such a system with a spherical primary and a transferred pupil at the fourth mirror to correct the spherical aberration. His design, working at f/10 with an f/2.0 primary, covered a field of 1.0° diameter with diffraction limited quality for a 4 m aperture. Notable are the more recent TEMOS proposals
Fig. 3.86. Spot-diagrams for the fast, wide-field, 4-mirror design of Fig. 3.85. The circle diameter is 1 arcsec by Baranne and Lemaitre [3.96] [3.97] and the proposals by Ardeberg et al. [3.92] [3.93] for a 25 m telescope with a very steep spherical primary (f/0.8),the latter at present (early 1994) with a field limited to about 3 arcmin diameter8. A segmented primary and segmented M4 are envisaged.
8 This field has subsequently been increased, mainly by increasing the relative size of the corrector mirrors.
A 4-mirror system which might eliminate or significantly reduce the field curvature [3.94] is shown in Fig. 3.87. The Baker concave mirror pair is replaced by a Schwarzschild-Bowen pair, as used in spectrographs. Similar proposals have been made by Baranne and Lemaitre [3.96] [3.97], but the potential of this system does not appear to have been analysed in detail. The pupil transfer situation is certainly less favourable than Baker-type form of Fig. 3.85 because the convex M3 forms a virtual image of the pupil far from
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